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French and Japanese (GMAT PREP 1)

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French and Japanese (GMAT PREP 1)

by alex.gellatly » Fri Aug 03, 2012 10:56 pm
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.

Thanks!
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Source: — Data Sufficiency |

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by Anurag@Gurome » Sat Aug 04, 2012 3:32 am
alex.gellatly wrote: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.

Thanks!
Say, number of students studying Japanese = J and number of students studying French = F. Now, J ≥ 100 and 4% of F study both Japanese and French.

Statement 1: 16 students at the school study both French and Japanese.
Therefore, 4% of F = 16
=> F = (16/0.04) = 400
As we don't have any concrete idea about the value of J, we cannot say whether F is greater than J or not.

Not sufficient

Statement 2: 10 percent of the students at the school who study Japanese also study French.
Therefore, 4% of F = 10% of J
=> F = J*(0.10)/(0.04) = (2.5)*J
=> F > J

Sufficient

The correct answer is B.
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by niketdoshi123 » Sat Aug 04, 2012 3:33 am
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by GmatMathPro » Sat Aug 04, 2012 6:10 am
alex.gellatly wrote: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.

Thanks!
Also, note that "students who study French that also study Japanese" (as paraphrased from the question) and "students who study Japanese that also study French" (as paraphrased from statement 2) both refer to the same quantity: the number of students who study both subjects. You can also think of them as both referring to the overlapping portion of the Venn diagram. Statement 2 tells us that this quantity is a BIGGER portion of the students that study Japanese (10%) than it is of the students who study French(4%). Thus, more students must study French.
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