What is the greatest prime factor of $42^2+75^2+6300?$

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Gmat_mission: Legendary Member; Posts: 1622; Joined: Thu Mar 01, 2018 7:22 amFollowed by: 2 members

by Gmat_mission » Thu May 21, 2020 1:22 am

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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

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Source: Beat The GMAT — Problem Solving | Thu May 21, 2020 1:22 am

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Re: What is the greatest prime factor of $42^2+75^2+6300?$

by Scott@TargetTestPrep » Sun May 31, 2020 4:12 am

Gmat_mission wrote: ↑
Thu May 21, 2020 1:22 am
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

Scott Woodbury-Stewart
Founder and CEO
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