GMAT FOCUS EDITION SAMPLE QUESTION QUANTITATIVE REASONING SECTION Problem Solving Question

 

Of 200 surveyed students, 20% of those who read book A also read book B and 25% of those who read book B also read book A. If each student read at least one of the books, what is the difference between the number of students who read only book A and the number of students who read only book B?

A. 20
B. 25
C. 30
D. 35
E. 40

 

Answer: B

 

Explanation:

Hello, my name is Claudio Hurtado, an expert teacher in preparing professionals to excel in the quantitative section of the GMAT FOCUS EDITION.

In the given scenario, we are informed that there are 200 students who read either book A or book B, KEEPING IN MIND THAT STUDENTS READ AT LEAST ONE OF THE BOOKS.

Additionally, it is indicated that a percentage of those who read one book also read the other book (key information).

Now, what image can you create in your mind that makes sense of the situation?

Very well, we can associate the situation with two circles.
Imagine two circles intersecting (having elements in common).

So, we will call one circle A (students who read book A) and the other circle B (students who read book B).

Let’s continue building with imagination:

The region where students who read book A, excluding those who read both books, will be called X.

The region where students who read both books are located will be called Y.

And the region where students who read book B, excluding those who read both books, will be called Z.

We are then told that 20% of the students who read book A also read the other book.

Bearing in mind that those who read book A, in our representation, are (x+y), and those who also read the other book are represented by Y.

We can write this as (20/100)(x+y)=y.

On the other hand, we are told that 25% of those who read book B also read the other book.

Which we can represent as (25/100)(y+z) = y.

Thus, our two equations would be: (1/5)(x+y) = y; (1/4)(y+z)=y.

In other words: (x+y)=5y and (y+z)=4y.

Then x=4y and z=3y.

Additionally, we are told that the total number of students is 200.

So, x + y + z = 200.

Which simplifies to 4y + y + 3y = 200; 8y=200.

Therefore, y=25.

We are asked to find x-z, which is 4y-3y=y=25, answer 25, option B.

 

If I wasn’t clear enough, please engage in the forum to clarify your doubts. Claudio Hurtado, Coach for the QUANTITATIVE REASONING SECTION of GMAT FOCUS +56 945 517 215 https://gmatchile.cl