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

Question

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.

chetan2u · Accepted Answer

savwildeye , the solution will revolve around the method as shown above. You can just ease your calculations with some steps..

Now  \frac{a}{b}=\frac{2b}{c}...........b^2=\frac{ac}{2}

Now, take a or c as 100, depending what is the base in choices and then check whether the above relation holds true..

a=100 and c=84.....
 b^2=\frac{ac}{2}=\frac{100*84}{2}=10^2*6*7 . 
 b is NOT an integer .

a=100 and c=98.....
 b^2=\frac{ac}{2}=\frac{100*98}{2}=10^2*7^2...b=10*7 . 
 b is an integer .

c=100 and a=72 ( here we take c as 100 ).....
 b^2=\frac{ac}{2}=\frac{72*100}{2}=10^2*6^2...b=10*6 . 
 b is an integer .

c=100 and a=112.5 ( here we take c as 100 ).....
 b^2=\frac{ac}{2}=\frac{112.5*100}{2}=50*112.5=25*225=5^2*15^2...b=5*15 . 
 b is an integer .

c=100 and a=128 ( here we take c as 100 ).....
 b^2=\frac{ac}{2}=\frac{128*100}{2}=10^2*8^2...b=10*8 . 
 b is an integer .

A

Mkrishnabdrr · Answer

ANS A https://uploads.tapatalk-cdn.com/20170624/eba836e8a8924e855381d2bb5b91444b.jpg

amanvermagmat · Answer

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.

Hence  A answer

dave13 · Answer

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

savwildeye · Answer

Are the solutions posted above the most efficient way to solve this question?  chetan2u ,  VeritasKarishma ,  Bunuel ,  nick1816 ,  GMATBusters

GMATBusters · Answer

The ratio of a to b is twice the ratio of b to c.

a/b = 2 *b/c

GMATBusters · Answer

The solution provided by amanvermagmat seems good

KarishmaB · Answer

\frac{a}{b} = \frac{2b}{c}

(A) c is 16% less than a.

\frac{a}{b} = \frac{200b}{84a}

a^2 = \frac{100}{42}b^2

100/42 is not a perfect square so not possible.

(B) c is 2% less than a.

\frac{a}{b} = \frac{200b}{98a}

a^2 = \frac{100}{49} b^2

100/49 is a perfect square - possible

and so on...

Kimberly77 · Answer

Great solution  chetan2u . 
When 
It will be C = 84a/100 or 100C = 84a
not sure how are we able to determine that a=100 and c=84? Could you help clarify this concept?

Lastly when 50∗112.5=25∗225, not sure how is possible to reduce 50 but doubling 112.5 here? thought can only either reduce or doubling both at the same time? Thanks

chetan2u · Answer

Hi

Firstly why a=100 and c=84.
As I mentioned, we can take any values. The question is CANNOT be true, so any values that fits in is correct. Here, we are talking of %, so we talk of a or c as 100.

Next 50*112.5 = 25*2*112.5=25*225

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