4GMAT Diagnostic Test Q10 - Data Sufficiency - Elementary Probability

GMAT QUANTITATIVE REASONING

ELEMENTARY PROBABILITY

DATA SUFFICIENCY

Diagnostic Test

Question

What is the probability that two students selected to the

elocution competition are both boys?

Statement 1: The ratio of boys to girls in the class is 3 : 4

Statement 2: There are 11more girls in the class.

Step 1

Get clarity on when the data is sufficient

What is the probability that two students selected are both boys?We will not even look at the statements while answering the following questions

When is the data sufficient and when not?

What is the probability that two students selected are both boys?We will not even look at the statements while answering the following questions

When is the data sufficient and when not?

The data is sufficient if we are able

to get ONE value for the probability.

What is the probability that two students selected are both boys?We will not even look at the statements while answering the following questions

When is the data sufficient and when not?

The data is sufficient if we are able

to get ONE value for the probability.

For instance, if we get more than one

value or if an unknown is part of the

expression, the data is NOT

sufficient.

What is the probability that two students selected are both boys?We will not even look at the statements while answering the following questions

When is the data sufficient and when not? What expression will give the probability ?

The data is sufficient if we are able

to get ONE value for the probability.

For instance, if we get more than one

value or if an unknown is part of the

expression, the data is NOT

sufficient.

What is the probability that two students selected are both boys?We will not even look at the statements while answering the following questions

When is the data sufficient and when not? What expression will give the probability ?

The data is sufficient if we are able

to get ONE value for the probability.

For instance, if we get more than one

value or if an unknown is part of the

expression, the data is NOT

sufficient.

Let the number of boys in the class

be ‘b’ and let there be ‘t’ total

students.

What is the probability that two students selected are both boys?We will not even look at the statements while answering the following questions

When is the data sufficient and when not? What expression will give the probability ?

The data is sufficient if we are able

to get ONE value for the probability.

For instance, if we get more than one

value or if an unknown is part of the

expression, the data is NOT

sufficient.

Let the number of boys in the class

be ‘b’ and let there be ‘t’ total

students.

Probability that two students

selected are both boys =

b(b-1)

t(t-1)

Step 2

Let’s evaluate statement 1 alone

Statement 1: The ratio of boys to girls in the class is 3 : 4

What is the probability that two students selected are both boys?

· Ratio of boys to girls 3 : 4

Statement 1: The ratio of boys to girls in the class is 3 : 4

What is the probability that two students selected are both boys?

· Ratio of boys to girls 3 : 4

If there are 3k boys, there will be 4k

girls and a total of 7k students.·

Statement 1: The ratio of boys to girls in the class is 3 : 4

What is the probability that two students selected are both boys?

· Ratio of boys to girls 3 : 4

If there are 3k boys, there will be 4k

girls and a total of 7k students.·

We determined in the last slide that

for ‘b’ boys and ‘t’ total students, the

required probability is b(b−1)t(t−1)

·

Statement 1: The ratio of boys to girls in the class is 3 : 4

What is the probability that two students selected are both boys?

· Ratio of boys to girls 3 : 4

If there are 3k boys, there will be 4k

girls and a total of 7k students.·

We determined in the last slide that

for ‘b’ boys and ‘t’ total students, the

required probability is b(b−1)t(t−1)

·

the probability = 3k(3k−1)7k(7k−1)

=3(3k-1)7(7k-1)

Statement 1: The ratio of boys to girls in the class is 3 : 4

What is the probability that two students selected are both boys?

· Ratio of boys to girls 3 : 4

If there are 3k boys, there will be 4k

girls and a total of 7k students.·

We determined in the last slide that

for ‘b’ boys and ‘t’ total students, the

required probability is b(b−1)t(t−1)

·

the probability = 3k(3k−1)7k(7k−1)

=3(3k-1)7(7k-1)

Notice that the probability expression comprises a ‘k’ term.

The probability value will depend on the value that k takes.

So, we CANNOT determine the probability uniquely.

Statement 1: The ratio of boys to girls in the class is 3 : 4

Statement 1 alone is NOT sufficient

What is the probability that two students selected are both boys?

· Ratio of boys to girls 3 : 4

If there are 3k boys, there will be 4k

girls and a total of 7k students.·

We determined in the last slide that

for ‘b’ boys and ‘t’ total students, the

required probability is b(b−1)t(t−1)

·

the probability = 3k(3k−1)7k(7k−1)

=3(3k-1)7(7k-1)

Notice that the probability expression comprises a ‘k’ term.

