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The Quest for 700: Weekly GMAT Challenge (Answer)

Yesterday, Manhattan GMAT posted a 700 level GMAT question on our blog. Today, they have followed up with the answer:

We can rearrange the equation, putting all the x’s on one side and all the y’s on the other side:

2xx2 = y2 – 2y

Now, list the values of 2n and n2 for the first several nonnegative integers n. In fact, go ahead and compute the differences both ways (both 2nn2 and n2 – 2n).

n 2n n2 2nn2 n2 – 2n
0 1 0 1 –1
1 2 1 1 –1
2 4 4 0 0
3 8 9 –1 1
4 16 16 0 0
5 32 25 7 –7
6 64 36 28 –28

From this point on, 2n grows much faster than n2, so the differences explode. This means that in order to have a valid equation (2xx2 = y2 – 2y), we will have to use small values of the integers. We want values in the 2nn2 column to match values in the n2 – 2n column, and to maximize the value of |xy|, we want to pick values from different rows—as far apart as possible.

If we pick x = 0 and y = 3 (or vice versa), then we get a valid equation:

20 – 02 = 32 – 23

1 – 0 = 9 – 8

These values of x and y are as far apart as possible, so we get |xy| = 3.

The correct answer is (D).




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