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In a group of 250 adults, is the number

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Source: — Data Sufficiency |
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by mbawisdom » Mon Mar 05, 2018 4:49 pm
lheiannie07 wrote:In a group of 250 adults, is the number of married (not necessarily to other group members) people at least 75?

(1) At least 65 percent of the men in the group are married.
(2) At least 30 percent of the women in the group are married.

Is there a sufficient statement in this problem?

OA C
(1) is not sufficient as we do not know the number of men in the group: if there were 20 men there would be 13-20 married men, but if there was 200 men there would be 130-200 married men.

(2) use the same logic as above the statement is not sufficient

(1) and (2) together:
M + W = 250
0.65M + 0.30W = lowest number of married people
0.35M + 0.30M +0.30W = lowest number of married people
0.35M + 0.30(M+W) = lowest number of married people
0.35M + 0.30(250) = lowest number of married people
0.35M + 75 = lowest number of married people

Thus, together, we know that there must be at least 75 married people in the group.

Answer is C.
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by Jay@ManhattanReview » Wed Mar 14, 2018 5:25 am
lheiannie07 wrote:In a group of 250 adults, is the number of married (not necessarily to other group members) people at least 75?

(1) At least 65 percent of the men in the group are married.
(2) At least 30 percent of the women in the group are married.

Is there a sufficient statement in this problem?

OA C
(1) At least 65 percent of the men in the group are married.

Insufficient as we do not know the number of men and how many married women are there in the group. If the count of men is high, say 200, then the answer is Yes; however if the count of men is low, say 50, then the answer is No.

(2) At least 30 percent of the women in the group are married.

Insufficient as we do not know the number of women and how many married men are there in the group.

(1) and (2) together

Say there are x men, thus there are (250 - x) women

Number of married adults ≥ 65% of x + 30% of (250 - x)

Number of married adults ≥ 65% of x + 30% of 250 - 30% of x

≥ 35% of x + 75

=> Number of married adults are at least 75. Sufficient.

The correct answer: C

Hope this helps!

-Jay
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