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Prep test I

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?

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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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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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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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by niraj_a » Sat Sep 13, 2008 3:06 pm
thanks, this makes sense.
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