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1. Number Series 1. 2. 3. A. 11 B. 12 C. 13 D. 14 4. A. 205 B. 208 C. 210 D. 211 5. A. 404 B. 414 C. 420 D. 445 6. A. 47 52 B. 46 52 C. 45 49 D. 46 51 7. A. B. C. D. E. 8.
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Aptitude Book

Nov 19, 2015

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1. Number Series

1.

2.

3.

A.11

B.12

C.13

D.14

4.

A.205

B.208

C.210

D.211

5.

A.404

B.414

C.420

D.445

6.

A.47 52

B.46 52

C.45 49

D.46 51

7.

A.B.C.D.E.

8.

A.B.C.D.E.38 32

9.

A.B.C.D.8 9

E.

10.

A.B.C.31 61

D.E.

11.

A.B.C.D.E.66 20

12.

A.B.C.D.E.26 32

13.

A.14 4

B.C.D.E.

14.

A.B.C.D.E.10 9

15.

A.B.C.D.E.66 82

1.

A.true

B.false

C.uncertain

2.

A.true

B.false

C.uncertain

3.

A.true

B.false

C.uncertain

4.

A.true

B.false

C.uncertain

5.

A.true

B.false

C.uncertain

6.A.trueB.falseC.uncertain

7.A.trueB.falseC.uncertain

8.A.trueB.falseC.uncertain9.A.trueB.falseC.uncertain

10.A.trueB.falseC.uncertain

11.

I:II:.III:

A.I onlyB.II onlyC.III onlyD.

12.Fact 2:.Fact 3:I:II:III:

A.B.C.D.

13.

A.B.C.D.

14.

A.B.C.D.

15.

A.B.C.D.

16.

A.B.C.D.

17.

A.B.C.D.

18.

A.251B.254C.255D.256

19.

A.B.C.D.

20.

A.B.C.D.

1.

A.B.2

1

times

2

C.2

3

times

4

D.3 times

2.The sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child?

A.4 years

B.8 years

C.10 years

D.None of these

Answer: Option AExplanation:Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years.

Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50

5x = 20

x = 4.

Age of the youngest child = x = 4 years.

3.A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 38 years now, the son's age five years back was:

A.14 years

B.19 years

C.33 years

D.38 years

Answer: Option AExplanation:Let the son's present age be x years. Then, (38 - x) = x2x = 38.

x = 19.

Son's age 5 years back (19 - 5) = 14 years.

4.A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 27, the how old is B?

A.7

B.8

C.9

D.10

E.11

Answer: Option DExplanation:Let C's age be x years. Then, B's age = 2x years. A's age = (2x + 2) years.

(2x + 2) + 2x + x = 27

5x = 25

x = 5.

Hence, B's age = 2x = 10 years.

5.Present ages of Sameer and Anand are in the ratio of 5 : 4 respectively. Three years hence, the ratio of their ages will become 11 : 9 respectively. What is Anand's present age in years?

A.24

B.27

C.40

D.Cannot be determined

E.None of these

Answer: Option AExplanation:Let the present ages of Sameer and Anand be 5x years and 4x years respectively.

Then,

5x + 3

=

11

4x + 3

9

9(5x + 3) = 11(4x + 3)

45x + 27 = 44x + 33

45x - 44x = 33 - 27

x = 6.

Anand's present age = 4x = 24 years.

6.A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is:

A.14 years

B.18 years

C.20 years

D.22 years

Answer: Option DExplanation:Let the son's present age be x years. Then, man's present age = (x + 24) years.

(x + 24) + 2 = 2(x + 2)

x + 26 = 2x + 4

x = 22.

7.Six years ago, the ratio of the ages of Kunal and Sagar was 6 : 5. Four years hence, the ratio of their ages will be 11 : 10. What is Sagar's age at present?

A.16 years

B.18 years

C.20 years

D.Cannot be determined

E.None of these

Answer: Option AExplanation:Let the ages of Kunal and Sagar 6 years ago be 6x and 5x years respectively.

Then,

(6x + 6) + 4

=

11

(5x + 6) + 4

10

10(6x + 10) = 11(5x + 10)

5x = 10

x = 2.

Sagar's present age = (5x + 6) = 16 years.

8.The sum of the present ages of a father and his son is 60 years. Six years ago, father's age was five times the age of the son. After 6 years, son's age will be:

A.12 years

B.14 years

C.18 years

D.20 years

Answer: Option DExplanation:Let the present ages of son and father be x and (60 -x) years respectively.

Then, (60 - x) - 6 = 5(x - 6)

54 - x = 5x - 30

6x = 84

x = 14.

Son's age after 6 years = (x+ 6) = 20 years..

9.At present, the ratio between the ages of Arun and Deepak is 4 : 3. After 6 years, Arun's age will be 26 years. What is the age of Deepak at present ?

A.12 years

B.15 years

C.19 and half

D.21 years

Answer: Option BExplanation:Let the present ages of Arun and Deepak be 4x years and 3x years respectively. Then,

4x + 6 = 26 4x = 20

x = 5.

Deepak's age = 3x = 15 years.

10.Sachin is younger than Rahul by 7 years. If their ages are in the respective ratio of 7 : 9, how old is Sachin?

A.16 years

B.18 years

C.28 years

D.24.5 years

E.None of these

Answer: Option DExplanation:Let Rahul's age be x years.

Then, Sachin's age = (x - 7) years.

x - 7

=

7

x9

9x - 63 = 7x2x = 63

x = 31.5

Hence, Sachin's age =(x - 7) = 24.5 years.

11.The present ages of three persons in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years).

A.8, 20, 28

B.16, 28, 36

C.20, 35, 45

D.None of these

Answer: Option BExplanation:Let their present ages be 4x, 7x and 9x years respectively.

Then, (4x - 8) + (7x - 8) + (9x - 8) = 56

20x = 80

x = 4.

Their present ages are 4x = 16 years, 7x = 28 years and 9x = 36 years respectively.

12.Ayesha's father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?

A.2 years

B.4 years

C.6 years

D.8 years

Answer: Option CExplanation:Mother's age when Ayesha's brother was born = 36 years.

Father's age when Ayesha's brother was born = (38 + 4) years = 42 years.

Required difference = (42 - 36) years = 6 years.

13.A person's present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. How old is the mother at present?

A.32 years

B.36 years

C.40 years

D.48 years

Answer: Option CExplanation:Let the mother's present age be x years.

Then, the person's present age =

2

x

years.

5

2

x + 8

=

1

(x + 8)

5

2

2(2x + 40) = 5(x + 8)

x = 40.

14.Q is as much younger than R as he is older than T. If the sum of the ages of R and T is 50 years, what is definitely the difference between R and Q's age?

A.1 year

B.2 years

C.25 years

D.Data inadequate

E.None of these

Answer & ExplanationAnswer: Option DExplanation:Given that:

1. The difference of age b/w R and Q = The difference of age b/w Q and T.

2. Sum of age of R and T is 50 i.e. (R + T) = 50.

Question: R - Q = ?.

Explanation:

R - Q = Q - T

(R + T) = 2Q

Now given that, (R + T) = 50

So, 50 = 2Q and therefore Q = 25.

Question is (R - Q) = ?

Here we know the value(age) of Q (25), but we don't know the age of R.

Therefore, (R-Q) cannot be determined.

15.The age of father 10 years ago was thrice the age of his son. Ten years hence, father's age will be twice that of his son. The ratio of their present ages is:

A.5 : 2

B.7 : 3

C.9 : 2

D.13 : 4

Answer: Option BExplanation:Let the ages of father and son 10 years ago be 3x and x years respectively.

Then, (3x + 10) + 10 = 2[(x + 10) + 10]

3x + 20 = 2x + 40

x = 20.

Required ratio = (3x + 10) : (x + 10) = 70 : 30 = 7 : 3.

4. Cubes and DiceThe sheet of paper shown in the figure (X) given on the left hand side, in each problem, is folded to form a box. Choose from amongst the alternatives (1), (2), (3) and (4), the boxes that are similar to the box that will be formed.

1.

Choose the box that is similar to the box formed from the given sheet of paper (X).

A.1 only

B.1 and 3 only

C.1, 3 and 4 only

D.1, 2, 3 and 4

Answer: Option CExplanation:When the sheet in fig. (X) is folded, then one of the faces of the cube formed will be of the form and this face will lie opposite the face bearing a square. Also, one of the blank faces lies opposite another blank face and the third blank face lies opposite the face bearing an '=' sign. Clearly, all the three blank faces cannot appear adjacent to each other. So, the cube shown in fig. (2) which has all the three blank faces adjacent to each other cannot be formed. Hence, only the cubes shown in figures A, C and D can be formed.

