GMAT PREP I SUM OF SQUARES

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pkw209: Master | Next Rank: 500 Posts; Posts: 266; Joined: Mon Oct 19, 2009 9:46 pm; Thanked: 8 times; GMAT Score:690

by pkw209 » Tue Jan 05, 2010 10:05 am

Hi everyone,

Just curious about the fastest method to solving this problem other than trial and error and reasoning. thanks.

FYI, I took this from Zuleron's list of gmat prep questions. The answer is E.

108) 75 can be written as the sum of the squares of 3 different positive integers. What is sum of these integers?

a. 17
b. 16
c. 15
d. 14
e. 13

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Source: Beat The GMAT — Problem Solving | Tue Jan 05, 2010 10:05 am

ace_gre: Senior | Next Rank: 100 Posts; Posts: 98; Joined: Mon Nov 23, 2009 2:30 pmFollowed by: 1 member; Thanked: 26 times

by ace_gre » Tue Jan 05, 2010 11:31 am

Not sure if this is the fastest way, but here is my approach.

Max number of the three can be 8.
Also 75 = odd number. So the three numbers that make up 75 can be:

1) even+even+odd
2) odd+odd+odd

1) Start with 2==>2^2 +4^2=4+16=20. Difference = 75-20=55 (in which case third number cannot be whole)
Next try 2^2 + 6^2 = 4 + 36=40
Next try 4^2+6^2=16+64=80 >75
Next try 8^2 = 64. Difference = 11. This cannot be sum of two square numbers.
So this combination of even+even+odd does not work.

2) The solution has to be all three odd numbers.
Start with 1==>1^2 + 3^2 + 5^2 = 35 < 75
Next try 1^2 + 5^2 + 7^2 = 75. (Other combinations would be 3^2 + 5 ^2 + 7^2 and this is >75)

For odd numbers we can try all combinations upto 7 and then stop because we already determined that the max number is 8.

Hence E.

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papgust: Community Manager; Posts: 1537; Joined: Mon Aug 10, 2009 6:10 pmFollowed by: 252 members; Thanked: 653 times

by papgust » Tue Jan 05, 2010 6:39 pm

Here's a quicker way of solving this question by Stuart,

https://www.beatthegmat.com/gmat-prep-t9319.html

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