The probability value will depend on the value that k takes.

So, we CANNOT determine the probability uniquely.

Statement 1: The ratio of boys to girls in the class is 3 : 4

Eliminate choices A and DStatement 1 alone is NOT sufficient

What is the probability that two students selected are both boys?

· Ratio of boys to girls 3 : 4

If there are 3k boys, there will be 4k

girls and a total of 7k students.·

We determined in the last slide that

for ‘b’ boys and ‘t’ total students, the

required probability is b(b−1)t(t−1)

·

the probability = 3k(3k−1)7k(7k−1)

=3(3k-1)7(7k-1)

Notice that the probability expression comprises a ‘k’ term.

The probability value will depend on the value that k takes.

So, we CANNOT determine the probability uniquely.

Statement 1: The ratio of boys to girls in the class is 3 : 4

Choices narrow down to B, C or E.

Eliminate choices A and DStatement 1 alone is NOT sufficient

What is the probability that two students selected are both boys?

· Ratio of boys to girls 3 : 4

If there are 3k boys, there will be 4k

girls and a total of 7k students.·

We determined in the last slide that

for ‘b’ boys and ‘t’ total students, the

required probability is b(b−1)t(t−1)

·

the probability = 3k(3k−1)7k(7k−1)

=3(3k-1)7(7k-1)

Notice that the probability expression comprises a ‘k’ term.

The probability value will depend on the value that k takes.

So, we CANNOT determine the probability uniquely.

Step 3

Let’s evaluate statement 2 alone.

Statement 2 : There are 11more girls in the class.

What is the probability that two students selected are both boys?

There are 11 more girls in the class

Statement 2 : There are 11more girls in the class.

What is the probability that two students selected are both boys?

There are 11 more girls in the class

· If the number of boys is 10, there

will be 21 girls and 31 students.

Statement 2 : There are 11more girls in the class.

What is the probability that two students selected are both boys?

There are 11 more girls in the class

· If the number of boys is 10, there

will be 21 girls and 31 students. Probability =

10×931×30

Statement 2 : There are 11more girls in the class.

What is the probability that two students selected are both boys?

There are 11 more girls in the class

· If the number of boys is 10, there

will be 21 girls and 31 students. Probability =

10×931×30

· If the number of boys is 20, there

will be 31 girls and 51 students.

Statement 2 : There are 11more girls in the class.

What is the probability that two students selected are both boys?

There are 11 more girls in the class

· If the number of boys is 10, there

will be 21 girls and 31 students. Probability =

10×931×30

· If the number of boys is 20, there

will be 31 girls and 51 students. Probability =

20×1951×50

Statement 2 : There are 11more girls in the class.

What is the probability that two students selected are both boys?

There are 11 more girls in the class

· If the number of boys is 10, there

will be 21 girls and 31 students. Probability =

10×931×30

· If the number of boys is 20, there

will be 31 girls and 51 students. Probability =

20×1951×50

We are NOT able to determine the probability uniquely with this statement.

Statement 2 : There are 11more girls in the class.

What is the probability that two students selected are both boys?

There are 11 more girls in the class

· If the number of boys is 10, there

will be 21 girls and 31 students. Probability =

10×931×30

· If the number of boys is 20, there

will be 31 girls and 51 students. Probability =

20×1951×50

We are NOT able to determine the probability uniquely with this statement.

Statement 2 alone is NOT sufficient

Statement 2 : There are 11more girls in the class.

Eliminate choice B

What is the probability that two students selected are both boys?

There are 11 more girls in the class

· If the number of boys is 10, there

will be 21 girls and 31 students. Probability =

10×931×30

· If the number of boys is 20, there

will be 31 girls and 51 students. Probability =

20×1951×50

We are NOT able to determine the probability uniquely with this statement.

Statement 2 alone is NOT sufficient

Statement 2 : There are 11more girls in the class.

Choices narrow down to C or E.

Eliminate choice B

What is the probability that two students selected are both boys?

There are 11 more girls in the class

· If the number of boys is 10, there

will be 21 girls and 31 students. Probability =

10×931×30

· If the number of boys is 20, there

will be 31 girls and 51 students. Probability =

20×1951×50

We are NOT able to determine the probability uniquely with this statement.

