dude you are sure about OA
i am hetting different answer

Yes the official answer is A.

I somehow figured out how to solve this question after posting here.

The only way 5^x=11^y is when x and y are both zero.

Therefore A is sufficient to solve the problem.

I am not sure about this approach.

What is source of this question?

A is not seems to me as a good answer. because , one can't solve the equation with 2 unknowns.
It would be better some math guys or instructor give an explanation. Thank you beforehand!

1) 5^x = 11^y
for example take x= 1, 2 , 3, 4
correspondingly, 5^x=5, 25, 125, 625

similarly for y=1 , 2 , 3
11^y= 11, 121, 1331

it clearly indicates that the unit digit for 5^x will always be 5 and for 11^y will always be 1. So you can never get any non-zero value which says 5^x = 11^y.

We know that zero to the power of any number will be 1. So 5^0 =1, similarly 11^0=1.

So x=y=0, is the only solution for above statement to hold true (5^x = 11^y).

Statement 1 is SUFFICIENT.

I hope it helps.

dongkim2 and EdWood:

First of all EdWood, kudos to you on your screenname. If nothing else, "Plan 9 From Outer Space" and "Glen or Glenda" provided fodder for Tim Burton's best movie.

But back to math...you guys have it right. 5^x = 11^y cannot be true unless both x and y are 0. I like EdWood's method of thinking about the units digits.

You can also consider prime factorization (my single favorite topic on the GMAT!)...

5^x will be some power of 5, since x is an integer, and any power of 5 breaks down into a prime factorization that includes only 5's (no 11's). Same with 11^y (no 5's as prime factors).

So the only way 5^x could possibly equal 11^y is if both x and y are 0, thus eliminating prime factors altogether.

blaster:

Applying the n-equations, n-variables rule is a great instinct to have, so it's great you've developed that. However, that rule applies strictly to LINEAR EQUATIONS. Because we're dealing with exponents here, the rule does not apply.

Another example would be quadratics. x^2 = 4 is a single equation with a single variable, but it produces two possible x values, because the equation is not linear.

Make sense?