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At least 100 students at a certain high school study japanes

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At least 100 students at a certain high school study japanes  [#permalink]

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New post Updated on: 16 Apr 2018, 12:26
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amitgovin wrote:
At least 100 students at a certain high school study Japanese. If 4 percent of the studetns 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.


A student asked me to provide a step-by-step solution using the Double Matrix method, so here goes....
This technique can be used for most questions featuring a population in which each member has two characteristics associated with it (aka overlapping sets questions).
Here, we have a population of students, and the two characteristics are:
- studies Japanese or does NOT study Japanese
- studies French or does NOT study French

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:
Image

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:
Image

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:
Image

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...
Image
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...
Image
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.
Image

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:

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Originally posted by GMATPrepNow on 14 Oct 2017, 09:15.
Last edited by GMATPrepNow on 16 Apr 2018, 12:26, edited 2 times in total.
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New post 14 Oct 2017, 18:38
amitgovin wrote:
At least 100 students at a certain high school study Japanese. If 4 percent of the studetns 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.


We are asked whether we can find if more students study French than Japanese.
The concept used here is , we can compare similar expressions of measuring in finding out which one of the measured is greater, say we can compare percentages or compare absolute numbers .

In statement 1 absolute number is given, and in the stem percentage is given. Also the first is about percentage of French studying Japanese and the second is the number who study both. We can intuitively understand there is insufficient information in this.

In statement 2 , percentage is given and we can now compare the percentage who study French and the percentage who study Japanese in the school. So sufficient.

Hence B.
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At least 100 students at a certain high school study japanes  [#permalink]

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New post 24 Nov 2018, 16:21
A more thorough video explanation can be found here:
https://www.youtube.com/watch?v=fmam6p_Ello&t=2s

We need a mathematical relationship between F and J. Statement (1) doesn not provide one, but (2) does:

.10(J) = .04(F)

proportion F/J = 4/10

For every 4 students taking Japanese, 10 take French. Sufficient information to answer the question. Answer B.

Note: Instead of writing a Venn diagram, its often easier to visualize things by writing a matrix with two columns and two rows

Columns: study Japanese (J), don't study J
Rows: study French (F), don't study F
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Re: At least 100 students at a certain high school study japanes  [#permalink]

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New post 01 May 2019, 17:13
amitgovin wrote:
At least 100 students at a certain high school study Japanese. If 4 percent of the studetns 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.


We can let f = the number of students who study French and j = number of who study Japanese, and we need to determine whether f is greater than j. Furthermore, we are given that j ≥ 100 and 4 percent of the students at the school who study French also study Japanese; in other words, 4 percent of the students at the school who study French study both languages.

Statement One Alone:

16 students at the school study both French and Japanese.

We can create the equation:

0.04f = 16

4f = 1600

f = 400

However, since we don’t know the value of j (except that it’s at least 100), statement one alone is not sufficient.

Statement Two Alone:

10 percent of the students at the school who study Japanese also study French.

In other words, 10 percent of the students at the school who study Japanese study both languages. Even though we don’t know the exact number of students who study both languages, we know that it’s 0.04f. Therefore,

0.1j = 0.04f

10j = 4f

2.5j = f

We see that the number of students who study French is 2.5 times those who study Japanese. So f is indeed greater than j. Statement two alone is sufficient.

Answer: B
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Re: At least 100 students at a certain high school study japanes   [#permalink] 01 May 2019, 17:13

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