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GMAT Diagnostic Test Question 22 Field: word problems (overlapping sets) Difficulty: 650

Rating:

60% of the San Diego Zoo visitors are single without children, and the rest are married with children. If 25% of the married visitors have multiple children, what percentage of the San Diego Zoo visitors have only one child?

There are \(100% - 60% = 40%\) married visitors in the zoo. If all married visitors have children, then we'll distinguish between two groups of married visitors, those with multiple children and those with only one child. Thus there are \(100% - 25% = 75%\) married visitors with only one child among all married visitors. We know that married visitors constitute 40% of all San Diego Zoo visitors and 75% of these married visitors have only one child. Consequently, \(40% * 75% = 30%\) of all San Diego Zoo visitors have only one child.
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To me this seems to be a 650 problem, and not 750.

i gotta agree, this seemed a little bit easier than a 750 might be. i'd think its a 650. MAYBE a 700. but then again, what would i know. i haven't taken the test yet and won't for about 3 more months.
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60% of the San Diego Zoo visitors are single and all of the San Diego Zoo family visitors have children. If 25% of families visiting the San Diego Zoo have multiple children, what percentage of the San Diego Zoo visitors have only one child?

A. 15 B. 20 C. 30 D. 50 E. 75

1) It assumes that single visitors do not have children. This is certainly not a reflection of real life, so how are we supposed to know this when we first read the question?

2) There's no such thing as a "family visitor" in the English language. If you're going to distinguish this from "single", then maybe use "married". Otherwise, it's impossible for the reader to know that to "single" and "family" are mutually disjoint sets.

Here's what I would write:

60% of the San Diego Zoo visitors are single without children, and the rest are married with children. If 25% of the married visitors have multiple children, what percentage of the San Diego Zoo visitors have only one child?

60% are single w/o children which equals 40% are married w/ children (1-.6) 25% of the 40% have multiple children. So 25% of 40% is 10% (.25*.4 = .1 or 10%)

So just subtract married w/ children(40%) from married visitors w/o multiple children (10%) and you get married with 1 child 40% - 10% (.4-.1) = 30%

I have to agree with AloneAndInsufficient, who mentioned the poor wording of the question. I got tripped up because apparently the question is including everybody in a family as one visitor.

"60% of the San Diego Zoo visitors are single and all of the San Diego Zoo family visitors have children. If 25% of families visiting the San Diego Zoo have multiple children, what percentage of the San Diego Zoo visitors have only one child?"

75 percent of families have one child. But the question, instead of counting two parents and a child as three people, it counts them as one. I was confused by that, because I thought 10 families with a child each would count as 30 people, rather than 10 visitors.

Maybe I'm the only one tripped up by that. But it's either something to correct in the diagnostic, or a good lesson to us newbies that the GMAT can sometimes use ambiguous wording and not to dig too deeply into the question.

Lets assume that 100 is our total number of visitors to the zoo. so, .6*100 will give us 60, so 100-60 will give us 40 married visitors with children. so, if we take .25 * 40 will give us 10; therefore, we can 40-10 will give us = 30. ___ Answer. C