M7MBA wrote: ↑

Sun Apr 11, 2021 12:24 pm

2015-10-26_2106.png

The table above shows the number of students in a certain high school class who are boys and the number of students in the class who are studying biology. What is the total number of students in the class?

(1) Of the boys in the class, 15 are studying biology.
(2) The number of girls in the class is twice the number of students in the class who are NOT studying biology.

Answer: B

Source: Official Guide

ASIDE: Since the diagram closely resembles a Double Matrix Method diagram, I'll treat it as such.

Target question: What is the total number of students in the class?

Statement 1: Of the boys in the class, 15 are studying biology.
Add this information to our diagram to get:


Since the top row must add to 18, we know that the top-right box must have 3 students.
Also, since the left-hand column must add to 26, we know that the bottom-left box must have 11 students.
Add this information to the diagram to get:


At this point, we still don't have a value for the bottom-right box, which means that are many possible scenarios. Here are two possible scenarios:

In the left-side diagram, there is a total of 49 students
In the right-side diagram, there is a total of 129 students

Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The number of girls in the class is twice the number of students in the class who are NOT studying biology.
We can add this information to our diagram as follows:


KEY CONCEPT #1: the sum of the rows must equal the sum of the columns.
So, we can write: 18 + 2x = 26 + x
Solve to get: x = 8

KEY CONCEPT #2: the total number of students = the sum of the two rows
So, the total number of students = 26 + 8 = 34
The answer to the target question is there are 34 students in the class
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent