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

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New post 15 Jul 2019, 23:10
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

72% (01:34) correct 28% (02:41) wrong based on 36 sessions

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Concentration: General Management
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Re: 4/5 of the women and 3/4 of the men speak Spanish. If there are 40% as  [#permalink]

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New post 15 Jul 2019, 23:25
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)
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Re: 4/5 of the women and 3/4 of the men speak Spanish. If there are 40% as  [#permalink]

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New post 16 Jul 2019, 01:04
Bunuel wrote:
\(\frac{4}{5}\) 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


Please see attached file for solution

IMO E
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Re: 4/5 of the women and 3/4 of the men speak Spanish. If there are 40% as   [#permalink] 16 Jul 2019, 01:04
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