Number properties and exponents

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Mr.Hollywood: Senior | Next Rank: 100 Posts; Posts: 34; Joined: Mon Oct 24, 2011 2:04 pm; Thanked: 1 times

by Mr.Hollywood » Tue Mar 06, 2012 12:50 am

X, Y and Z are all positive even integers. What could be the answer of X^2+Y^2+Z^2

A) 234
B) 138
C) 862
D) 636

Does anybody have a clue how to approach or solve this?

Thank you!

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Source: Beat The GMAT — Problem Solving | Tue Mar 06, 2012 12:50 am

Neo Anderson: Senior | Next Rank: 100 Posts; Posts: 92; Joined: Thu Oct 06, 2011 8:06 am; Thanked: 18 times

by Neo Anderson » Tue Mar 06, 2012 6:58 am

X, Y and Z are all positive even integers. What could be the answer of X^2+Y^2+Z^2

as all are even integers, squaring each term will have component of 2 being squared, thus the term individually and the sum of all terms X^2+Y^2+Z^2 should be divisible by 2 squared that is 4,
among the given options, only 636 is divisible by 4. hence the answer

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