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# A class consists of boys and girls only. On a final exam in History, t

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A class consists of boys and girls only. On a final exam in History, t  [#permalink]

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26 Sep 2019, 02:55
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75% (hard)

Question Stats:

22% (01:00) correct 78% (01:49) wrong based on 27 sessions

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A class consists of boys and girls only. On a final exam in History, the average score of the girls is 72 and the average score of the boys is 70. Is the average score of the class 71?

(1) Smith is one of the classmates and Smith has the same number of boy classmates as girl classmates.

(2) The number of students in the class is 101.

Source: Nova GMAT

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Re: A class consists of boys and girls only. On a final exam in History, t  [#permalink]

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26 Sep 2019, 02:57
A class consists of boys and girls only. On a final exam in History, the average score of the girls is 72 and the average score of the boys is 70. Is the average score of the class 71?

(1) Smith is one of the classmates and Smith has the same number of boy classmates as girl classmates.

(2) The number of students in the class is 101.

Source: Nova GMAT

Basically the same question but with different numbers: https://gmatclub.com/forum/a-class-cons ... fl=similar
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Re: A class consists of boys and girls only. On a final exam in History, t  [#permalink]

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18 Oct 2019, 17:41
Please can someone explain how the 2nd statement is suff?
Senior RC Moderator
Joined: 02 Nov 2016
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Re: A class consists of boys and girls only. On a final exam in History, t  [#permalink]

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19 Oct 2019, 08:14
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harshi17 wrote:
Please can someone explain how the 2nd statement is suff?

Official Explanation

The average score of the class will be exactly in the middle between 70 and 72 (at 71) only if the weight of the number of boys equals the weight of the number of girls. The weight of the boys equals the weight of the girls only if the number of boys equals the number of girls.

So, the question can be transformed to “In the class, is the number of girls equal to the number of boys?”

Statement (1): Smith is one of the classmates and Smith has the same number of boy classmates as girl classmates.

Statement (1) says Smith has as many boy classmates as girl classmates. If Smith is a girl, the class will have one girl more; and if Smith is a boy, the class will have one boy more. So, whether Smith is a girl or a boy is irrelevant. The average is not in the middle. The statement answers the question as “No.”

Statement (2):Suppose we have an equal number of boys and girls, and suppose the number is n. Then the class size is $$n + n = 2n$$, which must be even. But we are given that the class size is 101, which is odd. Hence, our assumption that we have an equal number of boys and girls is false. Hence, there is an unequal weight of boys and girls, and the average is not in the middle. The statement is sufficient to answer the question as “No.” The number of students in the class is 101.

The answer is (D).

Hope it helps
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Re: A class consists of boys and girls only. On a final exam in History, t   [#permalink] 19 Oct 2019, 08:14
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