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05 Mar 2017, 09:02
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Please explain without using X
The difference between two number is 5 and the difference of their squire is 135. The sum of the number is?
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The difference between two number is 5 and the difference of their squire is 135. The sum of the number is?
Sent from my HUAWEI CUN-U29 using GMAT Club Forum mobile app
06 Mar 2017, 20:34
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Let \(a\) and \(b\) be two numbers, where \(a > b\).
Then \(a - b = 5\) and \(a^2 - b^2 = 135\).
We have \(135 = a^2 - b^2 = (a+b)(a-b) = 5(a+b)\) and \(a + b = 27\).
Therefore, the sum of those numbers is \(27\).
In brief, when two numbers are given, the difference of their squares is the multiple of their difference and their sum.
Here, we can get the value of their sum, since we have the differences of their squares and that of themselves, respectively.
