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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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Math Expert
Joined: 02 Sep 2009
Posts: 58332
4/5 of the women and 3/4 of the men speak Spanish. If there are 40% as  [#permalink]

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15 Jul 2019, 23:10
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Difficulty:

35% (medium)

Question Stats:

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

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$$\frac{4}{5}$$ 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

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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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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$$= \frac{55}{70} = \frac{11}{14}$$

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Joined: 03 Jun 2019
Posts: 1684
Location: India
Re: 4/5 of the women and 3/4 of the men speak Spanish. If there are 40% as  [#permalink]

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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
Attachments

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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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