Japanese and French

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netigen: Legendary Member; Posts: 631; Joined: Mon Feb 18, 2008 11:57 pmFollowed by: 3 members; Thanked: 29 times

by netigen » Sat May 24, 2008 3:51 pm

At least 100 students at a certain high school study Japanese. If 4 percent of the students 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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Source: Beat The GMAT — Data Sufficiency | Sat May 24, 2008 3:51 pm

aatech: Master | Next Rank: 500 Posts; Posts: 192; Joined: Tue Apr 29, 2008 7:41 am; Thanked: 14 times

by aatech » Sat May 24, 2008 5:57 pm

IMO C

Suppose F students study French.. and J students study Japanese

Then, 4F/100 study both, Japanese and French

Stmt 1 - 16 students study French and Japanese

So, 4F/100 = 16 => F = 400 students study French. However, Q does not say anything else so NOT SUFF

Stmt 2 - 10J/100 study both French and Japanese... We cannot determine anything about French Students so NOT SUFF

Together, 10J/100 = 4F/100 = 16

Solve to get J = 160 which is less than 400 SUFF

OA??

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netigen: Legendary Member; Posts: 631; Joined: Mon Feb 18, 2008 11:57 pmFollowed by: 3 members; Thanked: 29 times

by netigen » Sat May 24, 2008 11:38 pm

OA is B

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luvaduva: Senior | Next Rank: 100 Posts; Posts: 84; Joined: Tue Feb 05, 2008 8:52 pm; Thanked: 8 times

by luvaduva » Sun May 25, 2008 12:01 am

For (2):

If # Students taking Japanese = 100 then the number of students taking Japanese and French = 10. # Students taking French = 4/100x = 10 = 250

250 > 100

If # Students taking Japanese = 200 then the number of students taking Japanese and French = 20. # Students taking French = 4/100x = 20 = 500

500 > 200

Answer is B.

***Alternatively***

(10/100)*J = (4/100)*F
10J = 4F
J/F = 2/5

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vittalgmat: Legendary Member; Posts: 621; Joined: Wed Apr 09, 2008 7:13 pmFollowed by: 4 members; Thanked: 33 times

by vittalgmat » Mon May 26, 2008 9:31 pm

luvaduva wrote:For (2):

If # Students taking Japanese = 100 then the number of students taking Japanese and French = 10. # Students taking French = 4/100x = 10 = 250

250 > 100

If # Students taking Japanese = 200 then the number of students taking Japanese and French = 20. # Students taking French = 4/100x = 20 = 500

500 > 200

Answer is B.

***Alternatively***

(10/100)*J = (4/100)*F
10J = 4F
J/F = 2/5

Small corrections to the above: 4/100x should be read as (4/100) *x
or 4x/100

rgds
-Vittal

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