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# The ratio of cats to dogs at a pet store is 11:15. The ratio of dogs

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Math Expert
Joined: 02 Sep 2009
Posts: 61510
The ratio of cats to dogs at a pet store is 11:15. The ratio of dogs  [#permalink]

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25 Nov 2019, 23:55
00:00

Difficulty:

45% (medium)

Question Stats:

70% (02:45) correct 30% (02:01) wrong based on 30 sessions

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The ratio of cats to dogs at a pet store is 11:15. The ratio of dogs to hamsters is 3:11. Let T be the total number of cats, dogs, and hamsters. What is $$\sqrt{T}$$?

(1) $$T<300$$
(2) $$\sqrt{T}$$ is an integer.

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Senior Manager
Joined: 13 Feb 2018
Posts: 499
GMAT 1: 640 Q48 V28
Re: The ratio of cats to dogs at a pet store is 11:15. The ratio of dogs  [#permalink]

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26 Nov 2019, 00:28
Cats -11x
Dogs - 15x

If we multiply Dog to hamster ratio by 5 we get
Dogs 15
Hams 55

Now we have everything for the equation
11x+15x+55x=81x=T
We need $$\sqrt{81x}$$

1 stm -- X may have several values 1, 2 or 3 -- Not suff
2 stm -- $$\sqrt{T}$$ is an integer -- clearly not sufficient

Together only x=1 satisfies $$\sqrt{T}$$ is an integer

I will bet on C
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Joined: 24 Nov 2016
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Re: The ratio of cats to dogs at a pet store is 11:15. The ratio of dogs  [#permalink]

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26 Nov 2019, 03:16
Bunuel wrote:
The ratio of cats to dogs at a pet store is 11:15. The ratio of dogs to hamsters is 3:11. Let T be the total number of cats, dogs, and hamsters. What is $$\sqrt{T}$$?

(1) $$T<300$$
(2) $$\sqrt{T}$$ is an integer.

c/d=11a/15a
d/h=3b/11b
d=15a, d=3b, 15a=3b, b=5a
T=11a+15a+11b=11a+15a+55a=81a=[81,162,243,…729…]

(1) $$T<300$$ insufic

T=[81,162]

(2) $$\sqrt{T}$$ is an integer. insufic

T=[81,729…]
√T=[9,27…]

(1&2) sufic

T=81
√T=9

Ans (C)
Re: The ratio of cats to dogs at a pet store is 11:15. The ratio of dogs   [#permalink] 26 Nov 2019, 03:16
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