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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:

Don’t be afraid to assign variables even when none are given in the problem. “Two positive numbers differ by 12” can be written as:

xy = 12

And “their reciprocals differ by 4/5” can be written as:

1/y – 1/x = 4/5

(Note: Here, we’ve assigned x as the bigger of the two numbers and y as the smaller, so we’ve intuited that 1/y is the larger reciprocal and 1/x the smaller, and so arranged them in that order to write 1/y – 1/x = 4/5).

Now we have a system of two variables and two equations. Note that it is NOT necessary to solve for x and y, since we are being asked for the product, xy.

First, let’s simplify the second equation by finding a common denominator for the terms on the left:

x/(xy) – y/(xy) = 4/5

(xy)/(xy) = 4/5

Note that the denominator is xy, which is exactly the quantity we want to find.

Since we know from the first equation that xy = 12, substitute 12:

12/(xy) = 4/5

60 = 4xy

15 = xy

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