It is currently 23 Oct 2017, 14:12

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Students in certain group know either English or French or both. If 30

Author Message
TAGS:

### Hide Tags

Intern
Joined: 05 Jan 2016
Posts: 7

Kudos [?]: 17 [0], given: 9

Students in certain group know either English or French or both. If 30 [#permalink]

### Show Tags

09 Jan 2016, 07:41
8
This post was
BOOKMARKED
00:00

Difficulty:

95% (hard)

Question Stats:

53% (02:32) correct 47% (02:50) wrong based on 90 sessions

### HideShow timer Statistics

Students in certain group know either English or French or both. If 30% of those who know English know French, and 60% of those who know French do not know English, which of the following could be the number of students in the group?

A) 12

B) 17

C) 23

D) 29

E) 31
[Reveal] Spoiler: OA

Kudos [?]: 17 [0], given: 9

Math Forum Moderator
Joined: 02 Aug 2009
Posts: 4994

Kudos [?]: 5534 [1], given: 112

Re: Students in certain group know either English or French or both. If 30 [#permalink]

### Show Tags

09 Jan 2016, 10:27
1
KUDOS
Expert's post
TeymurHajiyev wrote:
Students in certain group know either English or French or both. If 30% of those who know English know French, and 60% of those who know French do not know English, which of the following could be the number of students in the group?

A) 12

B) 17

C) 23

D) 29

E) 31

Hi,
venn diag would make it easy to comprehend..

let students who Know only english =E..
let students who Know only french =F..
let students who Know both english and french = B..

total =E+F+B..
1) If 30% of those who know English know French..
this means that 30% of students knowing english is B..
B=.3(E+B)...
7B=3E..
$$E=7B/3$$...(i)

2)60% of those who know French do not know English
or .6(F+B)= F..
6B=4F..
$$F=\frac{3B}{2}$$..(ii)

add values found in (i) and (ii) in total..
so $$Total=E+F+B=\frac{7B}{3}+ \frac{3B}{2} + B= \frac{29}{6} * B$$...

Total has to be an integer.. so
Total as $$\frac{29B}{6}$$... gives min value of B as 6 and Total as 29..
ans D
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 5534 [1], given: 112

Current Student
Joined: 20 Mar 2014
Posts: 2675

Kudos [?]: 1730 [1], given: 792

Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: Students in certain group know either English or French or both. If 30 [#permalink]

### Show Tags

09 Jan 2016, 10:29
1
KUDOS
TeymurHajiyev wrote:
Students in certain group know either English or French or both. If 30% of those who know English know French, and 60% of those who know French do not know English, which of the following could be the number of students in the group?

A) 12

B) 17

C) 23

D) 29

E) 31

Attachment:

2016-01-09_12-24-54.jpg [ 25.29 KiB | Viewed 1321 times ]

Refer to the above screenshot for description of the variables. Text in black is given information while the text in red denotes values calculated.

From the picture, NF = 0.7E ....(1)

and from the fact that 60% of french learners do learn english as well ---> 0.3E=0.4F --> 3E=4F ...(2)

Finally, T=F+NF = F+0.7E ...(3)

Substituting the value of E from (2), you get T = 29F/15. Now as Total number of students MUST BE INTEGERS, one way to ensure that is to assume F = multiple of 15 = 15 (as example), giving you T = 29 as 1 possible value.

Thus, D is the correct answer.

Hope this helps.
_________________

Thursday with Ron updated list as of July 1st, 2015: http://gmatclub.com/forum/consolidated-thursday-with-ron-list-for-all-the-sections-201006.html#p1544515
Inequalities tips: http://gmatclub.com/forum/inequalities-tips-and-hints-175001.html
Debrief, 650 to 750: http://gmatclub.com/forum/650-to-750-a-10-month-journey-to-the-score-203190.html

Kudos [?]: 1730 [1], given: 792

Intern
Joined: 05 Jan 2016
Posts: 7

Kudos [?]: 17 [0], given: 9

Re: Students in certain group know either English or French or both. If 30 [#permalink]

### Show Tags

10 Jan 2016, 05:09
Thank you, guys! You've done an awesome job!

Kudos [?]: 17 [0], given: 9

Director
Joined: 12 Dec 2016
Posts: 897

Kudos [?]: 11 [0], given: 865

Location: United States
GMAT 1: 700 Q49 V33
GPA: 3.64
Re: Students in certain group know either English or French or both. If 30 [#permalink]

### Show Tags

17 Apr 2017, 15:37
TeymurHajiyev wrote:
Thank you, guys! You've done an awesome job!

hi, do you have more similar questions like this? I really like the such kind of question.

Kudos [?]: 11 [0], given: 865

Math Expert
Joined: 02 Sep 2009
Posts: 41913

Kudos [?]: 129505 [0], given: 12201

Re: Students in certain group know either English or French or both. If 30 [#permalink]

### Show Tags

17 Apr 2017, 21:26
Expert's post
1
This post was
BOOKMARKED
chesstitans wrote:
TeymurHajiyev wrote:
Thank you, guys! You've done an awesome job!

hi, do you have more similar questions like this? I really like the such kind of question.

Hope it helps.
_________________

Kudos [?]: 129505 [0], given: 12201

Director
Joined: 13 Mar 2017
Posts: 534

Kudos [?]: 123 [1], given: 62

Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: Students in certain group know either English or French or both. If 30 [#permalink]

### Show Tags

02 Aug 2017, 02:56
1
KUDOS
TeymurHajiyev wrote:
Students in certain group know either English or French or both. If 30% of those who know English know French, and 60% of those who know French do not know English, which of the following could be the number of students in the group?

A) 12

B) 17

C) 23

D) 29

E) 31

Students know either English or French or both

30% of those who know English know French
60% of those who know French do not know English -> 40% of those who know French know English.

Let the no. of people who know English be x. So the people who knows both = 0.3x
and the number of people who know french be y. So the people who knows both = 0.4y

0.3x = 0.4y
x = 4y/3

Total number of people = x + y - 0.4y = 4y/3 + y -4/10 y = 7y/3 - 2/5y = 29y/15.

So total number of people must be a multiple of 29

_________________

MBA Social Network : WebMaggu

Appreciate by Clicking +1 Kudos ( Lets be more generous friends.)

Kudos [?]: 123 [1], given: 62

Re: Students in certain group know either English or French or both. If 30   [#permalink] 02 Aug 2017, 02:56
Display posts from previous: Sort by