SEAMC 2007 Multiple Choice Section. You will have exactly 1½ minutes to read each question and select the best answer. Following this slide will be.

SEAMC 2007SEAMC 2007Multiple Choice SectionMultiple Choice Section



You will have exactly 1½ You will have exactly 1½ minutes minutes

to read each question and to read each question and select the best answer.select the best answer.

Following this slide will be a Following this slide will be a practice question to try. practice question to try.

Here is the practice question:Here is the practice question:


Question 0 (practice)Question 0 (practice)In the diagram, the value of In the diagram, the value of xx is is equal to:equal to:

A.A. 3434

B.B. 3333

C.C. 4646

D.D. 2323

60o

20o54o

x o

x o


And the answer of course is …And the answer of course is …

A.A. 3434

B.B. 3333

C.C. 4646

D.D. 2323




Shade the square of the letter Shade the square of the letter of your preferred choice of of your preferred choice of

answer.answer.For example, the answer to the previous question was D:For example, the answer to the previous question was D:

A B C DA B C D



Question 1Question 1The average of four numbers is 48. If 8 The average of four numbers is 48. If 8 is subtracted from each number, the is subtracted from each number, the average of the four new numbers is:average of the four new numbers is:

A.A. 1616

B.B. 4040

C.C. 4646

D.D. 4444


Question 2Question 2PQRS is a rectangle enclosing 2 circles each of PQRS is a rectangle enclosing 2 circles each of radius 2cm. The area of rectangle PQRS, in radius 2cm. The area of rectangle PQRS, in square centimeters, is:square centimeters, is:

A.A. 88

B.B. 1616

C.C. 2424

D.D. 3232S R

QP


Question 3Question 3The number of nails weighing 5 grams each The number of nails weighing 5 grams each that can be made from 11.5 kilograms of wire that can be made from 11.5 kilograms of wire is:is:

A.A. 230230

B.B. 22 300300

C.C. 2323 000000

D.D. 230230 000000


Question 4Question 4One of the elephants in the zoo is on a special diet, and One of the elephants in the zoo is on a special diet, and eats every day a portion of carrots which is equal to eats every day a portion of carrots which is equal to what one of the rabbits eats in 1 year (365 days). what one of the rabbits eats in 1 year (365 days). Together, in one day, the elephant and rabbit eat 111 Together, in one day, the elephant and rabbit eat 111 kilograms of carrots. How many kilograms of carrots kilograms of carrots. How many kilograms of carrots does the rabbit eat in one day?does the rabbit eat in one day?

A.A. C.C.

B.B. D.D.

2

1

165

111

122

37

61

19


Question 5Question 5The digits 1, 2, 3 and 5 can be arranged to The digits 1, 2, 3 and 5 can be arranged to form 24 different four-digit numbers. The form 24 different four-digit numbers. The number of even numbers in this set is:number of even numbers in this set is:

A.A. 1818

B.B. 1212

C.C. 66

D.D. 22


Question 6Question 6Between the last 5 questions, a diagram Between the last 5 questions, a diagram of a famous fractal has been of a famous fractal has been momentarily displayed. The name of momentarily displayed. The name of this fractal is:this fractal is:

A.A. Pascal’s TrianglePascal’s Triangle

B.B. Koch SnowflakeKoch Snowflake

C.C. Sierpinski’s TriangleSierpinski’s Triangle

D.D. Mandelbrot SetMandelbrot Set


Question 7Question 7The value of the product The value of the product

where the where the

nnthth factor is , is: factor is , is:

A.A. 441441

B.B. 40414041

C.C. 44104410

D.D. 40014001

)400

411)...(

16

91)(

9

71)(

4

51)(

1

31(

2

121

n

n


Question 8Question 8If the figure shown is folded to form a cube, then three If the figure shown is folded to form a cube, then three faces meet at every vertex. The numbers on the three faces meet at every vertex. The numbers on the three faces meeting at any vertex can be multiplied together. faces meeting at any vertex can be multiplied together. What is the largest such product for the vertices of this What is the largest such product for the vertices of this cube?cube?

A.A. 120120

B.B. 9090

C.C. 7272

D.D. 6060

4

1

2

3

5 6


Question 9Question 9How many positive integers less than How many positive integers less than 1000 have the sum of their digits equal 1000 have the sum of their digits equal to 6?to 6?