2.

Choose the box that is similar to the box formed from the given sheet of paper (X).

A.1 only

B.2 only

C.1 and 3 only

D.1, 2, 3 and 4 only

Answer: Option BExplanation:When the sheet in fig. (X) is folded to form a cube, then 'F' appears opposite 'B', 'E' appears opposite 'C' and 'A' appears opposite 'D' Therefore, the cube in fig. (1) which shows 'F' adjacent to 'B' the cube in fig. (3) which shows 'E' adjacent to 'C' and the cube in fig. (4) which shows 'A' adjacent to 'D' cannot be formed. Hence, only the cube in fig.(2) can be formed.

3.

Choose the box that is similar to the box formed from the given sheet of paper (X).

A.1 only

B.2 only

C.3 only

D.4 only

Answer: Option BExplanation:When the sheet in fig. (X) is folded to form a cube, then the half-shaded face appears opposite to the face bearing a rhombus, the face with a black circle appears opposite to one of the two blank faces and the face with a '+' sign appears opposite to the other blank face. Clearly, the cubes shown in figures (1) and (4) cannot be formed since they have the half-shaded face adjacent to the face bearing the rhombus. Also, though the cube shown in fig. (3) has faces that can appear adjacent to each other but the cube formed by folding the sheet in fig. (X) cannot be rotated to form fig. (3). Hence, the cube in fig. (3) cannot be formed. Thus, only the cube shown in fig. (2) can be formed.

4.

Choose the box that is similar to the box formed from the given sheet of paper (X).

A.1 only

B.2 only

C.3 only

D.4 only

Answer: Option AExplanation:When the sheet shown in fig. (X) is folded to form a cube then the two half-shaded faces lie opposite to each other, the face bearing a square lies opposite to one of the two blank faces and the face bearing a circle lies opposite to the other blank face. Therefore, the cubes shown in figures (2) and (3) which have the two half-shaded faces adjacent to each other, cannot be formed by folding the sheet shown in fig. (X). Also, though the cube shown in fig. (4) has faces that can appear adjacent to each other but the cube formed by folding the sheet in fig. (X) cannot be rotated to form the cube in fig. (4). Hence, only the cube in fig. (1) can be formed.

5.

Choose the box that is similar to the box formed from the given sheet of paper (X).

A.2 and 3 only

B.1, 3 and 4 only

C.2 and 4 only

D.1 and 4 only

Answer: Option BExplanation:When the sheet in fig. (X) is folded to form a cube, then the face bearing a dot lies opposite to one of the shaded faces. Therefore, the cube shown in fig. (2) which has both the shaded faces adjacent to the face bearing the dot, cannot be formed. Hence, the cubes shown in figures (1), (2) and (4) can be formed.

6.When the following figure is folded to form a cube, how many dots lie opposite the face bearing five dots?

A.1

B.2

C.3

D.4

Answer: Option CExplanation:When this figure is folded to form a cube then the face bearing three dots will lie opposite the face bearing five dots.

7.Which of the following finished patterns can be obtained from the piece of cardboard (X) shown below?

A.1

B.2

C.3

D.4

Answer: Option AExplanation:The pattern on fig. (X) and also the fact that the faces are rectangle, indicate that only fig. (1) can be obtained by folding fig. (X).

8.How many dots lie opposite to the face having three dots, when the given figure is folded to form a cube?

A.2

B.4

C.5

D.6

Answer: Option DExplanation:When this figure is folded to form a cube then the face bearing six dots will lie opposite the face bearing three dots.

9.Choose the box that is similar to the box formed from the given sheet of paper (X).

A.1 and 2 only

B.2 and 3 only

C.2 and 4 only

D.1, 2, 3 and 4

Answer: Option DExplanation:When a cube is formed by folding the sheet shown in fig. (X), then the two half-shaded faces lie opposite to each other and one. of the three blank faces appears opposite to the face bearing a dot. Clearly, each one of the four cubes shown in figures (1), (2), (3) and (4) can be formed by folding the sheet shown in fig. (X).

10.Choose the box that is similar to the box formed from the given sheet of paper (X).

A.1 and 2 only

B.1 and 3 only

C.3 and 4 only

D.1, 2, 3 and 4

Answer: Option BExplanation:When a cube is formed by folding the sheet shown in fig. (X), then and are the two faces and these two faces lie opposite to each other. Also, the face bearing the 'x' sigh lies opposite to the face bearing the black circle and the face bearing the white circle lies opposite to the face bearing the square (having a dot inside it). Now, the cubes in figures (2) and (4) consist of faces which are not formed when the sheet in fig. (X) is folded. Hence, these two cubes are not, formed. Therefore, only the cubes in figures (1) and (3) are formed.

11.What will be the number at the bottom, if 5 is at the top; the two positions of the dice being as given below:

A.1

B.2

C.3

D.6

Answer: Option BExplanation:From figures (i) and (ii), it is clear that 4, 1, 3 and 6 he adjacent to 2. Therefore, 5 must lie opposite 2. Thus, if 5 is at the top, then 2 must be at the bottom.

12.If the total number of dots on opposite faces of a cubical block is always 7, find the figure which is correct.

A.Fig.1

B.Fig.2

C.Fig.3

D.Fig.4

Answer: Option BExplanation:Since the total number of dots on opposite faces is always 7, therefore, 1 dot appears opposite 6 dots, 2 dots appear opposite 5 dots and 3 dots appear opposite 4 dots.

13.Two positions of a block are given below. When 1 is at the top, which number will be at the bottom?

A.2

B.3

C.4

D.6

Answer: Option DExplanation:Number 2 is common to the two positions of the dice. We assume the dice in fig. (ii) to be rotated so that 2 remains on the top face (i.e. face V as per activity 1) and the numbers 3 and 6 move to the faces hidden behind 5 and 1 respectively [in fig. (i)]. Then, clearly, 5 lies opposite 3 and 6 lies opposite 1. Hence, when 1 is at the top, then 6 will be at the bottom.

14.What number is opposite 3 in the figure shown below? The given two positions are of the same dice whose each surface bears a number among 1, 2, 3, 4, 5 and 6.

A.2

B.4

C.5

D.6

Answer: Option CExplanation:From figures (i) and (ii), we conclude that 2, 6, 1 and 4 appear adjacent to 5. Therefore, 3 must appear opposite 5, Conversely, the number opposite 3 is 5.

15.Two positions of a dice are shown below. Identify the number at the bottom when the top is '3'?

A.2

B.4

C.5

D.6

Answer: Option CExplanation:The number 6 is common to both the positions of the dice. We assume the dice in fig. (ii) to be rotated so that 6 remains on the FR-LH face (i. e. on face IV as per activity 1) and the numbers 1 and 3 move to the faces hidden behind 4 and 5 respectively [in fig. (i)]. Then, 5 lies on FR-RH face (i.e. face I), 4 lies on Top face {i.e. face V), 3 lies on RR-LH face (i.e. face III) and 1 lies on Bottom face (i.e. face VI). Thus, 3 lies opposite 5. Hence, when the top is 3, then the number at the bottom is 5.

16.A dice is numbered from 1 to 6 in different ways.

If 1 is adjacent to 2, 4 and 6, then which of the following statements is necessarily true?

A.2 is opposite to 6

B.1 is adjacent to 3

C.3 is adjacent to 5

D.3 is opposite to 5

Answer: Option CExplanation:If 1 is adjacent to 2, 4 and 6 then either 3 or 5 lies opposite to 1. So, the numbers 3 and 5 cannot lie opposite to each other. Hence, 3 is adjacent to 5 (necessarily).

17.A cube has six different symbols drawn over its six faces. The symbols are dot, circle, triangle, square, cross and arrow. Three different positions of the cube are shown in figures X, Y, and Z.

Which symbol is opposite the dot?

A.Circle

B.Triangle

C.Arrow

D.Cross

Answer: Option DExplanation:From figures X and Y, we conclude that dot, circle, square and cross lie adjacent to the triangle. Therefore, the arrow must lie opposite the triangle. From figures X and Z, we conclude that dot, triangle, arrow and cross lie adjacent to the circle. Therefore, the square must lie opposite the circle. Thus, the arrow lies opposite the triangle, the square lies opposite the circle and consequently, the cross lies opposite the dot.

As analysed above, the cross lies opposite the dot.

