ans shd be D

pradeepkaushal9518 wrote:is the positive square root of a an integer?

1.a=b^4 and b is an integer
2.a=81

Step 1 of the Kaplan Method for Data Sufficiency: Analyze the Stem

We see "is", we think "yes/no" question. So, if the positive square root of a is always an integer, sufficient; if the positive square root of a is never an integer, sufficient; if the positive square root of a is only sometimes an integer, insufficient.

When will the positive square root of a be an integer? When a is a perfect square. So, the question is really asking:

Is a a perfect square?

Step 2 of the Kaplan Method for Data Sufficiency: Evaluate the Statements

(2) a=81. 81 is a perfect square, so that's a definite "yes"... sufficient, eliminate A, C and E.

I started with (2) because it's simpler; now if I'm stuck, I have a 50/50 shot at getting the question correct. Always start with the simpler statement!

(1) a=b^4 and b is an integer

Well, b^4 = (b^2) * (b^2) = (b^2)^2

Since b is an integer, b^2 is also an integer. a = (b^2)^2, so a IS the square of an integer - another definite yes, sufficient, eliminate B.

We could also have quickly tested (1) by picking values for b.

if b = 1, a = 1. Is 1 a perfect square? YES
if b = 2, a = 16. Is 16 a perfect square? YES
if b = 3, a = 81. Is 81 a perfect square? YES

By this point we should accept that as long as b is an integer a will always be a perfect square - that's a definite yes, sufficient.

Each statement is sufficient alone: choose D!

thanks stuart and rahul for your great explanations really it helps