Data Sufficiency

Vincen wrote: ↑

Mon Mar 22, 2021 7:24 am

At least 100 students at a certain high school study Japanese. If 4 percent of the students at the school who study French also study Japanese do more students at the school study french than Japanese?

(1) 16 students at the school study both French and Japanese
(2) 10 percent of the students at the school who study Japanese also study French.

Answer: B

Source: GMAT Prep

Let's let J = the TOTAL number of students taking Japanese
And let F = the TOTAL number of students taking French

When we sketch our diagram, we get:


Target question: Is F greater than J?

Given: 4 percent of the students at the school who study French also study Japanese
Since we let F = the TOTAL number of students taking French, we can say that 4% of F = number of students taking BOTH French and Japanese.
In other words, 0.04F = number of students taking BOTH French and Japanese
We can also say that 96% of the students who study French do NOT study Japanese
In other words, 0.96F = number of students taking French but NOT Japanese

So, our diagram now looks like this:


Statement 1: 16 students at the school study both French and Japanese
Since 0.04F = number of students taking BOTH French and Japanese, we can write: 0.04F =16
When we solve this equation for F, we get F = 400
So, 0.96F = 384
So, our diagram now looks like this:


Is this enough information to determine whether or not F is greater than J?
No.

For example, we COULD fill in the remaining boxes this way...

In this case, F = 400 and J = 116, which means F IS greater than J

However, we COULD also fill in the remaining boxes this way...

In this case, F = 400 and J = 1016, which means F is NOT greater than J

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

Statement 2: 10 percent of the students at the school who study Japanese also study French.
J = the TOTAL number of students taking Japanese
So, 0.1J = number of students taking BOTH French and Japanese

Notice that we already determined that 0.04F = number of students taking BOTH French and Japanese
So, we now have two ways to represent the SAME value.


So, it MUST be the case that 0.1J = 0.04F
Let's see what this tells us.
First, to make things easier, let's multiply both sides by 100 to get: 10J = 4F
Divide both sides by 10 to get: J = 4F/10
Divide both sides by F to get: J/F = 4/10
From this, we can conclude that F IS greater than J
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B