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
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
Live EA class + 6 months of EA OnDemand
  • Expert-led weekly online sessions
  • EA Masterclass access between classes
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.

130-point score guarantee
$0to start then $127/mo
  • Personalized study plan and analytics
  • Thousands of lessons and practice questions

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

Permutation and Combination using Sets

Expert replies
by s91arvindh » Sun May 04, 2014 7:41 pm
In a class of 25 students, every student takes either Spanish, Latin or French or two of the three but not all three. 9 take Spanish, 7 take Latin and 5 take exactly two languages.Number of students who take French ?

[spoiler]
Answer 14[/spoiler]

Note: The above question is from a handout which is intended for understanding the concepts
Last edited by s91arvindh on Sun May 04, 2014 8:00 pm, edited 1 time in total.
Join the discussion
Source: — Problem Solving |

by [email protected] » Sun May 04, 2014 7:53 pm
Hi s91arvindh,

This looks like the set-up to a question, but there doesn't appear to be an actual question attached.

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image
Join the discussion

by s91arvindh » Sun May 04, 2014 8:01 pm
Hi Rich,

Sorry Missed to attach the question and I have edited the question
Join the discussion

by Tushar14 » Sun May 04, 2014 8:27 pm
Simple way to solve,
Lets assume F number takes French, S takes Spanish = 9 and L takes Latin = 7.

Now, total number of students is 25.
So, F + S + L - 5(coz this number would be attached to any language group) = 25
or, F + 9 + 7 - 5 = 25
F = 25 - 16 + 5 = 14, is the number of students who take up French...

I am not sure if this is correct approach, but wanted to give a try and get feedback from experts.
Join the discussion

Re: Permutation and Combination using Sets

by Stuebs » Fri Jun 19, 2020 3:57 pm
I understand how the answer was found, but am confused why it has to be 14. Couldn’t the 5 students be taking Spanish and Latin, making it 9 who study French? Or couldn’t they be taking any combination of two out of the three languages, making those who study French anywhere between 9 and 14? I’m confused, please help! 😅
Join the discussion

s91arvindh wrote:
Sun May 04, 2014 7:41 pm
In a class of 25 students, every student takes either Spanish, Latin or French or two of the three but not all three. 9 take Spanish, 7 take Latin and 5 take exactly two languages.Number of students who take French ?

[spoiler]
Answer 14[/spoiler]

Note: The above question is from a handout which is intended for understanding the concepts
I'm not a big fan of memorizing formulas, so here's a way to solve the question using diagrams.
We're going to start from the center and work our way out.

Each student studies either Spanish, Latin, or French, or two of the three, but no students study all three languages.
First we can place 0 in the intersection of all three circles.
Image



5 study exactly two language
Since we aren't told that the distribution of those five students who study exactly two languages, we can distribute them anyway we want.
Here's one option:
Image



9 study Spanish, 7 study Latin
We'll add 5 and 4 in order to meet the conditions above
Image


There are 25 students in the class
So far, we've accounted for 14 of the 25 students.
So the remaining 11 students must study only French
Image

So the TOTAL number of students studying French = 2 + 0 + 1 + 11 = 14

Answer: C

Cheers,
Brent
Last edited by Brent@GMATPrepNow on Mon Aug 24, 2020 5:33 pm, edited 1 time in total.
Brent Hanneson - Creator of GMATPrepNow.com
Image
Join the discussion

Re: Permutation and Combination using Sets

by gentvenus » Thu Aug 20, 2020 12:39 pm
Quantity A: 14
Quantity B: 14

Answer: C
Join the discussion

s91arvindh wrote:
Sun May 04, 2014 7:41 pm
In a class of 25 students, every student takes either Spanish, Latin or French or two of the three but not all three. 9 take Spanish, 7 take Latin and 5 take exactly two languages.Number of students who take French ?

[spoiler]
Answer 14[/spoiler]

Note: The above question is from a handout which is intended for understanding the concepts
Solution:

We can use the formula:

Total = Spanish + Latin + French - Exactly Two Sets - 3 * All Three Sets + None

Since All Three Sets and None are both 0, we have:

25 = 9 + 7 + F - 5

25 = 11 + F

14 = F

Answer: 14

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage
Join the discussion

gentvenus wrote:
Thu Aug 20, 2020 12:39 pm
Quantity A: 14
Quantity B: 14

Answer: C
Ha!
ME: Why is that guy writing Quantity A? It's like he's confusing this with a GRE question.

Took me longer than I care to admit to figure out what you were doing :-)
This question is also on a GRE prep forum (https://greprepclub.com/forum/in-a-clas ... 10288.html) and after answering it there, I thought I'd paste it hear as well. Looks like I forgot to delete the GRE stuff :-)
Brent Hanneson - Creator of GMATPrepNow.com
Image
Join the discussion