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# In a certain class, 1/5 of the boys are shorter than

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Founder
Joined: 18 Apr 2015
Posts: 6185
Followers: 99

Kudos [?]: 1199 [1] , given: 5699

In a certain class, 1/5 of the boys are shorter than [#permalink]  21 Aug 2017, 12:09
1
KUDOS
Expert's post
00:00

Question Stats:

54% (03:43) correct 45% (03:31) wrong based on 11 sessions

In a certain class, $$\frac{1}{5}$$ of the boys are shorter than the shortest girl in the class, and $$\frac{1}{3}$$ of the girls are taller than the tallest boy in the class. If there are 16 stu­dents in the class and no two people have the same height, what percent of the students are taller than the shortest girl and shorter than the tallest boy?

A. 25%

B. 50%

C. 62.5%

D. 66.7%

E. 75%
[Reveal] Spoiler: OA

_________________
Director
Joined: 03 Sep 2017
Posts: 521
Followers: 1

Kudos [?]: 355 [1] , given: 66

Re: In a certain class, 1/5 of the boys are shorter than [#permalink]  19 Sep 2017, 08:18
1
KUDOS
I've done it in many ways but I am continuing to get choice E. How is it possible?
Founder
Joined: 18 Apr 2015
Posts: 6185
Followers: 99

Kudos [?]: 1199 [2] , given: 5699

Re: In a certain class, 1/5 of the boys are shorter than [#permalink]  19 Sep 2017, 09:44
2
KUDOS
Expert's post
OE

Quote:
Given the information about the fraction of boys who are shorter than the shortest girl and the fraction of girls who are taller than the tallest boy, the number of boys in the class must be a multiple of 5 while the number of girls must be a multiple of 3 (since the number of boys and girls must take on integer values). The only combination of a multiple of 5 and multiple of 3 that sum to 16 is 2 x 5 = 10 boys and 2 x 3 = 6 girls. Of the 10 boys, 2 are shorter than the shortest girl. Of the 6 girls, 2 are taller than the tallest boy. Therefore, the order of heights must be as follows:

B,B,G _,_,_,_,_,_, B,G,G

This implies that there must be exactly 10 students that are taller than the shortest girl and shorter than the tallest boy. This equals $$\frac{10}{16} = \frac{5}{8} = 62.5 %$$

Ask if something is still unclear.

regards
_________________
Re: In a certain class, 1/5 of the boys are shorter than   [#permalink] 19 Sep 2017, 09:44
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