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The number 75 can be written as the sum of the squares of 3 [#permalink]
 26 Dec 2011, 11:15
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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? A. 17 B. 16 C. 15 D. 14 E. 13 Guys - as the OA is not provided can someone please help me and explain how to solve this?
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The numbers are 5,7, and 1. The answer is Option (E).
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I think this question has been discussed earlier also.
squares of natural numbers, which are below 75,are 1,4,9,16,25,36,49,64
1+25+49=75 is the only option
so numbers are 1,5,7
sum =13
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enigma123 wrote: 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
Guys - as the OA is not provided can someone please help me and explain how to solve this? Responding to a pm. I think brute force with some common sense should be used to solve this problem. Write down all perfect squares less than 75: 1, 4, 9, 16, 25, 36, 49, 64. Now, 75 should be the sum of 3 of those 8 numbers. Also to simplify a little bit trial and error, we can notice that as 75 is an odd numbers then either all three numbers must be odd (odd+odd+odd=odd) OR two must be even and one odd (even+even+odd=odd). We can find that 75 equals to 1+25+49=1^2+5^2+7^2=75 --> 1+5+7=13. Answer: E.
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Director
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Re: The number 75 can be written as the sum of the squares of 3 [#permalink]
24 Jan 2012, 18:37
Thanks for a very clear explanation Bunuel.
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Bunuel wrote: I think brute force with some common sense should be used to solve this problem.
Write down all perfect squares less than 75: 1, 4, 9, 16, 25, 36, 49, 64.
Now, 75 should be the sum of 3 of those 8 numbers. Also to simplify a little bit trial and error, we can notice that as 75 is an odd numbers then either all three numbers must be odd (odd+odd+odd=odd) OR two must be even and one odd (even+even+odd=odd).
Very elegant solution. I got this question in my GMAT Prep 1. I also figured that it would require brute force. But Bunuel's point about 75 being an odd number and therefore being a sum of either odd-odd-odd or odd-even-even adds an elegant touch to the brute force approach.
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Re: The number 75 can be written as the sum of the squares of 3 [#permalink]
18 Apr 2012, 20:11
thanks for the solution... was hoping for another solution other than just brute calculation. bunel you rock tho.
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The number 75 can be written as the sum of 3 different posit [#permalink]
19 May 2013, 11:58
The number 75 can be written as the sum of 3 different positive integers. What is the sum of these 3 integers?
A. 17
B. 16
C. 15
D. 14
E. 13
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Re: The number 75 can be written as the sum of 3 different posit [#permalink]
19 May 2013, 14:09
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Re: The number 75 can be written as the sum of 3 different posit
[#permalink]
19 May 2013, 14:09
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