18.Two positions of a dice are shown below. When there are two dots at the bottom, the number of dots at the top will be

A.3

B.5

C.6

D.Cannot be determined

Answer: Option AExplanation:Number 1 is common to both the positions of the dice. We assume the dice in fig. (ii) to be rotated so that 1 dot moves to the top face (i.e. face V as per activity 1) i.e. to the same position as in fig. (i) and 2 and 4 dots move to the faces hidden behind the faces with 3 and 5 dots respectively. Thus, the combined figure will have 1 dot on the Top (i.e. on face V), 5 dots on Front face (i.e. on face I), 3 dots on RHS face (i.e. face II), 4 dots on the Rear face (i.e. face III) and 2 dots on the LHS face (i.e. face IV). Clearly, 3 dots lie on the face opposite the face having 2 dots. Therefore, when there are 2 dots at the bottom, the number of dots at the top will be 3.

19.In a dice a, b, c and d are written on the adjacent faces, in a clockwise order and e and f at the top and bottom. When c is at the top, what will be at the bottom?

A.a

B.b

C.c

D.d

Answer: Option AExplanation:Clearly, the six faces are labelled as

Face I -> a, Face IV -> b, Face III -> c, Face II -> d, Face V -> e, Face VI -> f

Therefore 'a' appears opposite 'c'.

Hence, when 'c' is at the top, then 'a' will be at the bottom.

20.Four usual dice are thrown on the ground. The total of numbers on the top faces of these four dice is 13 as the top faces showed 4, 3, 1 and 5 respectively. What is the total of the faces touching the ground?

A.12

B.13

C.15

D.Cannot be determined

Answer: Option CExplanation:In a usual dice, the sum of the numbers on any two opposite faces is always 7. Thus, 1 is opposite 6, 2 is opposite 5 and 3 is opposite 4.

Consequently, when 4, 3, 1 and 5 are the numbers on the top faces, then 3, 4, 6 and 2 respectively are the numbers on the face touching the ground. The total of these numbers = 3 + 4 + 6 + 2 = 15.

5. Blood Relation Test

Introduction:The questions which are asked in this section depend uponRelation. You should have a sound knowledge of the blood relation in order to solve the questions.

To remember easily the relations may be divided into two sides as given below:

1. 1. Relations of Paternal side:2. Father's father Grandfather

3. Father's mother Grandmother

4. Father's brother Uncle

5. Father's sister Aunt

6. Children of uncle Cousin

7. Wife of uncle Aunt

8. Children of aunt Cousin

9. Husband of aunt Uncle

2. Relations of Maternal side:1. Mother's father Maternal grandfather

2. Mother's mother Maternal grandmother

3. Mother's brother Maternal uncle

4. Mother's sister Aunt

5. Children of maternal uncle Cousin

6. Wife of maternal uncle Maternal aunt

Relations from one generation to next:

1.Introducing a man, a woman said, "He is the only son of the mother of my mother." How is the woman related to the man?

A.Mother

B.Sister

C.Niece

D.Maternal aunt

Answer:OptionCExplanation:The man is the only son of the mother of the woman. Hence, the man is the maternal uncle of the woman. So, the woman is the niece of the man.

2.Pointing to Gopi, Nalni says, "I am the daughter of the only son of his grandfather." How Nalni is related to Gopi?

A.Niece

B.Daughter

C.Sister

D.Cannot be determined

Answer:OptionCExplanation:Nalni is the daughter of the only son of Gopi's grandfather. Hence, it's clear that Nalni is the sister of Gopi.

3.A's son B is married with C whose sister D is married to E the brother of B. How D is related to A?

A.Sister

B.Daughter's-in-law

C.Sister-in-law

D.Cousin

Answer:OptionBExplanation:Since E is the brother of B

Therefore, A is the father of E

but D is the wife of E.

Hence, D is the daughter-in-law of A.

4.A $ B means A is the father of B; A # B means A is the sister of B; A * B means A is the daughter of B and A @ B means A is the brother of B. Which of the following indicates that M is the wife of Q?

A.Q $ R # T @ M

B.Q $ R @ T # M

C.Q $ R * T # M

D.Q $ R @ T * M

Answer:OptionDExplanation:Q $ R Q is the father of R

R @ T R is the brother of T

Hence, Q is the father of T

T * M T is the daughter of M

Hence, M is the mother of T

Hence, M is the wife of Q.

5.If A $ B means A is the brother of B; B * C means B is the son of C; C @ D means C is the wife of D and A # D means A is the son of D, how C is related to A?

A.Maternal grandmother

B.Maternal aunt

C.Aunt

D.Mother

Answer:OptionDExplanation:A $ B A is the brother of B

B * C B is the son of C

Hence, A is the son of C

C @ D C is the wife of D

Hence, C is the mother of A.

6.Pointing to a girl Sandeep said, "She is the daughter of the only sister of my father." How is sandeep related to the girl?

A.Uncle

B.Cousin

C.Father

D.Grandfather

Answer:OptionBExplanation:The girl is the daughter of the sister of Sandeep's father. Hence, the girl is the cousin or Sandeep is the cousin of the girl.

7.Pointing to a boy in the photograph Reena said, "He is the only son of the only child of my grandfather." How Reena is related to that boy?

A.Mother

B.Sister

C.Aunt

D.Cannot be determined

Answer:OptionBExplanation:The boy in the photograph is the only son of Reena's grandfather's only son; i.e., the boy is the only son of Reena's father.

Hence, the boy is the brother of Reena or Reena is the sister of the boy.

8.If M x N means M is the daughter of N; M + N means M is the father of N; M % N means M is the mother of N and M - N means M is the brother of N then P % Q + R - T x K indicates which relation of P to K?

A.Daughter-in-law

B.Sister-in-law

C.Aunt

D.None of these

Answer:OptionDExplanation:P % Q P is the mother of Q

Q + R Q is the father of R

R - T R is the brother of T

Hence, Q is the father of T

T x K T is the daughter of K

Hence, Q is the husband of K.

Therefore, P is the mother-in-law of K.

9.If P + Q means P is the brother of Q; P x Q means P is the father of Q and P - Q means P is the sister of Q, which of the following relations shows that I is the niece of K?

A.K + Y + Z - I

B.K + Y x I - Z

C.Z - I x Y + K

D.K x Y + I - Z

Answer:OptionBExplanation:K + Y K is the brother of Y

Y x I Y is the father of I

Hence, K is the uncle of I

and I - Z I is the sister of Z

Hence, I is the niece of K.

10.Pointing towards a girl, Abhisek says, "This girl is the daughter of only a child of my father." What is the relation of Abhisek's wife to that girl?

A.Daughter

B.Mother

C.Aunt

D.Sister

Answer:OptionBExplanation:Only the child of my father means 'Abhisek' himself. This means the girl is the daughter od Abhisek. Hence, Abhisek's wife is the mother of the girl.

11.Anupam said to a lady sitting in a car, "The only daughter of the brother of my wife is the sister-in-law of the brother of your sister." How the husband of the lady is related to Anupam?

A.Maternal uncle

B.Uncle

C.Father

D.Son-in-law

Answer:OptionDExplanation:Anupam's son-in-law is the brother of the lady who was sitting in the car. Hence, the husband is also the son-in-law of Anupam.

12.Deepak said to Nitin, "That boy playing with the football is the younger of the two brothers of the daughter of my father's wife." How is the boy playing football related to Deepak?

A.Son

B.Brother

C.Cousin

D.Brother-in-law

Answer:OptionBExplanation:Father's wife mother. Hence, the daughter of the mother means sister and sister's younger brother means brother. Therefore, the boy is the brother of Deepak.

13.Pointing a photograph X said to his friend Y, "She is the only daughter of the father of my mother." How X is related to the person of photograph?

A.Daughter

B.Son

C.Nephew

D.Cannot be decided

Answer:OptionBExplanation:'The only daughter of the father of X's mother' means mother of X.

Hence X is the son of the lady in the photograph.

14.If A + B means A is the sister of B; A x B means A is the wife of B, A % B means A is the father of B and A - B means A is the brother of B. Which of the following means T is the daughter of P?

A.P x Q % R + S - T

B.P x Q % R - T + S

C.P x Q % R + T - S

D.P x Q % R + S + T

Answer:OptionBExplanation:P x Q P is the wife of Q

Q % R Q is the father of R

R - T R is the brother of T

T + S T is the sister of S.

Therefore, T is the daughter of P.

15.Pointing to a woman, Abhijit said, "Her granddaughter is the only daughter of my brother." How is the woman related to Abhijit?

A.Sister

B.Grandmother

C.Mother-in-law

D.Mother

Answer:OptionDExplanation:Daughter of Abhijit's brother niece of Abhijit. Thus the granddaughter of the woman is Abhijit's niece.

Hence, the woman is the mother of Abhijit.

16.Amit said - "This girl is the wife of the grandson of my mother". How is Amit related to the girl?

A.Brother

B.Grandfather

C.Husband

D.Father-in-law

Answer:OptionDExplanation:The girl is the wife of grandson of Amit's mother i.e., the girl is the wife of son of Amit. Hence, Amit is the father-in-law of the girl.

