ziyuenlau wrote:What is the greatest prime factor of 42^2+75^2+6300 ?
(A) 3
(B) 7
(C) 11
(D) 13
(E) 79
The given expression looks like the red portion of the following:
(a+b)² =
a² + b² + 2ab.
Test where (42 + 75)² = 42² + 75² + 6300:
(42 + 75)²
= 42² + 75² + 2*42*75
= 42² + 75² +
2*
6*7*
5*
5*3
= 42² + 75² +
10*
30*21
= 42² + 75² + 6300.
Success!
Thus:
42² + 75² + 6300 = (42+75)² = 117².
Of the five answer choices, the greatest value that divides evenly into 117 is
D:
117 = 13*9.
The correct answer is
D.
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