In a group of 100 people, 40 study English and 30 study French. The nu

Question

Tough and Tricky questions: Overlapping Sets.

In a group of 100 people, 40 study English and 30 study French. The number of people in the group who study neither language is twice the number of people who study both. How many people in the group study both languages?

A. 10
B. 20
C. 26
D. 30
E. 34

Kudos for a correct  solution .

littlewarthog · Answer

The equation for this question is:

English + French - both + neither = 100 
The rationale behind this equation is that by simply adding the students that study English and the students that study French, we double-count the students that study both, as they are part of both groups. We therefore have to subtract them again.

From that follows: 
- both + neither = 30
- both + 2*both = 30
This is the information given in the question.

Then we get: both = 30

Answer D.

g106 · Answer

Number of people in the group = 100
Number of people study both = x
Number of people who study neither = 2x

total number of people = 100 = (40-x) + (30-x) +2x+x
 => 100 = 70+x
 x = 30

Ans D

PareshGmat · Answer

Answer = D. 30 Refer diagram below: fre.png 40 + x + 30-x + 2x = 100 x = 30

Bunuel · Answer

OFFICIAL SOLUTION:

(D) Here we will use the formula for Set Overlap.

The general formula when there are two groups is:

Total Number of Different People =
(# in Group 1) + (# in Group 2) + (# in Neither Group)– (# in Both Groups).

The reason we subtract out the number of people in both groups is that they have been counted twice unless we subtract them out.

Let’s define some variables here:
T = Total number of people.
E = Number of people who study English. 
F = Number of people who study French. 
N = Number of people who study neither language. 
B = Number of people who study both languages.

Using these variables we can now write the equation:
T = E + F + N – B.

We are given numbers for T, E, and F, and we are told that N = 2B.

Let’s substitute these into our equation and solve:
T = E + F + N – B
100 = 40 + 30 + 2B – B
B = 30.

The correct answer is choice (D).

sjavvadi · Answer

Untitled.png Attached pic shows the solution

LeoN88 · Answer

let x study both the languages and 2x don't study either,

Now: 40 + (30-x) + 2x = 100

X = 30

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In a group of 100 people, 40 study English and 30 study French. The nu

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