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DS- French/Japanese

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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by vishal_2804 » Fri Apr 19, 2013 7:19 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
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by Anju@Gurome » Fri Apr 19, 2013 7:21 am
vishal_2804 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
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.
So, 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.
So, 4% of F = 10% of J
--> F must be greater than J as a smaller percentage of F is equal to larger percentage of J.

Sufficient

The correct answer is B.

Another problem on the same concept >> https://www.beatthegmat.com/ds-overlappi ... tml#618171
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by hutch27 » Sat Apr 20, 2013 6:57 am
Looks like you could use the double matrix method for this problem. That's what I used and it helped me see things a little easier. The problems tricky though, where's it from?
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by Brent@GMATPrepNow » Sat Apr 20, 2013 7:16 am
hutch27 wrote:Looks like you could use the double matrix method for this problem. That's what I used and it helped me see things a little easier. The problems tricky though, where's it from?
Yes, this is a great candidate for the Double Matrix method. This technique can be used for most questions featuring a population in which each member has two criteria associated with it.
Here, the criteria are:
- taking or not taking French
- taking or not taking Japanese

For more information about this technique (and some additional practice questions), check out these 3 BTG articles:

- https://www.beatthegmat.com/mba/2011/05/ ... question-1
- https://www.beatthegmat.com/mba/2011/05/ ... question-2
- https://www.beatthegmat.com/mba/2011/05/ ... question-3

Cheers,
Brent
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by gmattesttaker2 » Wed Oct 16, 2013 8:44 pm
Brent@GMATPrepNow wrote:
hutch27 wrote:Looks like you could use the double matrix method for this problem. That's what I used and it helped me see things a little easier. The problems tricky though, where's it from?
Yes, this is a great candidate for the Double Matrix method. This technique can be used for most questions featuring a population in which each member has two criteria associated with it.
Here, the criteria are:
- taking or not taking French
- taking or not taking Japanese

For more information about this technique (and some additional practice questions), check out these 3 BTG articles:

- https://www.beatthegmat.com/mba/2011/05/ ... question-1
- https://www.beatthegmat.com/mba/2011/05/ ... question-2
- https://www.beatthegmat.com/mba/2011/05/ ... question-3

Cheers,
Brent

Hello Brent,

I was trying to solve Statement 2 as follows:

Let x = total students in the school
and j = number of students who studay Japanese

So from Statement 2,
10/100 ( j ) = 4/100 (x)
=> 10/100 ( greater than or equal to 100 ) = 4/100 (x)
=> greater than or equal to 10 = 4/100 (x)
=> greater than or equal to 10 = 1/25 (x)
=> x = greater than or equal to 250

I was not sure though how we can prove f > j. I was just wondering if you can please assist. Thanks a lot for your valuable time and help.

Best Regards,
Sri
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by Brent@GMATPrepNow » Thu Oct 17, 2013 7:06 am
gmattesttaker2 wrote: Hello Brent,

I was trying to solve Statement 2 as follows:

Let x = total students in the school
and j = number of students who studay Japanese

So from Statement 2,
10/100 ( j ) = 4/100 (x)
=> 10/100 ( greater than or equal to 100 ) = 4/100 (x)
=> greater than or equal to 10 = 4/100 (x)
=> greater than or equal to 10 = 1/25 (x)
=> x = greater than or equal to 250

I was not sure though how we can prove f > j. I was just wondering if you can please assist. Thanks a lot for your valuable time and help.

Best Regards,
Sri
Hey Sri,

There's a problem with your entry of (4/100)x in the top-left box.
This suggests that 4% of ALL students study Japanese and French. However, the question doesn't say this, It says 4 percent of the students who study french also study Japanese
In other words, 4% of the French students also study Japanese.
So, you can let F = the # of French students, which means the top-left box will be (4/100)F
See what happens when you go from there.

Cheers,
Brent
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by gmattesttaker2 » Fri Oct 18, 2013 9:10 pm
Brent@GMATPrepNow wrote:
gmattesttaker2 wrote: Hello Brent,

I was trying to solve Statement 2 as follows:

Let x = total students in the school
and j = number of students who studay Japanese

So from Statement 2,
10/100 ( j ) = 4/100 (x)
=> 10/100 ( greater than or equal to 100 ) = 4/100 (x)
=> greater than or equal to 10 = 4/100 (x)
=> greater than or equal to 10 = 1/25 (x)
=> x = greater than or equal to 250

I was not sure though how we can prove f > j. I was just wondering if you can please assist. Thanks a lot for your valuable time and help.

Best Regards,
Sri
Hey Sri,

There's a problem with your entry of (4/100)x in the top-left box.
This suggests that 4% of ALL students study Japanese and French. However, the question doesn't say this, It says 4 percent of the students who study french also study Japanese
In other words, 4% of the French students also study Japanese.
So, you can let F = the # of French students, which means the top-left box will be (4/100)F
See what happens when you go from there.

Cheers,
Brent
Hi Brent,

Thanks for your explanation. It is clear now where I was going wrong. Thanks a lot for your help.

Best Regards,
Sri
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by teebabie » Sat Sep 17, 2016 1:10 am
vishal_2804 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

Please...How can I solve this question using the double matrix method. I sincerely need help..Thanks
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by Brent@GMATPrepNow » Sat Sep 17, 2016 3:56 am
teebabie wrote:
vishal_2804 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

Please...How can I solve this question using the double matrix method. I sincerely need help..Thanks
Someone uses the Double Matrix Method here: https://www.beatthegmat.com/at-least-100 ... 74669.html
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by Matt@VeritasPrep » Thu May 11, 2017 8:17 pm
We could also skip the matrix and just do a little algebra.

Say we have
f = only French
j = only Japanese
b = both
n = neither

We know that 4% of French = Both, so .04*(f + b) = b, or .04f = .96b. From there:

S1:

b = 16

So b = 16, f = 384. Doesn't give us j, so NOT SUFFICIENT.

S2:

.10*(j + b) = b, or .10j = .9b. Now let's think about what we've got. Since .96b is only .04f, but .90b is .10j, f must be bigger than j: a bigger portion of b (.96) gives us a smaller portion of f (.04)!
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