17.Pointing towards a man, a woman said, "His mother is the only daughter of my mother." How is the woman related to the man?

A.Mother

B.Grandmother

C.Sister

D.Daughter

Answer:OptionAExplanation:Only daughter of my mother myself.

Hence, the woman is the mother of the man.

18.If P $ Q means P is the brother of Q; P # Q means P is the mother of Q; P * Q means P is the daughter of Q in A # B $ C * D, who is the father?

A.D

B.B

C.C

D.Data is inadequate

Answer:OptionAExplanation:A is the mother of B, B is the brother of C and C is the daughter of D. Hence, D is the father.

A (Parents) D

| |

| |

B - is - Brother - of - C

19.Introducing Salman, Aamir says, "She is the wife of only nephew of only brother of my mother." How Salman is related to Aamir?

A.Wife

B.Sister

C.Sister-in-law

D.Data is inadequate

Answer:OptionAExplanation:Brother of mother means maternal uncle. Hence only nephew of Aamir's maternal uncle means Aamir himself. Therefore Salman is the wife of Aamir.

20.Introducing a boy, a girl said, "He is the son of the daughter of the father of my uncle." How is the boy related to the girl?

A.Brother

B.Nephew

C.Uncle

D.Son-in-law

Answer:OptionAExplanation:The father of the boy's uncle the grandfather of the boy and daughter of the grandfather sister of father.

21.

A.Brother

B.Uncle

C.Cousin

D.Data is inadequate

Answer:OptionAExplanation:The man in the photograph is the son of the only son of Lata's grandfather i.e., the man is the son of Lata's father. Hence, the man is the brother of Lata.

22.If A + B means A is the father of B; A - B means A is the brother B; A % B means A is the wife of B and A x B means A is the mother of B, which of the following shows that M is the maternal grandmother of T?

A.M x N % S + T

B.M x N - S % T

C.M x S - N % T

D.M x N x S % T

Answer:OptionAExplanation:M x N M is the mother of N

N % S N is the wife of S

and S + T is the father of T.

Hence, M is the maternal grandmother of T.

23.Pointing to a photograph. Bajpai said, "He is the son of the only daughter of the father of my brother." How Bajpai is related to the man in the photograph?

A.Nephew

B.Brother

C.Father

D.Maternal Uncle

Answer:OptionDExplanation:The man in the photo is the son of the sister of Bajpai. Hence, Bajpai is the maternal uncle of the man in the photograph.

24.A is the son of C; C and Q are sisters; Z is the mother of Q and P is the son of Z. Which of the following statements is true?

A.P and A are cousins

B.P is the maternal uncle of A

C.Q is the maternal grandfather of A

D.C and P are sisters

Answer:OptionBExplanation:C and Q are sisters and A is the son of C. Hence, C is the mother of A or Z is the mother Q.

Hence, Z is the maternal grandmother of A. P is the son of Z. Hence, P is the maternal uncle of A.

25.If X + Y means X is the daughter of Y; X - Y means X is the brother of Y; X % Y means X is the father of Y and X x Y means X is the sister of Y. Which of the following means I is the niece of J?

A.J - N % C x I

B.I x C - N % J

C.J + M x C % I

D.I x C + N - J

Answer:OptionDExplanation:I x C I is the sister of C

C + N C is the daughter of N

and N - J N is the brother of I.

Hence, I is niece of J.

6. Direction Sense Test

Introduction:There are four main directions - East, West, North and South as shown below:

There are four cardinal directions - North-East (N-E), North-West (N-W), South-East (S-E), and South-West (S-W) as shown below:

1. At the time of sunrise if a man stands facing the east, his shadow will be towards west.

2. At the time of sunset the shadow of an object is always in the east.

3. If a man stands facing the North, at the time of sunrise his shadow will be towards his left and at the time of sunset it will be towards his right.

4. At 12:00 noon, the rays of the sun are vertically downward hence there will be no shadow.

1.One morning after sunrise, Vimal started to walk. During this walking he met Stephen who was coming from opposite direction. Vimal watch that the shadow of Stephen to the right of him (Vimal). To Which direction Vimal was facing?

A.East

B.West

C.South

D.Data inadequate

Answer:OptionCExplanation:Sun rises in the east. So the shadow of a man will always falls towards the west. Since the shadow of Stephen is to the right of Vimal. Hence Vimal is facing towards South.

2.Golu started from his house towards North. After covering a distance of 8 km. he turned towards left and covered a distance of 6 km. What is the shortest distance now from his house?

A.10 km.

B.16 km.

C.14 km

D.2 km.

Answer:OptionAExplanation:

3.P started from his house towards west. After walking a distance of 25 m. He turned to the right and walked 10 m. He then again turned to the right and walked 15 m. After this he is to turn right at 135oand to cover 30 m. In which direction should he go?

A.West

B.South

C.South-West

D.South-East

Answer:OptionCExplanation:

Hence he should go in the South-West direction.

4.X started to walk straight towards south. After walking 5 m he turned to the left and walked 3 m. After this he turned to the right and walked 5 m Now to which direction X is facing?

A.North-East

B.South

C.North

D.South-West

Answer:OptionBExplanation:

Hence X will face in the end towards South.

5. Dev, Kumar, Nilesh, Ankur and Pintu are standing facing to the North in a playground such as given below:

1. Kumar is at 40 m to the right of Ankur.

2. Dev is are 60 m in the south of Kumar.

3. Nilesh is at a distance of 25 m in the west of Ankur.

4. Pintu is at a distance of 90 m in the North of Dev.

5.1.

Which one is in the North-East of the person. Who is to the left of Kumar?

A.Dev

B.Nilesh

C.Ankur

D.Pintu

Answer:OptionDExplanation:

Ankur is in the left of Kumar. Hence Pintu is in North-East of Ankur.

5.2.

If a boy starting from Nilesh, met to Ankur and then to Kumar and after this he to Dev and then to Pintu and whole the time he walked in a straight line, then how much total distance did he cover?

A.215 m

B.155 m

C.245 m

D.185 m

Answer:OptionAExplanation:Required distance = 25 m + 40 m + 60 m + 90 m

Required distance = 215 m

6. Each of the following questions is based on the following information:

1. A # B means B is at 1 metre to the right of A.

2. A $ B means B is at 1 metre to the North of A.

3. A * B means B is at 1 metre to the left of A.

4. A @ B means B is at 1 metre to the south of A.

5. In each question first person from the left is facing North.

6.1.

According to X @ B * P, P is in which direction with respect to X?

A.North

B.South

C.North-East

D.South-West

Answer:OptionDExplanation:According to X @ B * Y

Hence P is in South-West of X.

6.2.

According to M # N $ T, T is in which direction with respect to M?

A.North-West

B.North-East

C.South-West

D.South-East

Answer:OptionBExplanation:According to M # N $ T

Hence T is in the North-East of M.

6.3.

According to P # R $ A * U, in which direction is U with respect to P?

A.East

B.West

C.North

D.South

Answer:OptionCExplanation:According to P # R $ A * U

Hence U is in North direction with respect to P.

7. Letter and Symbol Series

Directions to SolveIn these series, you will be looking at both the letter pattern and the number pattern. Fill the blank in the middle of the series or end of the series.

1.

SCD, TEF, UGH, ____, WKL

A.CMN

B.UJI

C.VIJ

D.IJT

Answer: Option CExplanation:There are two alphabetical series here. The first series is with the first letters only: STUVW. The second series involves the remaining letters: CD, EF, GH, IJ, KL.

2.

B2CD, _____, BCD4, B5CD, BC6D

A.B2C2D

B.BC3D

C.B2C3D

D.BCD7Answer: Option BExplanation:Because the letters are the same, concentrate on the number series, which is a simple 2, 3, 4, 5, 6 series, and follows each letter in order.

3.

FAG, GAF, HAI, IAH, ____

A.JAK

B.HAL

C.HAK

D.JAI

Answer: Option AExplanation:The middle letters are static, so concentrate on the first and third letters. The series involves an alphabetical order with a reversal of the letters. The first letters are in alphabetical order: F, G, H, I , J. The second and fourth segments are reversals of the first and third segments. The missing segment begins with a new letter.

4.

ELFA, GLHA, ILJA, _____, MLNA

A.OLPA

B.KLMA

C.LLMA

D.KLLA

Answer: Option DExplanation:The second and forth letters in the series, L and A, are static. The first and third letters consist of an alphabetical order beginning with the letter E.

5.

