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15 Jul 2019, 23:10
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E
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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
A. 1/14
B. 3/14
C. 7/14
D. 9/14
E. 11/14
firas92
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Concentration: General Management
Schools: Tepper '23 (M$) Foster '23 (D)
GMAT 1: 740 Q50 V40
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15 Jul 2019, 23:25
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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)
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)
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?
The fraction of the group which speak Spanish = 11x/14x = 11/14
IMO E
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
