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# The ratio of a to b is twice the ratio of b to c.  If a, b, and c are

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Joined: 14 Nov 2016
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The ratio of a to b is twice the ratio of b to c.  If a, b, and c are  [#permalink]

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23 Jun 2017, 17:56
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Difficulty:

95% (hard)

Question Stats:

34% (02:58) correct 66% (02:27) wrong based on 143 sessions

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The ratio of a to b is twice the ratio of b to c.  If a, b, and c are positive integers, which of the following statements cannot be true?

(A) c is 16% less than a.
(B) c is 2% less than a.
(C) a is 28% less than c.
(D) a is 12.5% greater than c.
(E) a is 28% greater than c.

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Re: The ratio of a to b is twice the ratio of b to c.  If a, b, and c are  [#permalink]

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23 Jun 2017, 20:28
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ANS A
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Re: The ratio of a to b is twice the ratio of b to c.  If a, b, and c are  [#permalink]

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23 Jun 2017, 21:35
1
We are given that:
a/b = 2b/c or ac = 2*b^2 or b^2 = ac/2
Since b^2 has to be a perfect square, ac/2 Also MUST be a perfect square. Lets now test the options

A) Let a=100x, c=84x (16% less).. Then b^2 = ac/2 = 8400x^2/2 = 4200x^2. This is NOT a perfect square as x^2 is a perfect square, but 4200 is not. So their product CANNOT be a perfect square. This is our answer

B) Let a=100x, so c=98x. b^2 = 9800x^2/2 = 4900x^2. 4900 is a perfect square so this is a perfect square.

C) Let c=100x, a=72x. b^2 = 7200x^2/2 = 3600x^2. 3600 is a perfect square so this is a perfect square.

D) Let c=100x, so a=112.5x. b^2 = 11250x^2/2 = 5625x^2. 5625 is a perfect square so this is a perfect square.

E) Let c=100x, so a =128x. b^2 = 12800x^2/2 = 6400x^2. 6400 is a perfect square so this is a perfect square.

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The ratio of a to b is twice the ratio of b to c.  If a, b, and c are  [#permalink]

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07 Oct 2018, 06:39
hazelnut wrote:
The ratio of a to b is twice the ratio of b to c.  If a, b, and c are positive integers, which of the following statements cannot be true?

(A) c is 16% less than a.
(B) c is 2% less than a.
(C) a is 28% less than c.
(D) a is 12.5% greater than c.
(E) a is 28% greater than c.

hey pushpitkc

can you pls explain whats wrong with my reasoning

once i read this -- > The ratio of a to b is twice the ratio of b to c.

i wrote this $$\frac{1a}{2b}$$ and $$\frac{1b}{4c}$$

thank you
The ratio of a to b is twice the ratio of b to c.  If a, b, and c are   [#permalink] 07 Oct 2018, 06:39
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