This is problem #34 on page 238 of Manhattan GMAT
's Advanced GMAT Quant
If y≠x, then [x^3 + (x^2 + x)(1-y) - y] / (x-y) = ?
(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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