A.A. 2828

B.B. 2727

C.C. 1919

D.D. 1818


Question 10Question 10A formula in physics states A formula in physics states

If RIf R11 = 3 and R = 3 and R22 = 6, then R is equal to = 6, then R is equal to

A.A. ½ ½

B.B. 22

C.C. 11//99

D.D. 99

21

111

RRR


Question 11Question 11A 3x8 rectangle is cut into 2 pieces as A 3x8 rectangle is cut into 2 pieces as indicated. The 2 pieces are rearranged to form indicated. The 2 pieces are rearranged to form a right-angled triangle. One side of the a right-angled triangle. One side of the resulting triangle has length resulting triangle has length

A.A. 9 9

B.B. 77

C.C. 66

D.D. 44

3 5

4 4

8


Question 12Question 12A cube with each edge of length 1 unit is A cube with each edge of length 1 unit is turned into a solid star by adding a square turned into a solid star by adding a square pyramid with each edge of length 1 unit to pyramid with each edge of length 1 unit to every face. The number of edges this new every face. The number of edges this new solid has is: solid has is:

A.A. 2828

B.B. 2424

C.C. 4848

D.D. 3636


Question 13Question 13The regular octagon shown has side length The regular octagon shown has side length 4cm. What is the area, in square centimeters, 4cm. What is the area, in square centimeters, of the shaded region? of the shaded region?

A.A. 16 16

B.B.

C.C. 2424

D.D.

)21(8

)21(16


Question 14Question 14What is the highest power of 2 which What is the highest power of 2 which divides exactly into 1divides exactly into 1 000000 000? 000?

A.A. 2233

B.B. 2255

C.C. 2266

D.D. 2288


Question 15Question 15What is the radius of the largest circle that What is the radius of the largest circle that can be drawn inside a quarter circle of radius can be drawn inside a quarter circle of radius 1 unit?1 unit?

A.A. C.C. ½ ½

B.B. D.D.

12

3

222

1?


Question 16Question 16If If nn is an integer, which of the following is an integer, which of the following must be an odd integer?must be an odd integer?

A.A. 55nn

B.B. nn2 2 + 5+ 5

C.C. 22nn22 + 5 + 5

D.D. nn33


Question 17Question 17In the diagram, all triangles are right In the diagram, all triangles are right isosceles triangles, and PQR is a isosceles triangles, and PQR is a straight line. Given that PQ is 12 units, straight line. Given that PQ is 12 units, what is the length of QR? what is the length of QR?

A.A. C.C.

B.B. 44 D.D.

5

13

4

33

2

23

P

Q

R


Question 18Question 18If the following were arranged in order If the following were arranged in order from biggest to smallest, the biggest from biggest to smallest, the biggest being the first, which would be the third being the first, which would be the third number? number? A.A. 2(2)2(2)77

B.B. 2(2)2(2)66 – 2 – 2

C.C. 2 + 2(2)2 + 2(2)66

D.D. 2277


Question 19Question 19

If xIf xyy = 3, then x = 3, then x3y3y + 2 equals + 2 equals

A.A. 11 11

B.B. 88

C.C. 2929

D.D. 3535


Question 20Question 20If four different positive integers m, n, p and q If four different positive integers m, n, p and q satisfy the equation (7 – m)(7 – n)(7 – p)(7 – satisfy the equation (7 – m)(7 – n)(7 – p)(7 – q) = 4 then the sum m+n+p+q is equal toq) = 4 then the sum m+n+p+q is equal to

A.A. 28 28

B.B. 2626

C.C. 2424

D.D. 2121


Question 21Question 21If If p p ++q q = = nn and where and where pp and and qq are both positive,are both positive,

then (then (pp – – qq))22 equals equals

mqp

11

A.A. C.C.

B.B. D.D.

n

mn 2

m

nmn 42

mnn 42 mn 2


Question 22Question 22For For mm and and nn integers, how many solutions ( integers, how many solutions (mm, , nn) of ) of

the inequality are there? the inequality are there?

A.A. 36 36

B.B. 4848

C.C. 1515

D.D. 5252

174 22 nm


Question 23Question 23Two parallel planes are 10cm apart. A point P Two parallel planes are 10cm apart. A point P lies on one of the planes. The set of points lies on one of the planes. The set of points which are all equally distant from the two which are all equally distant from the two planes and 6cm from P is:planes and 6cm from P is:

A.A. a point a point

B.B. a straight linea straight line

C.C. a circlea circle

D.D. a hollow spherea hollow sphere



equals equals 137137

A.A. C.C.

B.B. D.D.

