commdiver wrote:

This is problem #34 on page 238 of

Manhattan GMAT's

Advanced GMAT Quant book.

If y≠x, then [x^3 + (x^2 + x)(1-y) - y] / (x-y) = ?

(A) [(x-1)^2]y

(B) (x+1)^2

(C) (x^2 + x +1)

(D) (x^2 + x +1)y

(E) (x^2 + x +1)(x-y)

Please see the spoiler below for my question:I picked 3 for x and 2 for y, but both C and E are correct for that. I redid the problem and picked 4 for x and 2 for y. That makes C the only correct answer. How can I avoid this problem in the future? If this were the real GMAT, I would have wasted a 30 seconds to a minute on this problem because I would have had to do it twice.

When you pick numbers, it is normal for you to get 2 or even 3 options that work out. The reason for this is that we tend to pick really easy numbers so that the calculation does not get cumbersome. I do not suggest you to pick harder numbers of course; I suggest you to pick even easier numbers so that the iterations don't take time.

I picked numbers to solve this too but I took numbers in which it took me a few secs to get to the correct option.

I said to myself, 'nothing says one of them can't be 0. Let x = 1 and y = 0'

Then [x^3 + (x^2 + x)(1-y) - y] / (x-y) = 3

(A) and (D) are outright out since they equal 0 because y is a factor in them. (B) gives 4 so out. (C) and (E) are the only possible options since they both give 3.

Now I notice that (C) and (E) differ in the product (x - y). So I want that the difference between them should not be 1 (I think you noticed this too). So now, I pick x = 2 and y = 0 (why to give up a good thing? y = 0 makes life easy)

[x^3 + (x^2 + x)(1-y) - y] / (x-y) = 14/2 = 7

Option (C) gives 7 while option (E) will give 7/2

Answer must be (C)

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