4/5 of the women and 3/4 of the men speak Spanish. If there are 40% as

Question

\frac{4}{5}  of the women and  \frac{3}{4}  of the men in a group speak Spanish. If there are 40% as many men as women in the group, what fraction of the group speaks Spanish?

A. 1/14
B. 3/14
C. 7/14
D. 9/14
E. 11/14

firas92 · Answer

Let's call the number of women in the group  x

Then the number of men is  0.4x

Total population is  x+0.4x=1.4x

Let's say that the total population is 70

This means that the number of women  (x)  is  50  and the number of men is  20

So, the number of Spanish speaking women is  \frac{4}{5}*50 = 40 
the number of Spanish speaking men is  \frac{3}{4}*20 = 15

Total Spanish speaking population is  40+15=55

So, the fraction of the group that speaks Spanish = \frac{55}{70} = \frac{11}{14}

Answer is  (E)

Kinshook · Answer

Given:   \frac{4}{5}  of the women and  \frac{3}{4}  of the men in a group speak Spanish.
 Asked:   If there are 40% as many men as women in the group, what fraction of the group speaks Spanish?

Speaking Spanish  Not Speaking Spanish  Total  
  Men  3x  x  4x  
  Women  8x  2x  10x  
  Total  11x  3x  14x

The fraction of the group which speak Spanish = 11x/14x = 11/14

IMO E

thewarrior29 · Answer

Just take the number of women is 100. so the number of men will be 40.
So, there are 4/5*100=80 women and 3/4*40=30 men speak Spanish.
Fraction=(80+30)/(100+40)=110/140=11/14

Sarkar007 · Answer

There 40% as many men as women,
Men=40
Women=100
Total=140
Now,
4/5 of the women=4/5*100=80
3/4 of the men=3/4*40=30
Total=110

The group speaks Spanish=110/140=11/14

ScottTargetTestPrep · Answer

We can let the number of women = 60. Thus, the number of men is 0.4 x 60 = 24.

Since 4/5 of the women speak Spanish, 4/5 x 60 = 48 speak Spanish.

Since 3/4 of the men speak Spanish, 3/4 x 24 = 18 speak Spanish.

Thus, the fraction of the group that speaks Spanish is:

(48 + 18)/84 = 66/84 = 11/14

Answer: E

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4/5 of the women and 3/4 of the men speak Spanish. If there are 40% as

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	Speaking Spanish	Not Speaking Spanish	Total
Men	3x	x	4x
Women	8x	2x	10x
Total	11x	3x	14x

GMAT Problem Solving (PS) Questions

4/5 of the women and 3/4 of the men speak Spanish. If there are 40% as

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