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

Question

Is  x = y ?

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

Bunuel · Answer

The answer is an easy E. If a = 0, then x can be equal as well as not equal y. Similar question to practice: is-x-y-1-ax-ay-2-a-2-x-a-2-y-82210.html

HKD1710 · Answer

stmt-1:

ax = ay
ax-ay = 0
a(x-y) = 0

either a=0 or x=y or both x=y & a=0 could be true. hence we do not know if x=y or not.

stmt-2:
a^2x = a^2y
a^2x - a^2y = 0
a^2 (x-y) = 0
either a=0 or x=y or both x=y & a=0 could be true. hence we do not know if x=y or not.

as both the statements are giving same options to consider but no concrete answer. hence insifficient.

Answer is E.

mkumar26 · Answer

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

HKD1710 · Answer

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

Yotosan · Answer

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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Bunuel · Answer

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.

Jinnraj · Answer

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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Bunuel · Answer

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.

gmatophobia · Answer

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

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

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