In Country X, 1/2 of the population can speak English, 1/3 can speak

Question

In Country X, 1/2 of the population can speak English, 1/3 can speak French, and 1/5 can speak both English and French. What fraction of the population of Country X can speak neither English nor French?

A. 2/15

B. 1/6

C. 3/10

D. 11/30

E. 13/30

A. 2/15

B. 1/6

C. 3/10

D. 11/30

E. 13/30

PS20358

BrentGMATPrepNow · Accepted Answer

One approach is to use the Double Matrix Method . This technique can be used for questions featuring a population in which each member has two characteristics associated with it (aka overlapping sets questions). Here, we have a population of citizens, and the two characteristics are: - speaks English or doesn't speak English - speaks French or doesn't speak French Aside: We can also use Venn diagrams and formulae to solve overlapping sets questions. However, as difficulty levels increase, it becomes harder to apply those other approaches, whereas the Double Matrix Method works every time. Since the question asks us to find the value of a FRACTION, that's assign a "nice" value to the population of Country X. When I scan the other choices, I see that all of the denominators are factors of 30. So let's let 30 equal the population of Country X. Our initial diagram looks something like this: https://i.imgur.com/lu39Kpl.png I placed a star in the box representing citizens who speak neither English nor French, since this is the value we want to determine. 1/2 of the population can speak English, 1/3 can speak French, and 1/5 can speak both English and French 1/2 of 30 = 15, which means 15 people speak English, which also means the remaining 15 people do not speak English. 1/3 of 30 = 10, which means 10 people speak French, which also means the remaining 20 people do not speak French. 1/5 of 30 = 6, which means 6 people speak both English and French When we add all of this to our diagram we get: https://i.imgur.com/Aui32kG.png From here, we can fill in the remaining information to get: https://i.imgur.com/Xg2lPwE.png What fraction of the population of Country X can speak neither English nor French? Out of the population of 30 people, 11 speak neither English nor French Fraction = 11 / 30 Answer: D This question type is VERY COMMON on the GMAT, so be sure to master the technique. To learn more about the Double Matrix Method, watch this video: https://www.youtube.com/watch?v=jK-tiBrrf04 EXTRA PRACTICE QUESTION https://www.youtube.com/watch?v=DsbPUSH_Wu4 More questions to practice with: EASY: https://gmatclub.com/forum/of-the-120-p ... 15386.html MEDIUM: https://gmatclub.com/forum/in-a-certain ... 21716.html HARD: https://gmatclub.com/forum/a-group-of-2 ... 24888.html KILLER: https://gmatclub.com/forum/a-certain-hi ... 32899.html

Archit3110 · Answer

2x2 matrix
---french---n f----total
Eng--6-----9-----15
NE --4------11---15
total--10----20---30
11/30
OPTION D

yashikaaggarwal · Answer

Let the population of country X be 30

Those who can speak only English will be A
Those who can speak only French be C
Those who can speak both be B

Now,
1/2 of total can speak English.
That will be A+B = 30*1/2=15
(Since only English is not stated. So both and only English will be included)

1/3 of total can speak French.
That will be C+B = 30*1/3=10
(Since only French is not stated. So both and only French will be included)

1/5 of total can speak both:
B = 1/5*30 = 6

Therefore A will be 15-6=9
And C will be 10-6=4

Those who can't speak English or French will be 30-9+4+6 = 11
The fraction who can't speak either of the language will be 11/30

Therefore D is the answer

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Kinshook · Answer

In Country X, 1/2 of the population can speak English, 1/3 can speak French, and 1/5 can speak both English and French. What fraction of the population of Country X can speak neither English nor French?

A. 2/15

B. 1/6

C. 3/10

D. 11/30

E. 13/30

Neither = Total - (English+ French - Both) = 1 - (1/2 + 1/3 - 1/5) = 1 - (15 + 10 - 6)/30 = 1 - 19/30 = 11/30

IMO D

ScottTargetTestPrep · Answer

We can let the total number of people = 60 and create the equation:

60 = 30 + 20 - 12 + N

22 = N

Thus, 22/60 = 11/30 of the people speak neither language.

Answer: D

DanTheGMATMan · Answer

Classic overlapping sets we know and love:

https://www.youtube.com/watch?v=MyTz1tHcDmw

elinelsa · Answer

How do we know that the 1/2 of the population that speaks English  only  speaks English. Imo that wasn't clear in the question and I assumed that the 1/5 was a part of those 1/2 and 1/3, thus giving the answer 1/6

DanTheGMATMan · Answer

They don't  only  speak English. That 1/2 is just the total that speak English, whether they also speak French or not. The 1.5 is part of that 1/2 that speak English

In Country X, 1/2 of the population can speak English, 1/3 can speak

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GMAT Problem Solving (PS) Questions

In Country X, 1/2 of the population can speak English, 1/3 can speak

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

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