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If all members of Set X are positive integers, what is...

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by swerve » Fri Nov 17, 2017 10:43 am
If all members of Set X are positive integers, what is the range of Set X?

1) The positive difference between the square of the largets number in Set X and the square of the smallest number in Set X is 99.
2) The sum of the largest number in Set X and the smallest number in Set X is 11.

The OA is C.

Please, can any expert explain this DS question for me? I have many difficulties to understand why that is the correct answer. Thanks.
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by GMATGuruNY » Fri Nov 17, 2017 11:02 am
swerve wrote:If all members of Set X are positive integers, what is the range of Set X?

1) The positive difference between the square of the largets number in Set X and the square of the smallest number in Set X is 99.
2) The sum of the largest number in Set X and the smallest number in Set X is 11.
Range = largest - smallest.
Let L = the largest number and S = the smallest number.
Question stem, rephrased:
What is value of L-S?

Note the following identity:
a² - b² = (a+b)(a-b).

Statement 1: L² - S² = 99.
Thus:
(L+S)(L-S) = 99.
Case 1: L+S = 99 and L-S = 1, with the result that (L+S)(L-S) = 99*1 = 99
In this case, L-S = 1.
Case 2: L+S = 11 and L-S = 9, with the result that (L+S)(L-S) = 11*9 = 99
In this case, L-S = 9.
Since L-S can be different values, INSUFFICIENT.

Statement 2: L+S = 11.
If L=10 and S=1, then L-S = 10-1 = 9.
If L=9 and S=2, then L-S = 9-2 = 7.
Since L-S can be different values, INSUFFICIENT.

Statements combined:
Only Case 2 satisfies both statements.
In Case 2, L-S = 9.
SUFFICIENT.

The correct answer is C.
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