CMM, EOO, GQQ, _____, KUU

A.GRR

B.GSS

C.ISS

D.ITT

Answer: Option CExplanation:The first letters are in alphabetical order with a letter skipped in between each segment: C, E, G, I, K. The second and third letters are repeated; they are also in order with a skipped letter: M, O, Q, S, U.

In these series, you will be looking at both the letter pattern and the number pattern. Fill the blank in the middle of the series or end of the series.

6.

ZA5, Y4B, XC6, W3D, _____

A.E7V

B.V2E

C.VE5D.VE7Answer: Option DExplanation:There are three series to look for here. The first letters are alphabetical in reverse: Z, Y, X, W, V. The second letters are in alphabetical order, beginning with A. The number series is as follows: 5, 4, 6, 3, 7.

7.

QPO, NML, KJI, _____, EDC

A.HGF

B.CAB

C.JKL

D.GHI

Answer: Option AExplanation:This series consists of letters in a reverse alphabetical order.

8.

JAK, KBL, LCM, MDN, _____

A.OEP

B.NEO

C.MEN

D.PFQ

Answer: Option BExplanation:This is an alternating series in alphabetical order. The middle letters follow the order ABCDE. The first and third letters are alphabetical beginning with J. The third letter is repeated as a first letter in each subsequent three-letter segment.

9.

BCB, DED, FGF, HIH, ___

A.JKJ

B.HJH

C.IJI

D.JHJ

Answer: Option AExplanation:This series consists of a simple alphabetical order with the first two letters of all segments: B, C, D, E, F, G, H, I, J, K. The third letter of each segment is a repetition of the first letter.

10.

P5QR, P4QS, P3QT, _____, P1QV

A.PQW

B.PQV2C.P2QU

D.PQ3U

Answer: Option CExplanation:The first two letters, PQ, are static. The third letter is in alphabetical order, beginning with R. The number series is in descending order beginning with 5.

11.QAR, RAS, SAT, TAU, _____

A.UAVB.UATC.TASD.TATAnswer: Option AExplanation:In this series, the third letter is repeated as the first letter of the next segment. The middle letter, A, remains static. The third letters are in alphabetical order, beginning with R.

12.DEF, DEF2, DE2F2, _____, D2E2F3

A.DEF3B.D3EF3C.D2E3FD.D2E2F2Answer: Option DExplanation:In this series, the letters remain the same: DEF.

The subscript numbers follow this series:

111, 112, 122, 222, 223, 233, 333, ...

8. Seating Arrangement

1. Five girls are sitting on a bench to be photographed. Seema is to the left of Rani and to the right of Bindu. Mary is to the right of Rani. Reeta is between Rani and Mary.

1.1.

Who is sitting immediate right to Reeta ?

A.Bindu

B.Rani

C.Mary

D.Seema

Answer:OptionCExplanation:

Mary is sitting immediate right to Reeta.

1.2.

Who is in the middle of the photograph ?

A.Bindu

B.Rani

C.Reeta

D.Seema

Answer:OptionBExplanation:

Rani is in the middle of the photograph.

1.3.

Who is second from the right ?

A.Mary

B.Rani

C.Reeta

D.Bindu

Answer:OptionCExplanation:

Reeta is sitting second from the right.

1.4.

Who is second from the left in photograph ?

A.Reeta

B.Mary

C.Bindu

D.Seema

Answer:OptionDExplanation:

Seema is sitting second from the left in photograph.

2. A, B, C, D, E, F and G are sitting in a row facing North :

1. F is to the immediate right of E.

2. E is 4thto the right of G.

3. C is the neighbour of B and D.

4. Person who is third to the left of D is at one of ends.

2.1.

Who are to the left of C ?

A.Only B

B.G, B and D

C.G and B

D.D, E, F and A

Answer:OptionCExplanation:

G an B are to the left of C.

2.2.

Which of the following statement is not true ?

A.E is to the immediate left of D

B.A is at one of the ends

C.G is to the immediate left of B

D.F is second to the right of D

Answer:OptionAExplanation:

2.3.

Who are the neighbours of B ?

A.C and D

B.C and G

C.G and F

D.C and E

Answer:OptionBExplanation:

C and G are the neighbours of B.

2.4.

What is the position of A ?

A.Between E and D

B.Extreme left

C.Centre

D.Extreme right

Answer:OptionDExplanation:

A is in extreme right.

3. Each of these questions are based on the information given below :

1. 8 persons E, F, G, H, I, J, K and L are seated around a square table - two on each side.

2. There are 3 ladies who are not seated next to each other.

3. J is between L and F.

4. G is between I and F.

5. H, a lady member is second to the left of J.

6. F, a male member is seated opposite to E, a lady member.

7. There is a lady member between F and I.

3.1.

Who among the following is to the immediate left of F ?

A.G

B.I

C.J

D.H

Answer:OptionCExplanation:

J is to the immediate left of F.

3.2.

What is true about J and K ?

A.J is male, K is female

B.J is female, K is male

C.Both are female

D.Both are male

Answer:OptionDExplanation:

Both are male.

3.3.

How many persons are seated between K and F ?

A.1

B.2

C.3

D.4

Answer:OptionCExplanation:

Three persons are seated between K and F(H, L and J) or E, I and G.

3.4.

Who among the following are three lady members ?

A.E, H and J

B.E, F and G

C.E, H and G

D.C, H and J

Answer:OptionCExplanation:

The three lady members are E, H and G.

3.5.

Who among the following is seated between E and H ?

A.F

B.I

C.K

D.Cannot be determined

Answer:OptionCExplanation:

K is seated between E and H.

4. Six friends are sitting in a circle and are facing the centre of the circle. Deepa is between Prakash and Pankaj. Priti is between Mukesh and Lalit. Prakash and Mukesh are opposite to each other.

4.1.

Who is sitting opposite to Prakash ?

A.Mukesh

B.Deepa

C.Pankaj

D.Lalit

Answer:OptionAExplanation:

Hence, Mukesh is sitting opposite to Prakash.

4.2.

Who is just right to Pankaj ?

A.Deepa

B.Lalit

C.Prakash

D.Priti

Answer:OptionAExplanation:

Hence, Deepa is sitting just right to Pankaj.

4.3.

Who are the neighbours of Mukesh ?

A.Prakash and Deepa

B.Deepa and Priti

C.Priti and Pankaj

D.Lalit and Priti

Answer:OptionCExplanation:

Hence, Priti and Pankaj are the neighbours of Mukesh.

4.4.

Who is sitting opposite to Priti ?

A.Prakash

B.Deepa

C.Pankaj

D.Lalit

Answer:OptionBExplanation:

Hence, Deepa is sitting opposite to Priti.

9. Clocks

Important Formulas :

1. Minute Spaces:The face or dial of watch is a circle whose circumference is divided into 60 equal parts, called minute spaces.

Hour Hand and Minute Hand:A clock has two hands, the smaller one is called thehour handorshort handwhile the larger one is calledminute handorlong hand.

i. In 60 minutes, the minute hand gains 55 minutes on the hour on the hour hand.

ii. In every hour, both the hands coincide once.

iii. The hands are in the same straight line when they are coincident or opposite to each other.

iv. When the two hands are at right angles, they are 15 minute spaces apart.

v. When the hands are in opposite directions, they are 30 minute spaces apart.

vi. Angle traced by hour hand in 12 hrs = 360

vii. Angle traced by minute hand in 60 min. = 360.

viii. If a watch or a clock indicates 8.15, when the correct time is 8, it is said to be 15 minutestoo fast.

On the other hand, if it indicates 7.45, when the correct time is 8, it is said to be 15 minutestoo slow.

1.An accurate clock shows 8 o'clock in the morning. Through how may degrees will the hour hand rotate when the clock shows 2 o'clock in the afternoon?

A.144

B.150

C.168

D.180

Answer:OptionDExplanation:Angle traced by the hour hand in 6 hours =

360

x 6

= 180.

12

2.The reflex angle between the hands of a clock at 10.25 is:

A.180

B.192

1

2

C.195

D.197

1

2

Answer:OptionDExplanation:Angle traced by hour hand in

125

hrs =

360

x

125

= 312

1

.

12

12

12

2

Angle traced by minute hand in 25 min =

360

x 25

= 150.

60

Reflex angle = 360 -

312

1

- 150

= 360 - 162

1

= 197

1

.

2

2

2

3.A clock is started at noon. By 10 minutes past 5, the hour hand has turned through:

A.145

B.150

C.155

D.160

Answer:OptionCExplanation:Angle traced by hour hand in 12 hrs = 360.

Angle traced by hour hand in 5 hrs 10 min.i.e.,31

hrs =

360

x

31

= 155.

6

12

6

4.A watch which gains 5 seconds in 3 minutes was set right at 7 a.m. In the afternoon of the same day, when the watch indicated quarter past 4 o'clock, the true time is:

A.59

7

min. past 3

12

B.4 p.m.