3

13

2

3

2 4 132


Question 25Question 25A cube measuring 3 units on each edge is A cube measuring 3 units on each edge is painted. It is then cut into 27 one-unit cubes. painted. It is then cut into 27 one-unit cubes. How many faces of the one-unit cubes are not How many faces of the one-unit cubes are not painted? painted?

A.A. 108 108

B.B. 8181

C.C. 7272

D.D. 3636






Shade the square of the letter Shade the square of the letter of your preferred choice of of your preferred choice of

answer.answer.For example, if the answer is C:For example, if the answer is C:

A B C DA B C D


Question 26Question 26If n is a positive integer and n(n+1) is If n is a positive integer and n(n+1) is divided by 3, the remainder can bedivided by 3, the remainder can be

A.A. 0 only0 only

B.B. 2 only2 only

C.C. 0 or 1 only0 or 1 only

D.D. 0 or 2 only0 or 2 only


Question 27Question 27A cart track is made up of one large A cart track is made up of one large semicircle, and three small semicircles each of semicircle, and three small semicircles each of radius 100m. What is the total length of the radius 100m. What is the total length of the track?track?

A.A. 150150ππ

B.B. 300300ππ

C.C. 450450ππ

D.D. 600 600ππ



If then equalsIf then equals5

2

32

1

x 12

1

x

A.A. 22 B.B. C.C. D.D. 2

3

3

2

2

1


Question 29Question 29If a, a+d, a+9d, (d>0), are the sides of If a, a+d, a+9d, (d>0), are the sides of a right-angled triangle, then the ratio a right-angled triangle, then the ratio a:d isa:d is

A.A. 4:1 4:1

B.B. 8:18:1

C.C. 20:2120:21

D.D. 20:120:1


Question 30Question 30A calendar watch loses one second per day. At A calendar watch loses one second per day. At this rate, the approximate length of time, in this rate, the approximate length of time, in years, for the watch to lose exactly 24 hours isyears, for the watch to lose exactly 24 hours is

A.A. C.C. 240240

B.B. D.D. 24002400

360

1

240

1



If then the value ofIf then the value of

isis

x ...5

1

4

1

3

1

2

11

2222

...8

1

6

1

4

1

2

11

2222

A.A. C.C.

B.B. D.D.

2

x

12

x

14

x

14

x


Question 32Question 32The figure below which can beThe figure below which can beobtained by rotating the figureobtained by rotating the figureon the right ison the right is

A.A. C.C.

B.B. D.D.


Question 33Question 33A square of side 2x has four equilateral A square of side 2x has four equilateral triangles drawn on its sides (and exterior to triangles drawn on its sides (and exterior to the square). The area of the figure formed isthe square). The area of the figure formed is

A.A. C.C.

B.B. D.D.

2)31(4 x

4

)31( 2x

2)34( x

2)341( x


Question 34Question 34Consider the set of 4-digit positive integers Consider the set of 4-digit positive integers where each integer is composed of four where each integer is composed of four different digits. When the smallest of these is different digits. When the smallest of these is subtracted from the largest, the result issubtracted from the largest, the result is

A.A. 8876 8876

B.B. 86428642

C.C. 88538853

D.D. 86468646


Question 35Question 35PBCQ is a trapezoid in which PQ:BC = 2:3.PBCQ is a trapezoid in which PQ:BC = 2:3.If the area of triangle ABC is 36, then the area If the area of triangle ABC is 36, then the area of the trapezoid PBCQ isof the trapezoid PBCQ is

A.A. 100 100

B.B. 9090

C.C. 8484

D.D. 7272

Q

A

CB

P


Question 36Question 36If If mm pens are bought at pens are bought at nn dollars each, and dollars each, and nn pens are bought at pens are bought at mm dollars each, then the dollars each, then the average cost per pen, in dollars, isaverage cost per pen, in dollars, is

A.A. mnmn C.C.

B.B. D. D. 11nm

mn

2

2

nm


Question 37Question 37Each side of a rhombus has length 10. Each side of a rhombus has length 10. The sum of the squares of the diagonals The sum of the squares of the diagonals equalsequals

A.A. 50 50

B.B. 100100

C.C. 200200

D.D. 400400


Question 38Question 38The slope of OA isThe slope of OA is

A.A. 44//33

B.B. 33//44

C.C. 55//33

D.D. 33//55 x

3

B

A

O

4

5

y


Question 39Question 39If the distance between consecutive fence If the distance between consecutive fence posts is 5 meters, the number of fence posts posts is 5 meters, the number of fence posts needed to build a fence around a triangular needed to build a fence around a triangular region with sides 20m, 20m, and 30m isregion with sides 20m, 20m, and 30m is

