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Given that w,x and y ≠ 0. we need to find whether x=y

From st 1, we have W^x=W^y

If W = 2 then x=y=2 then yes because different values of x=y will prove st1 to be insufficient in this case Consider w=1, then x and y can have any values as 1^(Some Power) = 1 Hence no St 1 is not sufficient. Consider w= -1 then x and y have same values for ex x=y=-3 or or x=-3 and y = -5.

Hence A and D ruled out

Consider st 2, we get w ≠1 still not sufficent....

Combining the 2 statements we get that there are still cases possible for w=-1 for which x ≠y and x=y

Ans E.

Actually if you look at st 2, it gives you ample hint to check for what values of w
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“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”

This DS question can be solved by TESTing VALUES (although recognizing the built-in Number Properties would help make solving this problem easier).

We're told that WXY is not = 0, so NONE of those variables can = 0. We're asked if X = Y. This is a YES/NO question.

To start, it's interesting that this prompt has 3 variables, but the question focuses on just 2 of them. That almost always means that the third variable (in this case, the W) will play a role in defining the other two variables.

Fact 1: W^X = W^Y

Since the 'base' on both sides of this equation are Ws, it might be tempting to think that this X = Y. However, you have to be thorough with your thinking....

IF... W = 2 X = 3 Y = 3 2^3 = 2^3 and the answer to the question is YES.

But what happens if W = 1 or W = -1? Do the exponents even matter at that point?

IF... W = 1 X = 1 Y = 5 1^1 = 1^5 and the answer to the question is NO. Fact 1 is INSUFFICIENT

Fact 2: WXY is NOT = XY

This pinpoints one specific restriction about W....W CANNOT = 1. Unfortunately, it doesn't tell us anything about X and Y

IF.... W =2 X = 1 Y = 1 The answer to the questions is YES.

IF... W = 2 X = 1 Y = 3 The answer to the question is NO. Fact 2 is INSUFFICIENT

Combined, we know... W^X = W^Y W CANNOT = 1

IF.... W = 2 X = 3 Y = 3 2^3 = 2^3 and the answer to the question is YES.

IF.... W = -1 X = 1 Y = 3 (-1)^1 = (-1)^3 and the answer to the question is NO. Combined, INSUFFICIENT.

IMPORTANT: When I scan the two statements, I can see that this question is testing us on our knowledge about when we can conclude that two exponents are equal. For statement 1, many students will conclude that, if w^x = w^y, then it must be true that x = y. HOWEVER, this is true only if w does NOT equal 0, 1 or -1 For example, if 1^x = 1^y, we can't then conclude that x = y Given all of this, we can jump straight to .....

Statements 1 and 2 combined There are many values of w, x and y that satisfy BOTH statements. Here are two: Case a: w = -1, x = 2 and y = 2. These values work because (-1)^2 = (-1)^2. In this case, the answer to the target question is YES, x = y Case b: w = -1, x = 2 and y = 4. These values work because (-1)^2 = (-1)^4. In this case, the answer to the target question is NO, x does NOT equal y Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Data Sufficiency questions 'test' a number of different skills (more than just 'math' skills), so you have to be thorough with your thinking - and make sure that you're considering all of the possibilities. When dealing with Fact 1 in this particular prompt, what if W = 1? In THAT situations, couldn't each of X and Y be almost anything (and by extension, is it possible that X and Y are NOT equal?)?