C.58

7

min. past 3

11

D.2

3

min. past 4

11

Answer:OptionBExplanation:Time from 7 a.m. to 4.15 p.m. = 9 hrs 15 min. =

37

hrs.

4

3 min. 5 sec. of this clock = 3 min. of the correct clock.

37

hrs of this clock =

1

hrs of the correct clock.

720

20

37

hrs of this clock =

1

x

720

x

37

hrs of the correct clock.

4

20

37

4

= 9 hrs of the correct clock.

The correct time is 9 hrs after 7 a.m.i.e.,4 p.m.

5.How much does a watch lose per day, if its hands coincide every 64 minutes?

A.32

8

min.

11

B.36

5

min.

11

C.90 min.

D.96 min.

Answer:OptionAExplanation:55 min. spaces are covered in 60 min.

60 min. spaces are covered in

60

x 60

min.

= 65

5

min.

55

11

Loss in 64 min. =

65

5

- 64

=

16

min.

11

11

Loss in 24 hrs =

16

x

1

x 24 x 60

min.

=

32

8

min.

11

64

11

6.At what time between 7 and 8 o'clock will the hands of a clock be in the same straight line but, not together?

A.5 min. past 7

B.5

2

min. past 7

11

C.5

3

min. past 7

11

D.5

5

min. past 7

11

Answer:OptionDExplanation:When the hands of the clock are in the same straight line but not together, they are 30 minute spaces apart.

At 7 o'clock, they are 25 min. spaces apart.

Minute hand will have to gain only 5 min. spaces.

55 min. spaces are gained in 60 min.

5 min. spaces are gained in

60

x 5

min

= 5

5

min.

55

11

Required time = 5

5

min. past 7.

11

7.At what time between 5.30 and 6 will the hands of a clock be at right angles?

A.43

5

min. past 5

11

B.43

7

min. past 5

11

C.40 min. past 5

D.45 min. past 5

Answer:OptionBExplanation:At 5 o'clock, the hands are 25 min. spaces apart.

To be at right angles and that too between 5.30 and 6, the minute hand has to gain (25 + 15) = 40 min. spaces.

55 min. spaces are gained in 60 min.

40 min. spaces are gained in

60

x 40

min

=

43

7

min.

55

11

Required time = 43

7

min. past 5.

11

8.The angle between the minute hand and the hour hand of a clock when the time is 4.20, is:

A.0

B.10

C.5

D.20

Answer:OptionBExplanation:Angle traced by hour hand in

13

hrs =

360

x

13

= 130.

3

12

3

Angle traced by min. hand in 20 min. =

360

x 20

= 120.

60

Required angle = (130 - 120) = 10.

9.At what angle the hands of a clock are inclined at 15 minutes past 5?

A.58

1

2

B.64

C.67

1

2

D.72

1

2

Answer:OptionCExplanation:Angle traced by hour hand in

21

hrs =

360

x

21

=

157

1

4

12

4

2

Angle traced by min. hand in 15 min. =

360

x 15

= 90.

60

Required angle =

157

1

- 90 = 67

1

2

2

10.At 3.40, the hour hand and the minute hand of a clock form an angle of:

A.120

B.125

C.130

D.135

Answer:OptionCExplanation:Angle traced by hour hand in 12 hrs. = 360.

Angle traced by it in

11

hrs =

360

x

11

= 110.

3

12

3

Angle traced by minute hand in 60 min. = 360.

Angle traced by it in 40 min. =

360

x 40

= 240.

60

Required angle (240 - 110) = 130.

11.How many times are the hands of a clock at right angle in a day?

A.22

B.24

C.44

D.48

Answer:OptionCExplanation:In 12 hours, they are at right angles 22 times.

In 24 hours, they are at right angles 44 times.

12.The angle between the minute hand and the hour hand of a clock when the time is 8.30, is:

A.80

B.75

C.60

D.105

Answer:OptionBExplanation:Angle traced by hour hand in

17

hrs =

360

x

17

= 255.

2

12

2

Angle traced by min. hand in 30 min. =

360

x 30

= 180.

60

Required angle = (255 - 180) = 75.

13.How many times in a day, are the hands of a clock in straight line but opposite in direction?

A.20

B.22

C.24

D.48

Answer:OptionBExplanation:The hands of a clock point in opposite directions (in the same straight line) 11 times in every 12 hours. (Because between 5 and 7 they point in opposite directions at 6 o'clcok only).

So, in a day, the hands point in the opposite directions 22 times.

14.At what time between 4 and 5 o'clock will the hands of a watch point in opposite directions?

A.45 min. past 4

B.40 min. past 4

C.50

4

min. past 4

11

D.54

6

min. past 4

11

Answer:OptionDExplanation:At 4 o'clock, the hands of the watch are 20 min. spaces apart.

To be in opposite directions, they must be 30 min. spaces apart.

Minute hand will have to gain 50 min. spaces.

55 min. spaces are gained in 60 min.

50 min. spaces are gained in

60

x 50

min. or 54

6

min.

55

11

Required time = 54

6

min. past 4.

11

15.At what time between 9 and 10 o'clock will the hands of a watch be together?

A.45 min. past 9

B.50 min. past 9

C.49

1

min. past 9

11

D.48

2

min. past 9

11

Answer:OptionCExplanation:To be together between 9 and 10 o'clock, the minute hand has to gain 45 min. spaces.

55 min. spaces gained in 60 min.

45 min. spaces are gained in

60

x 45

min or 49

1

min.

55

11

The hands are together at 49

1

min. past 9.

11

10. Calendar

Important Formulas :

1. Odd Days:We are supposed to find the day of the week on a given date.

For this, we use the concept of 'odd days'.

In a given period, the number of days more than the complete weeks are called odd days.

2. Leap Year:(i). Every year divisible by 4 is a leap year, if it is not a century.

(ii). Every 4thcentury is a leap year and no other century is a leap year.

Note:A leap year has 366 days.Examples:i. Each of the years 1948, 2004, 1676 etc. is a leap year.

ii. Each of the years 400, 800, 1200, 1600, 2000 etc. is a leap year.

iii. None of the years 2001, 2002, 2003, 2005, 1800, 2100 is a leap year.

3. Ordinary Year:The year which is not a leap year is called anordinary years. An ordinary year has 365 days.

4. Counting of Odd Days:1 ordinary year = 365 days = (52 weeks + 1 day.)

1 ordinary year has 1 odd day.

1 leap year = 366 days = (52 weeks + 2 days)

1 leap year has 2 odd days.

100 years = 76 ordinary years + 24 leap years

= (76 x 1 + 24 x 2) odd days = 124 odd days.

= (17 weeks + days)5 odd days.

Number of odd days in 100 years = 5.

Number of odd days in 200 years = (5 x 2)3 odd days.

Number of odd days in 300 years = (5 x 3)1 odd day.

Number of odd days in 400 years = (5 x 4 + 1)0 odd day.

Similarly, each one of 800 years, 1200 years, 1600 years, 2000 years etc. has 0 odd days.

Day of the Week Related to Odd Days:No. of days:0123456

Day:Sun.Mon.Tues.Wed.Thurs.Fri.Sat.

1.It was Sunday on Jan 1, 2006. What was the day of the week Jan 1, 2010?

A.Sunday

B.Saturday

C.Friday

D.Wednesday

Answer:OptionCExplanation:On 31stDecember, 2005 it was Saturday.

Number of odd days from the year 2006 to the year 2009 = (1 + 1 + 2 + 1) = 5 days.

On 31stDecember 2009, it was Thursday.

Thus, on 1stJan, 2010 it is Friday.

2.What was the day of the week on 28thMay, 2006?

A.Thursday

B.Friday

C.Saturday

D.Sunday

Answer:OptionDExplanation:28 May, 2006 = (2005 years + Period from 1.1.2006 to 28.5.2006)

Odd days in 1600 years = 0

Odd days in 400 years = 0

5 years = (4 ordinary years + 1 leap year) = (4 x 1 + 1 x 2)6 odd days

Jan. Feb. March April May

(31 + 28 + 31 + 30 + 28 ) = 148 days

148 days = (21 weeks + 1 day)1 odd day.

Total number of odd days = (0 + 0 + 6 + 1) = 70 odd day.

Given day is Sunday.

3.What was the day of the week on 17thJune, 1998?

A.Monday

B.Tuesday

C.Wednesday

D.Thursday

Answer:OptionCExplanation:17thJune, 1998 = (1997 years + Period from 1.1.1998 to 17.6.1998)

Odd days in 1600 years = 0

Odd days in 300 years = (5 x 3)1

97 years has 24 leap years + 73 ordinary years.

