Is x = y? (1) ax = ay (2) a^2x = a^2y

stmt-1:
a (x-y) = 0 Consider the values for which this statement is correct.

If a = 5 and x=y then we say YES X=Y is the answer.
If a = 0 and x=4,y=2 then then 0*2 = 0. in this case X not equal Y. then we say NO X NOT EQUAL Y.

If you get both YES and NO as the answer from one statement then that statement is insufficient.

stmt-2:
a^2 (x-y) = 0 Consider the values for which this statement is correct.
If a = 5 and x=y then we say YES X=Y is the answer.
If a = 0 and x=4,y=2 then then 0*2 = 0. in this case X not equal Y. then we say NO X NOT EQUAL Y.

combine both
a (x-y) = 0
a^2 (x-y) = 0

If a = 5 and x=y then we say YES X=Y is the answer.
If a = 0 and x=4,y=2 then then 0*2 = 0. in this case X not equal Y. then we say NO X NOT EQUAL Y.

Now even after combining the statements you get BOTH YES & NO as the answer. hence answer cannot be C.

Let me know if this is still not clear. Happy to help

The square of a number is NOT always positive. It's positive OR 0, if the number itself is 0. So, the square of a number is always non-negative.

If you divide (reduce) ax = ay by a you assume, with no ground for it, that a does not equal to zero thus exclude a possible solution (notice that a=0 satisfies the equation). Never reduce equation by variable (or expression with variable), if you are not certain that variable (or expression with variable) doesn't equal to zero. We cannot divide by zero.

Basically, if a = 0, then x and y can be any numbers, equal or not.

Check more tips on Algebra here: https://gmatclub.com/forum/algebra-tips- ... 75003.html

Hope it helps.

why we take a=0 even we need only x=y so why not option c ?

Isn't a^2 always positive. And if that is the case then statement 2, a^2 not equal to zero and now for any positive number a^2x will equal a^2y?
Bunuel please correct me if I'm wrong.

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I might be missing a fundamental concept here but can someone pls clarify why I just can't divide both sides of equation with a? That simply leaves x = y. Isnt that algebraically allowed? Bunuel could you pls assist.

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Statement 1

(1) \(ax = ay\)

\(a(x-y) = 0\)

Therefore either a = 0 or x = y. The information presented is not sufficient. Eliminate A and D.

Statement 2

(2) \(a^2x = a^2y\)

\(a^2(x-y) = 0\)

Therefore either a = 0 or x = y. The information presented is not sufficient. Eliminate B.

Combined

The statements combined are not sufficient either as both cases are common to Statement 1 and Statement 2.

Option E