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Oxana: Junior | Next Rank: 30 Posts; Posts: 18; Joined: Sun Jul 27, 2008 8:59 am; Thanked: 1 times

by Oxana » Fri Sep 12, 2008 7:06 pm

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

17
16
15
14
13

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Source: Beat The GMAT — Problem Solving | Fri Sep 12, 2008 7:06 pm

anju: Master | Next Rank: 500 Posts; Posts: 258; Joined: Thu Mar 29, 2007 3:15 amFollowed by: 1 member; Thanked: 7 times

by anju » Fri Sep 12, 2008 7:22 pm

the squares are 49, 25 and 1
so the sum of numbers is 13

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niraj_a: Legendary Member; Posts: 708; Joined: Sun Jun 01, 2008 4:59 amFollowed by: 1 member; Location: USA; Thanked: 13 times

by niraj_a » Sat Sep 13, 2008 1:39 pm

anju,

could you post the steps you used to get to the answer? is taking the time to compute every possible combination the only method?

i broke 75 down to its prime factors of 5, 5, and 3, and these total to 13, but i thought that had to be wrong.

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mals24: Legendary Member; Posts: 683; Joined: Tue Jul 22, 2008 1:58 pmFollowed by: 2 members; Location: Dubai; Thanked: 73 times

by mals24 » Sat Sep 13, 2008 2:19 pm

The only perfect square that is a factor of 75 = 25

subtracting 25 from 75 you get 50
Now 50 can be written as 49 + 1 both the numbers are perfect squares of 7 and 1 respectively.

Hence 75 = 49+1+25
and 7+1+5=13

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niraj_a: Legendary Member; Posts: 708; Joined: Sun Jun 01, 2008 4:59 amFollowed by: 1 member; Location: USA; Thanked: 13 times

by niraj_a » Sat Sep 13, 2008 3:06 pm

thanks, this makes sense.

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