Number of odd days in 97 years ( 24 x 2 + 73) = 121 = 2 odd days.

Jan. Feb. March April May June

(31 + 28 + 31 + 30 + 31 + 17) = 168 days

168 days = 24 weeks = 0 odd day.

Total number of odd days = (0 + 1 + 2 + 0) = 3.

Given day is Wednesday.

4.What will be the day of the week 15thAugust, 2010?

A.Sunday

B.Monday

C.Tuesday

D.Friday

Answer:OptionAExplanation:15thAugust, 2010 = (2009 years + Period 1.1.2010 to 15.8.2010)

Odd days in 1600 years = 0

Odd days in 400 years = 0

9 years = (2 leap years + 7 ordinary years) = (2 x 2 + 7 x 1) = 11 odd days4 odd days.

Jan. Feb. March April May June July Aug.

(31 + 28 + 31 + 30 + 31 + 30 + 31 + 15) = 227 days

227 days = (32 weeks + 3 days)3 odd days.

Total number of odd days = (0 + 0 + 4 + 3) = 70 odd days.

Given day is Sunday.

5.Today is Monday. After 61 days, it will be:

A.Wednesday

B.Saturday

C.Tuesday

D.Thursday

Answer:OptionBExplanation:Each day of the week is repeated after 7 days.

So, after 63 days, it will be Monday.

After 61 days, it will be Saturday.

6.If 6thMarch, 2005 is Monday,what was the day of the week on 6thMarch, 2004?

A.Sunday

B.Saturday

C.Tuesday

D.Wednesday

Answer:OptionAExplanation:The year 2004 is a leap year. So, it has 2 odd days.

But, Feb 2004 not included because we are calculating from March 2004 to March 2005. So it has 1 odd day only.

The day on 6thMarch, 2005 will be 1 day beyond the day on 6thMarch, 2004.

Given that, 6thMarch, 2005 is Monday.

6thMarch, 2004 is Sunday (1 day before to 6thMarch, 2005).

7.On what dates of April, 2001 did Wednesday fall?

A.1st, 8th, 15th, 22nd, 29thB.2nd, 9th, 16th, 23rd, 30thC.3rd, 10th, 17th, 24thD.4th, 11th, 18th, 25thAnswer:OptionDExplanation:We shall find the day on 1stApril, 2001.

1stApril, 2001 = (2000 years + Period from 1.1.2001 to 1.4.2001)

Odd days in 1600 years = 0

Odd days in 400 years = 0

Jan. Feb. March April(31 + 28 + 31 + 1) = 91 days0 odd days.

Total number of odd days = (0 + 0 + 0) = 0

On 1stApril, 2001 it was Sunday.

In April, 2001 Wednesday falls on 4th, 11th, 18thand 25th.

8.How many days are there inxweeksxdays?

A.7x2B.8xC.14xD.7

Answer:OptionBExplanation:xweeksxdays = (7x+x) days = 8xdays.

9.The last day of a century cannot be

A.Monday

B.Wednesday

C.Tuesday

D.Friday

Answer:OptionCExplanation:100 years contain 5 odd days.

Last day of 1stcentury is Friday.

200 years contain (5 x 2)3 odd days.

Last day of 2ndcentury is Wednesday.

300 years contain (5 x 3) = 151 odd day.

Last day of 3rdcentury is Monday.

400 years contain 0 odd day.

Last day of 4thcentury is Sunday.

This cycle is repeated.

Last day of a century cannot be Tuesday or Thursday or Saturday.

10.On 8thFeb, 2005 it was Tuesday. What was the day of the week on 8thFeb, 2004?

A.Tuesday

B.Monday

C.Sunday

D.Wednesday

Answer:OptionCExplanation:The year 2004 is a leap year. It has 2 odd days.

The day on 8thFeb, 2004 is 2 days before the day on 8thFeb, 2005.

Hence, this day is Sunday.

11.The calendar for the year 2007 will be the same for the year:

A.2014

B.2016

C.2017

D.2018

Answer:OptionDExplanation:Count the number of odd days from the year 2007 onwards to get the sum equal to 0 odd day.

Year : 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017

Odd day : 1 2 1 1 1 2 1 1 1 2 1

Sum = 14 odd days0 odd days.

Calendar for the year 2018 will be the same as for the year 2007.

12.Which of the following is not a leap year?

A.700

B.800

C.1200

D.2000

Answer:OptionAExplanation:The century divisible by 400 is a leap year.

The year 700 is not a leap year.

13.On 8thDec, 2007 Saturday falls. What day of the week was it on 8thDec, 2006?

A.Sunday

B.Thursday

C.Tuesday

D.Friday

Answer:OptionDExplanation:The year 2006 is an ordinary year. So, it has 1 odd day.

So, the day on 8thDec, 2007 will be 1 day beyond the day on 8thDec, 2006.

But, 8thDec, 2007 is Saturday.

8thDec, 2006 is Friday.

14.January 1, 2008 is Tuesday. What day of the week lies on Jan 1, 2009?

A.Monday

B.Wednesday

C.Thursday

D.Sunday

Answer:OptionCExplanation:The year 2008 is a leap year. So, it has 2 odd days.

1stday of the year 2008 is Tuesday (Given)

So, 1stday of the year 2009 is 2 days beyond Tuesday.

Hence, it will be Thursday.

15.January 1, 2007 was Monday. What day of the week lies on Jan. 1, 2008?

A.Monday

B.Tuesday

C.Wednesday

D.Sunday

Answer:OptionBExplanation:The year 2007 is an ordinary year. So, it has 1 odd day.

1stday of the year 2007 was Monday.

1stday of the year 2008 will be 1 day beyond Monday.

Hence, it will be Tuesday.

11. Time and Distance

Important Formulas :

1. Speed, Time and Distance:Speed =Distance,Time =Distance,Distance = (Speed x Time).

TimeSpeed

2. km/hr to m/sec conversion:x km/hr =x x5m/sec.

18

3. m/sec to km/hr conversion:x m/sec =x x18km/hr.

5

4. If the ratio of the speeds of A and B is a : b, then the ratio of the

the times taken by then to cover the same distance is1:1or b : a.

ab

5. Suppose a man covers a certain distance at x km/hr and an equal distance at y km/hr. Then,

the average speed during the whole journey is2xykm/hr.

x + y

Problems :

1.A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour?

A.3.6

B.7.2

C.8.4

D.10

Answer:OptionBExplanation:Speed =

600

m/sec.

5 x 60

= 2 m/sec.

Converting m/sec to km/hr

=

2 x

18

km/hr

5

= 7.2 km/hr.

2.An aeroplane covers a certain distance at a speed of 240 kmph in 5 hours. To cover the same distance in 1hours, it must travel at a speed of:

A.300 kmph

B.360 kmph

C.600 kmph

D.720 kmph

Answer:OptionDExplanation:Distance = (240 x 5) = 1200 km.

Speed = Distance/Time

Speed = 1200/(5/3) km/hr. [We can write 1hours as 5/3 hours]

Required speed =

1200 x

3

km/hr

= 720 km/hr.

5

3.In covering a distance of 30 km, Abhay takes 2 hours more than Sameer. If Abhay doubles his speed, then he would take 1 hour less than Sameer. Abhay's speed is:

A.5 kmph

B.6 kmph

C.6.25 kmph

D.7.5 kmph

Answer:OptionAExplanation:Let Abhay's speed bexkm/hr.

Then,

30

-

30

= 3

x2x6x= 30

x= 5 km/hr.

4.A man covered a certain distance at some speed. Had he moved 3 kmph faster, he would have taken 40 minutes less. If he had moved 2 kmph slower, he would have taken 40 minutes more. The distance (in km) is:

A.35

B.36

2

3

C.37

1

2

D.40

Answer:OptionDExplanation:Let distance =xkm and usual rate =ykmph.

Then,

x-

x=

40

2y(y+ 3) = 9x....(i)

yy+ 3

60

And,

x-

x=

40

y(y- 2) = 3x....(ii)

y-2

y60

On dividing (i) by (ii), we get:x= 40.

5.In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. The duration of the flight is:

A.1 hour

B.2 hours

C.3 hours

D.4 hours

Answer:OptionAExplanation:Let the duration of the flight bexhours.

Then,

600

-

600

= 200

xx+ (1/2)

600

-

1200

= 200

x2x+ 1

x(2x+ 1) = 3

2x2+x- 3 = 0

(2x+ 3)(x- 1) = 0

x= 1 hr. [neglecting the -ve value ofx]

6.A man complete a journey in 10 hours. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km.

