Data sufficieny : exponenets

[pia_nag]

Hi ,

This is a questions from one of your CAT exams for data sufficiency :


If x, y and z are integers, what is y - z?

(1) 100^x = 2^y5^z
(2) 10^y = 20^x5^z+1

The answer to this says it is A.
But shouldnt the answer be C

From statement 2 :
We can easily decipher 10^2 = 20^1 x 5^0+1
Henxw y = 2 ; x =1 ; z=0 and we can calculate y-z.

Please confirm.

[nimish.tiwari]

From 1:
(2^2 * 5^2)^x = 2^y * 5^z
==> 2^2x * 5^2x = 2^y * 5^z
==> 2x=y & 2x=z
==> y-z = 0.
So, (1) is sufficient.

From 2:
(2 * 5)^y = (2^2 * 5)^x * 5^z+1
==> 2^y * 5^y = 2^2x * 5^x+z+1
==> y=2x & y=x+z+1
This cannot be solved further. So, (2) is not sufficient.

Hence, (A).

[Kweku.Amoako]

pia_nag

The numbers you picked solves the problem but there could be more set of numbers that will solve the problem as well eg 10^4 = (20^2)*5^(1+1) in this case y = 4, x = 2 and z = 1 ....so not sufficient

[Ben Ku]

nimish.tiwari's response is good and clearly shows why statement (1) is sufficient.

pia_nag, you need to make sure you evaluate the statements separately before putting them together. The GMAT often tricks the test-taker by putting two statements that obviously are sufficient when taken together, but the test-taker overlooks that one of the statements might be sufficient on its own.