A.A. 11 11

B.B. 1313

C.C. 1414

D.D. 1515


Question 40Question 40A bag contains 80 jelly beans – 20 are red, 20 A bag contains 80 jelly beans – 20 are red, 20 are green, 20 are yellow and 20 are blue. The are green, 20 are yellow and 20 are blue. The least number that a blindfolded person must least number that a blindfolded person must eat to be certain of having eaten at least one eat to be certain of having eaten at least one of each colour isof each colour is

A.A. 5 5

B.B. 77

C.C. 2323

D.D. 6161


Question 41Question 41If If xx, , yy and and zz are positive and , are positive and ,

and , then and , then xx equals equals

ayx

xy

c

zy

yz

bzx

xz

A.A. C.C.

B.B. D.D.

bcacab

abc

bcacab

abc

2

abacbc

abc

2

abbcac

abc


Question 42Question 42As everyone knows, a normal cat has 18 claws, 5 on As everyone knows, a normal cat has 18 claws, 5 on each front leg and 4 on each back leg. At Harry’s Home each front leg and 4 on each back leg. At Harry’s Home for Distressed Cats there are 4 three-legged cats, each for Distressed Cats there are 4 three-legged cats, each one with a different leg missing. How many claws do one with a different leg missing. How many claws do they have all together?they have all together?

A.A. 52 52

B.B. 5454

C.C. 6464

D.D. 6868


Question 43Question 43Three darts are thrown at the dartboard Three darts are thrown at the dartboard illustrated. The three scores are added illustrated. The three scores are added together, a miss counts as zero. What is the together, a miss counts as zero. What is the smallest total score which is impossible to smallest total score which is impossible to obtain?obtain?

A.A. 14 14

B.B. 1818

C.C. 1919

D.D. 222213

8

12

23


Question 44Question 44The last digit in the sum 3The last digit in the sum 31717 + 7 + 71313 is is

A.A. 0 0

B.B. 11

C.C. 22

D.D. 44


Question 45Question 45Red rose plants are on sale for $3 each and yellow ones Red rose plants are on sale for $3 each and yellow ones for $5 each. A young guy wants to buy a mixture of for $5 each. A young guy wants to buy a mixture of both types (at least one of each) and decides to buy 13 both types (at least one of each) and decides to buy 13 in total, buying more yellow ones than red ones. The in total, buying more yellow ones than red ones. The number of dollars that the young guy spends could benumber of dollars that the young guy spends could be

A.A. 51 51

B.B. 5757

C.C. 5858

D.D. 6565



If then If then LL equals equals

A.A. C.C.

B.B. D.D.

LHG

4

4

)( 2HG 2)(

4

HG

22

4

HG 4

22 HG



equals equals

A.A. 22n+2n+2

B.B. 222n+22n+2

C.C. 442n+22n+2

D.D. 442n+12n+1

11 22 nn


Question 48Question 48For all positive integers For all positive integers x and and y such that such that

the greatest value that the greatest value that y can have is can have is

A.A. 6060

B.B. 8484

C.C. 156156

D.D. 288288

12

111

yx


Question 49Question 49Each circle has an area of 1cmEach circle has an area of 1cm22. . The area of the overlap between any pair of The area of the overlap between any pair of intersecting circles is intersecting circles is 11//88 cm cm22. . The total area in cmThe total area in cm22 of the region enclosed by the 5 of the region enclosed by the 5 circles iscircles is

A.A. 44

B.B. 4½ 4½

C.C. 4433//88

D.D. 4¾ 4¾


Question 50Question 50Some M&M’s had been eaten without the shop owner’s Some M&M’s had been eaten without the shop owner’s permission by one or more of the 5 kids in the shop. permission by one or more of the 5 kids in the shop. When questioned, they gave the following answers:When questioned, they gave the following answers:

A.A. 1 1

B.B. 22

C.C. 33

D.D. 44

E.E. 5 5

Ace: One of us ate themAce: One of us ate themBea: Two of us ate themBea: Two of us ate themCec: Three of us ate themCec: Three of us ate themDee: Four of us ate themDee: Four of us ate themEve: All of us ate themEve: All of us ate them

The owner knew from past The owner knew from past behaviour that the guilty ones behaviour that the guilty ones always lied while the others told always lied while the others told the truth. The number of kids who the truth. The number of kids who ate the M&M’s wasate the M&M’s was


SEAMC 2007 Multiple Choice Section. You will have exactly 1½ minutes to read each question and select the best answer. Following this slide will be.

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