# DS Question of the Day

If a^x=b^y, where a, b, x, and y are positive integers, is x divisible by y?

(1) a is an odd number
(2) y is an odd number

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1. Erlan says:

(2) is enough to answer the question.

Regarding(1), I think it wanted to sound like a is an odd number.
Then (1) is not enough to answer the question.

2. Erlan says:

Sorry, (1) is also enough to answer the question.

3. JT says:

well, if a^x = b^y, then we know that at least one these is true
1) x divides y OR
2) y divides x OR
3) a=b=1, in which case x and y can be anything (1^3 = 1^5 for example).

I don’t see how knowing the second fact, that y is odd, helps at all.

Knowing (1), what the value of is, allows us to eliminate my third possibility, but then we still don’t know whether x|y or y|x since we don’t know which is bigger?

So I think the answer cannot be determined even with both facts.

4. Aliva says:

i am not really convinced with the question
statement states simply ‘a’
which could mean anything
Gmat Team ,need your sincencere concern and help
I am not able to find where I am wrong??

5. BSankar says:

let a = 2, x = 4
than a^x = 16
and b = 4, y = 2
than b^y = 16.

Do anyone have any other example. I hope y is a even number always.

6. BSankar says:

so y is divisible by x..

7. dp says:

Option E

8. deepak says:

a^x = b^y.

Eqn : 2^4 = 4^2 will solve this.But there is also something we need to take care of ,a = b = 1.So irrespective of the powers the eqn will be satisfied always.

Statement 1: Nt suff.

Statement 2 : Nt suff.

Combining both the statements : Nt suff.

I will go with option E

9. Nitin Sharma says:

E

10. Kofi DL says:

Statement 1 is necessary and sufficient to answer the question…

11. aryan says:

125 = 5 ^ 3 …. option E

12. keerthi says:

E

13. tarun says:

If a is odd then B must be odd

5^4=25^2

3^4=9^2

hence a is sufficient

14. ramesh says:

15. ramesh says:

how 1, i am not getting

here in first a is odd a is base but we do not no x donot know y value also value so this is not sufficient to tel x divisable by y

in second y value odd we donot know x value k this is also not

would we give the answer to that problem we want to know x value and y value from this options we cannot find out value of x so my answer is E