BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Target Test Prep · GMAT

Choose how you want to prepare

Learn live with an expert or move at your own pace. Every option includes the complete TTP study system.

★★★★★5.0559 reviews
Vote for Target Test Prep, Newsweek Readers’ Choice Awards 2026
NEWSWEEK READERS’ CHOICE 2026

BIG NEWS! Target Test Prep has been nominated, and they’d love your vote!

TTP has worked incredibly hard to build the best test prep experience possible, and winning Newsweek’s 2026 Readers’ Choice Award for Best Test Prep would mean a lot to them. If TTP has helped you, they’d be incredibly grateful for your vote. You can vote once each day through September 9.

Vote for TTP
GMATLiveTeach 7 seats left
Chris Peckover
NEXT LIVE COHORT

Oct 13 to Jan 7, 2027

with Chris Peckover

Schedule
Tue, Thu · 8:00 to 10:00 PM ET
Included
40 live hours + 6 months of GMAT OnDemand
  • Live instruction and real-time questions
  • Class recordings and assigned practice
View class & enroll
Limited cohort · enrollment openTarget Test Prep
EALiveTeach 5 seats left
Logan Thompson
EXECUTIVE ASSESSMENT

Sep 6 to Dec 6, 2026

with Logan Thompson

Schedule
Sun · 9:30 AM to 12:30 PM ET
Included
40 hours of live online classes plus six months of access to the complete TTP EA OnDemand course.
  • 165+ EA Score Guarantee
  • 4,100+ Quant, Verbal, and Integrated Reasoning practice questions
  • 400+ hours of in-depth video lessons
  • 3,000+ step-by-step video solutions
View EA class & enroll
Limited cohort · enrollment openTarget Test Prep
GMATOnDemand Start anytime
SELF-PACED MASTERCLASS

Target Test Prep GMAT OnDemand

Complete access from day one. Study on your schedule.

715+ score guarantee
$0to start then $127/mo
  • Personalized study plan and analytics
  • Thousands of lessons and practice questions
Start free 5-day trial
Read 559 reviewsTarget Test Prep

Compare the format, schedule, and included access before enrolling. Prices and seat counts shown reflect the supplied offer details.

DS- French/Japanese

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Junior | Next Rank: 30 Posts
Posts: 25
Joined: Wed Nov 17, 2010 7:54 am
Thanked: 1 times
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
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Quantitative Reasoning |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 511
Joined: Wed Aug 11, 2010 9:47 amFollowed by: 86 members
Location: Delhi, India
Thanked: 344 times

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
Anju Agarwal
Quant Expert, Gurome

Backup Methods : General guide on plugging, estimation etc.
Wavy Curve Method : Solving complex inequalities in a matter of seconds.

§ GMAT with Gurome § Admissions with Gurome § Career Advising with Gurome §
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Master | Next Rank: 500 Posts
Posts: 141
Joined: Fri Sep 07, 2012 10:25 pmFollowed by: 1 member
Location: NY
Thanked: 5 times

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?
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members
Location: Vancouver, BC
Thanked: 5254 times
GMAT Score:770

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
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Legendary Member
Posts: 641
Joined: Tue Feb 14, 2012 3:52 pmFollowed by: 8 members
Thanked: 11 times

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
Attachments
Matrix.png
Double Matrix
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members
Location: Vancouver, BC
Thanked: 5254 times
GMAT Score:770

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
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Legendary Member
Posts: 641
Joined: Tue Feb 14, 2012 3:52 pmFollowed by: 8 members
Thanked: 11 times

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
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Newbie | Next Rank: 10 Posts
Posts: 1
Joined: Sat Sep 17, 2016 12:23 am
GMAT Score:560

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
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members
Location: Vancouver, BC
Thanked: 5254 times
GMAT Score:770

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
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
GMAT Instructor
Posts: 2630
Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members
Location: East Bay all the way
Thanked: 625 times
GMAT Score:780

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)!
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1