A.220 km

B.224 km

C.230 km

D.234 km

Answer:OptionBExplanation:(1/2)x+

(1/2)x= 10

21

24

x+

x= 20

21

24

15x= 168 x 20

x=

168 x 20

= 224 km.

15

7.A man on tour travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. The average speed for the first 320 km of the tour is:

A.35.55 km/hr

B.36 km/hr

C.71.11 km/hr

D.71 km/hr

Answer:OptionCExplanation:Total time taken =

160

+

160

hrs.

=

9

hrs.

64

80

2

Average speed =

320 x

2

km/hr

= 71.11 km/hr.

9

8.Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?

A.9

B.10

C.12

D.20

Answer:OptionBExplanation:Due to stoppages, it covers 9 km less.

Time taken to cover 9 km =

9

x 60

min

= 10 min.

54

9.If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance travelled by him is:

A.50 km

B.56 km

C.70 km

D.80 km

Answer:OptionAExplanation:Let the actual distance travelled bexkm.

Then,

x=

x+ 20

10

14

14x= 10x+ 200

4x= 200

x= 50 km.

10.The ratio between the speeds of two trains is 7 : 8. If the second train runs 400 km in 4 hours, then the speed of the first train is:

A.70 km/hr

B.75 km/hr

C.84 km/hr

D.87.5 km/hr

Answer:OptionDExplanation:Let the speed of two trains be 7xand 8xkm/hr.

Then, 8x=

400

= 100

4

x=

100

= 12.5

8

Speed of first train = (7 x 12.5) km/hr = 87.5 km/hr.

11.A car moves at a speed of 80 km / hr. What is the speed of the car in metres per second?

A.8 m / sec

B.20 * 1 / 9 m / sec

C.22 * 2 / 9 m / sec

D.None of these

Answer:OptionCExplanation:

Speed = (80 * 5 / 18) m / sec = 200 / 9 m / sec = 22 2 / 9 m / sec.

12.An athlete runs 200 metres race in 24 seconds. His speed is:

A.20 km / hr

B.24 km / hr

C.28.5 km / hr

D.30 km / hr

Answer:OptionDExplanation:

Speed = 200 / 4 m / sec = 25 / 3 m / sec = ( (25 / 3) * (18 / 5)) km / hr = 30 km / hr.

13.Which of the following trains is the fastest ?

A.25 m / sec

B.1500 m / min

C.90 km / hr

D.None of these

Answer:OptionDExplanation:

25 m / sec = (25 * 18 / 5) km / hr = 90 km / hr.

And, 25 m / sec = (25 * 60) m / min = 1500 m / min.

So, all the three speeds are equal.

14.A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour?

A.3.6

B.7.2

C.90 km / hr

D.None of these

Answer:OptionBExplanation:

Speed = ( 600 / ( 5 * 60) ) m / sec = 2 m / sec = ( 2 * ( 18 / 5 ) km / hr = 7.2 km / hr.

15.A man walking at the rate of 5 km / hr crosses a bridge in 15 minutes. The length of the bridge (in metres) is :

A.600

B.750

C.1000

D.1250

Answer:OptionDExplanation:

Speed = ( 5 * ( 5 / 18 ) ) m / sec = 25 / 18 m / sec.

Distance covered in 15 minutes = ( (25 * 18 ) * 15 * 60 ) m = 1250 m.

16.How long will a boy take to run round a square field of side 35 metres, if he runs at the rate of 9 km / hr ?

A.50 sec

B.52 sec

C.54 sec

D.56 sec

Answer:Option DExplanation:

Speed = 9 km/hr = (9*(5/18)) m/sec = 5/2 m/sec

Distance = (35*4) m = 140 m.

Time Taken = (140*(2/5)) sec = 56 sec.

17.A car is running at a speed of 108 km / hr. What distance will it cover in 15 seconds ?

A.45 metres

B.55 metres

C.450 metres

D.Cannot be determined

Answer:Option CExplanation:

Speed = 108 kmph = (108*(5/18)) m/sec = 30 m/sec.

Distance covered in 15 sec = (30*15) m = 450 m.

18.Two men start together to walk to a certain destination, one at 3 kmph and another at 3.75 kmph. The latter arrives half an hour before the former. The distance is :

A.6 km

B.7.5 km

C.8 km

D.9.5 km

Answer:Option BExplanation:

Let the distance be x km. Then,

(x/3) - (x/3.75) = (1/2) ( 25x 2x = 375 ( x=(3.75/0.50) = (15/2) = 7.5 km

19.If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance travelled by him is :

A.50 km

B.56 km

C.70 km

D.80 km

Answer:Option AExplanation:

Let the actual distance travelled be x km. Then,

(x/10) = ((x+20)/14) ( 14x = 10x + 200 ( 4x = 200 ( x = 50 km.

20.The ratio between the speeds of two trains is 7 : 8. If the second train runs 400 kms in 4 hours, then the speed of the first train is :

A.70 km/hr

B.75 km/hr

C.84 km/hr

D.87.5 km/hr

Answer:Option DExplanation:

Let the speeds of train be 7x and 8x km/hr.

Then, 8x = 400/4 = 100 x=(100/8) = 12.5

Speed of first train = (7*12.5) km/hr = 87.5 km/hr.

12. Height and Distance

Important Formulas :

1. Trigonometry:

In a right angled OAB, where BOA =,

i. sin =Perpendicular----------------=AB---;

HypotenuseOB

ii. cos =Base--------------=OA---;

HypotenuseOB

iii. tan =Perpendicular----------------=AB---;

BaseOA

iv. cosec =1-------=OB---;

sin AB

v. sec =1------=OB---;

cos OA

vi. cot =1------=OA---;

tan AB

2. Trigonometrical Identities: sin2 + cos2 = 1.

1 + tan2 = sec2.

1 + cot2 = cosec2.3. Values of T-ratios:0(/6)

30(/4)

45(/3)

60(/2)

90

sin 01/23/21

cos 13/21/20

tan 01/313Not defined

4. Angle of Elevation:

Suppose a man from a point O looks up at an object P, placed above the level of his eye. Then, the angle which the line of sight makes with the horizontal through O, is called the anlge of elevation of P as seen from O.

Angle of elevation of P from O = AOP.

5. Angle of Depression:

Suppose a man from a point O looks down at an object P, placed below the level of his eye, then the angle which the line of sight makes with the horizontal through O, is called the angle of depression of P as seen from O.Problems :

1.Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30 and 45 respectively. If the lighthouse is 100 m high, the distance between the two ships is:

A.173 m

B.200 m

C.273 m

D.300 m

Answer:OptionCExplanation:Let AB be the lighthouse and C and D be the positions of the ships.

Then, AB = 100 m,ACB = 30 andADB = 45.

AB

= tan 30 =

1

AC = AB x3= 1003m.

AC

3

AB

= tan 45 = 1 AD = AB = 100 m.

AD

CD = (AC + AD)

= (1003+ 100) m

= 100(3+ 1)

= (100 x 2.73) m

= 273 m.

2.The angle of elevation of a ladder leaning against a wall is 60 and the foot of the ladder is 4.6 m away from the wall. The length of the ladder is:

A.2.3 m

B.4.6 m

C.7.8 m

D.9.2 m

Answer:OptionDExplanation:Let AB be the wall and BC be the ladder.

Then,ACB = 60 and AC = 4.6 m.

AC

= cos 60 =

1

BC

2

BC

= 2 x AC

= (2 x 4.6) m

= 9.2 m.

3.An observer 1.6 m tall is 203away from a tower. The angle of elevation from his eye to the top of the tower is 30. The heights of the tower is:

A.21.6 m

B.23.2 m

C.24.72 m

D.None of these

Answer:OptionAExplanation:Let AB be the observer and CD be the tower.

Draw BECD.

Then, CE = AB = 1.6 m,

BE = AC = 203m.

DE

= tan 30 =

1

BE

3

DE =

203

m = 20 m.

3

CD = CE + DE = (1.6 + 20) m = 21.6 m.

4.From a point P on a level ground, the angle of elevation of the top tower is 30. If the tower is 100 m high, the distance of point P from the foot of the tower is:

A.149 m

B.156 m

C.173 m

D.200 m

Answer & ExplanationAnswer:OptionCExplanation:Let AB be the tower.

Then,APB = 30 and AB = 100 m.

AB

= tan 30 =

1

AP

3

AP

= (AB x3) m

= 1003m

= (100 x 1.73) m

= 173 m.

5.The angle of elevation of the sun, when the length of the shadow of a tree3times the height of the tree, is:

A.30

B.45

C.60

D.90

Answer:OptionAExplanation:Let AB be the tree and AC be its shadow.

LetACB =.

Then,

AC

=

3 cot=3

AB

= 30.