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# Fewer than 48 children were surveyed about their pet preferences

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Manager
Joined: 25 Sep 2018
Posts: 186
Location: United States (CA)
Concentration: Finance, Strategy
GMAT 1: 640 Q47 V30
GPA: 3.97
WE: Investment Banking (Investment Banking)

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05 Oct 2018, 06:33
5
00:00

Difficulty:

65% (hard)

Question Stats:

43% (01:31) correct 57% (01:41) wrong based on 27 sessions

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Fewer than 48 children were surveyed about their pet preferences. Some of the children prefer foxes, some prefer wolfs, while the remaining prefer vultures. How many of the children surveyed prefer foxes as pets?
1) The ratio of the number of children who prefer foxes to the number of children who prefer wolfs is 4 to 3.
2) The ratio of the number of children who prefer foxes to the total number of children surveyed is 5 to 9.

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Re: Fewer than 48 children were surveyed about their pet preferences  [#permalink]

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05 Oct 2018, 06:51
Fewer than 48 children were surveyed about their pet preferences. Some of the children prefer foxes, some prefer wolfs, while the remaining prefer vultures. How many of the children surveyed prefer foxes as pets?

So f+w+v<48

1) The ratio of the number of children who prefer foxes to the number of children who prefer wolfs is 4 to 3.
F:w=4:3
We can have all three f:w:c = 4:3:1..total 4x+3x+X=8x so numbers could be 8,16,24,32,40
Ratio could be 4:3:2=9x could be 9,18,27
Accordingly f will change but will be a multiple of 4
Insufficient

2) The ratio of the number of children who prefer foxes to the total number of children surveyed is 5 to 9.
f:t=5:9 so total is multiple of 7 and f a multiple of 5..
Insufficient

Combined..
f is a multiple of 4 and 5 so a multiple of 20..
If it is 20, total is 9*4=36..
If we take f as next multiple of 20 that is 40, t becomes 9*4*2=72 >48 so not possible
So total is 36 and f is 20
Sufficient

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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

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Re: Fewer than 48 children were surveyed about their pet preferences   [#permalink] 05 Oct 2018, 06:51
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