Statement 2 alone is NOT sufficient

Step 4

Let’s combine data from both the

statements.

Statements Together : The ratio of boys to girls in the class is 3 : 4 and there are 11 more girls in the class

What is the probability that two students selected are both boys?

We determined that for ‘b’ boys and ‘t’ total

students, the required probability is b(b−1)t(t−1)

·

Statements Together : The ratio of boys to girls in the class is 3 : 4 and there are 11 more girls in the class

What is the probability that two students selected are both boys?

We determined that for ‘b’ boys and ‘t’ total

students, the required probability is b(b−1)t(t−1)

·

From statement 1, we know there are 3k boys

and 4k girls.·

Statements Together : The ratio of boys to girls in the class is 3 : 4 and there are 11 more girls in the class

What is the probability that two students selected are both boys?

We determined that for ‘b’ boys and ‘t’ total

students, the required probability is b(b−1)t(t−1)

·

From statement 1, we know there are 3k boys

and 4k girls.·

From statement 2, we know 4k – 3k = k = 11.·

Statements Together : The ratio of boys to girls in the class is 3 : 4 and there are 11 more girls in the class

What is the probability that two students selected are both boys?

We determined that for ‘b’ boys and ‘t’ total

students, the required probability is b(b−1)t(t−1)

·

From statement 1, we know there are 3k boys

and 4k girls.·

So, the class has 33 boys and 44 girls and 77

students.·

From statement 2, we know 4k – 3k = k = 11.·

Statements Together : The ratio of boys to girls in the class is 3 : 4 and there are 11 more girls in the class

What is the probability that two students selected are both boys?

We determined that for ‘b’ boys and ‘t’ total

students, the required probability is b(b−1)t(t−1)

·

From statement 1, we know there are 3k boys

and 4k girls.·

So, the class has 33 boys and 44 girls and 77

students.·

From statement 2, we know 4k – 3k = k = 11.·

Probability = 33×3277×76

Statements Together : The ratio of boys to girls in the class is 3 : 4 and there are 11 more girls in the class

What is the probability that two students selected are both boys?

We determined that for ‘b’ boys and ‘t’ total

students, the required probability is b(b−1)t(t−1)

·

From statement 1, we know there are 3k boys

and 4k girls.·

So, the class has 33 boys and 44 girls and 77

students.·

From statement 2, we know 4k – 3k = k = 11.·

Probability = 33×3277×76

Using the two statements together, we could determine the probability uniquely.

Statements Together : The ratio of boys to girls in the class is 3 : 4 and there are 11 more girls in the class

What is the probability that two students selected are both boys?

We determined that for ‘b’ boys and ‘t’ total

students, the required probability is b(b−1)t(t−1)

·

From statement 1, we know there are 3k boys

and 4k girls.·

So, the class has 33 boys and 44 girls and 77

students.·

From statement 2, we know 4k – 3k = k = 11.·

Probability = 33×3277×76

Using the two statements together, we could determine the probability uniquely.

Together the statements are SUFFICIENT.

Statements Together : The ratio of boys to girls in the class is 3 : 4 and there are 11 more girls in the class

Eliminate choice E

What is the probability that two students selected are both boys?

We determined that for ‘b’ boys and ‘t’ total

students, the required probability is b(b−1)t(t−1)

·

From statement 1, we know there are 3k boys

and 4k girls.·

So, the class has 33 boys and 44 girls and 77

students.·

From statement 2, we know 4k – 3k = k = 11.·

Probability = 33×3277×76

Using the two statements together, we could determine the probability uniquely.

Together the statements are SUFFICIENT.

Statements Together : The ratio of boys to girls in the class is 3 : 4 and there are 11 more girls in the class

Answer is choice C

Eliminate choice E

What is the probability that two students selected are both boys?

We determined that for ‘b’ boys and ‘t’ total

students, the required probability is b(b−1)t(t−1)

·

From statement 1, we know there are 3k boys

and 4k girls.·

So, the class has 33 boys and 44 girls and 77

students.·

From statement 2, we know 4k – 3k = k = 11.·

Probability = 33×3277×76

Using the two statements together, we could determine the probability uniquely.

Together the statements are SUFFICIENT.

Try this variant

What is the probability that a student selected to the

elocution competition is a boy?

Statement 1: The ratio of boys to girls in the class is 3 : 4

Statement 2: There are 11more girls in the class.

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