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# Kumail, a noted sneaker enthusiast, has a collection consisting of

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Joined: 02 Sep 2009
Posts: 52390
Kumail, a noted sneaker enthusiast, has a collection consisting of  [#permalink]

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24 Apr 2017, 02:29
00:00

Difficulty:

65% (hard)

Question Stats:

59% (02:17) correct 41% (02:15) wrong based on 80 sessions

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Kumail, a noted sneaker enthusiast, has a collection consisting of sneakers made by Brand A and Brand B. 5/7 of the Brand A sneakers are low-tops, and 1/3 of the Brand A low-tops are running shoes. If Kumail owns 7 more pairs of Brand B sneakers than Brand A sneakers, what is the minimum possible number of pairs of sneakers in his collection?

A. 21
B. 28
C. 36
D. 40
E. 49

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Kumail, a noted sneaker enthusiast, has a collection consisting of  [#permalink]

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24 Apr 2017, 03:42
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Kumail, a noted sneaker enthusiast, has a collection consisting of sneakers made by Brand A and Brand B. 5/7 of the Brand A sneakers are low-tops, and 1/3 of the Brand A low-tops are running shoes. If Kumail owns 7 more pairs of Brand B sneakers than Brand A sneakers, what is the minimum possible number of pairs of sneakers in his collection?

No of Brand A sneaker should be divisible by 7 and 3 so that we can 5/7 of it as low-tops and 1/3 of low-top as running shows.

So min no of brand A would be 7x3 = 21 pairs.

no of brand B pairs is 7 more than brand A. So no of brand B sneakers = 28

21+28=49

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Re: Kumail, a noted sneaker enthusiast, has a collection consisting of  [#permalink]

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24 Apr 2017, 04:54
Brand A's running shoes = 1/3*5/7*s or 5/21*s
where s is the total number of shoes.
The minimum shoes needed in Brand A are 21,
in order to have a whole number(since the number of shoes cant be a fraction)
Brand B contains 7 shoes more, 28 in total.
The sum of minimum number of shoes is 49(Option E)
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Re: Kumail, a noted sneaker enthusiast, has a collection consisting of  [#permalink]

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27 Apr 2017, 16:00
1
Bunuel wrote:
Kumail, a noted sneaker enthusiast, has a collection consisting of sneakers made by Brand A and Brand B. 5/7 of the Brand A sneakers are low-tops, and 1/3 of the Brand A low-tops are running shoes. If Kumail owns 7 more pairs of Brand B sneakers than Brand A sneakers, what is the minimum possible number of pairs of sneakers in his collection?

A. 21
B. 28
C. 36
D. 40
E. 49

We are given that 5/7 of the Brand A sneakers are low-tops and 1/3 of the Brand A low-tops are running shoes. Thus, the number of Brand A sneakers must be a multiple of 7 x 3 = 21. Since the smallest positive multiple of 21 is 21, the least number of Brand A sneakers is 21.

Since Kumail owns 7 more pairs of Brand B sneakers than those of Brand A, the minimum number of Brand B sneakers is 28. Thus, the minimum possible number of pairs of sneakers in his collection is 21 + 28 = 49.

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Re: Kumail, a noted sneaker enthusiast, has a collection consisting of &nbs [#permalink] 27 Apr 2017, 16:00
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