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Number Systems

by sukhman » Wed Oct 16, 2013 9:49 am
If q, r, and s are consecutive even integers and q < r < s, which of the following CANNOT be the value ofs^2 - r^2 - q^ 2?

(A) -20 (B) 0 (C) 8 (D) 12 (E) 16

for me answer was a after plugging in numbers but its c
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by [email protected] » Wed Oct 16, 2013 10:49 am
Hi sukhman,

Your approach to TEST values is a good choice. You can "brute force" this question quickly by following the instructions and TESTing values. Here's how I solved it...

We're told that Q, R and S are consecutive EVEN integers, so we're restricted there. Using these values, here are the results (note that we're looking for what CANNOT be the value):

0, 2, 4 = 16 - 4 - 0 = 12 Eliminate D
2, 4, 6 = 36 - 16 - 4 = 16 Eliminate E
-2, 0, 2 = 4 - 0 - 4 = 0 Eliminate B
-4, -2, 0 = 0 - 4 - 16 = -20 Eliminate A

Final Answer: C

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by GMATGuruNY » Wed Oct 16, 2013 11:02 am
sukhman wrote:If q, r, and s are consecutive even integers and q < r < s, which of the following CANNOT be the value ofs^2 - r^2 - q^ 2?

(A) -20 (B) 0 (C) 8 (D) 12 (E) 16

for me answer was a after plugging in numbers but its c
q², r² and s² are THREE CONSECUTIVE EVEN PERFECT SQUARES.
MAKE A LIST of possible values:
4, 16, 36, 64, 100, 144...

s² - r²- q² = 144-100-64 = -20.
s² - r²- q² = 100-64-36 = 0.
s² - r²- q² = 64-36-16 = 12.
s² - r²- q² = 36-16-4 = 16.

Since A, B, D, and E are possible, the correct answer is C.
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