What is the greatest prime factor of \(42^2+75^2+6300?\)

[Gmat_mission]

What is the greatest prime factor of \(42^2+75^2+6300?\)

a) 3
b) 7
c) 11
d) 13
e) 79

[spoiler]OA=D[/spoiler]

Source: Veritas Prep

[Scott@TargetTestPrep]

What is the greatest prime factor of \(42^2+75^2+6300?\)

a) 3
b) 7
c) 11
d) 13
e) 79

[spoiler]OA=D[/spoiler]

Solution:

Consider the perfect square (a + b)^2, which expands to a^2 + b^2 + 2ab.

This pattern can be applied to (42 + 75)^2, which expands to 42^2 + 75^2 + 2(42)(75). Note that the third term of this expansion 2(42)(75) = 6300. Thus, we see that 42^2 + 75^2 + 6300 = (42 + 75)^2. Now, perform the addition inside the parentheses, obtaining 117^2 = (3^2 x 13)^2. We see that the greatest prime factor is 13.

Answer: D