Source: Official Guide for GMAT Review 2016 Data Sufficiency ; #150

1

The table above shows the number of

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 Explanation

1

Gravatar David Recine, Magoosh Tutor

The answer is B: Statement 2 alone is sufficient but statement 1 alone is not sufficient to answer the question asked.

Statement 1 only allows us to know how many boys are not studying biology. (There are 18 boys total, so if 15 boys are studying biology, 3 boys must NOT be studying biology.)

Statement 2, on the other hand, sets up a formula for calculating the total number of students in class. Let's take a closer look at that statement.

We'll say that the number of students NOT studying biology is X. From the table already know that the number of students who ARE studying biology is 26. So:

26 + X = the total number of students.

Now, from Statement 2, we also know that the total number of girls is two times the amount of students NOT taking biology. In other words, the number of girls is 2X. And from the table, we know that the total number of boys in the class is 18. The number of girls plus the number of boys would have to be the total number of students, right? So:

2X + 18 = the total number of students.

In other words, we have these two equations:

26 + X = the total number of students
2X + 18 = the total number of students

These equations both equal the same thing, so they equal each other.

This can be expressed as:

26 + X = 2X + 18

From there, you can get X on one side and solve for it:

26 = X + 18
26-18 = X
X = 8

Now you can go back to one of the original equations, plug in 8 for X, and get the total number of students.

26 + 8 = 34

So Statement 2, without Statement 1, tells you there are 34 students total.

Bear in mind that since this is a Data Sufficiency problem, you don't actually need to solve everything, to the point where you get your answer of 34. Once you determine that you have two equivalent expressions for the total number of students, both of which contain the exact same unknown variable (X), you can know that the problem is solvable with the information from Statement 2 alone. And that's all you need to know to correctly select answer B.

Aug 7, 2017 • Comment

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Section 6.3 Data Sufficiency

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