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The number 75 can be written as the sum of the squares of 3

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The number 75 can be written as the sum of the squares of 3 [#permalink] New post 26 Dec 2011, 10:15
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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?
[Reveal] Spoiler: OA

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Re: Number 75 [#permalink] New post 26 Dec 2011, 10:20
The numbers are 5,7, and 1. The answer is Option (E).
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Re: Number 75 [#permalink] New post 27 Dec 2011, 02:53
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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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Re: Number 75 [#permalink] New post 19 Jan 2012, 18:19
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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.

Similar question to practice: the-number-90-can-be-written-as-the-sum-of-the-squares-of-128396.html
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Re: The number 75 can be written as the sum of the squares of 3 [#permalink] New post 24 Jan 2012, 17:37
Thanks for a very clear explanation Bunuel.
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Re: Number 75 [#permalink] New post 12 Mar 2012, 22:59
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] New post 18 Apr 2012, 19:11
thanks for the solution... was hoping for another solution other than just brute calculation. bunel you rock tho.
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Re: The number 75 can be written as the sum of the squares of 3 [#permalink] New post 17 Jun 2014, 01:21
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Re: The number 75 can be written as the sum of the squares of 3 [#permalink] New post 29 Jun 2014, 19:12
is there any way to solve this one faster? I find myself just trying to add the different numbers and spending 3 mins on this questions, just due to the calculations. any tricks on this one? Thanks.
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Re: The number 75 can be written as the sum of the squares of 3 [#permalink] New post 08 Aug 2014, 00:23
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GMAT17325 wrote:
is there any way to solve this one faster? I find myself just trying to add the different numbers and spending 3 mins on this questions, just due to the calculations. any tricks on this one? Thanks.


75 can be expressed as addition of squares of same integer as follows

75 = 5^2 + 5^2 + 5^2

Leaving one square term as it is; try to search for other options

75 = 5^2 + 50

Closest is 1 & 49

75 = 5^2 + 1 + 49

75 = 5^2 + 1^2 + 7^2

Answer = 5+1+7 = 13 = E
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Re: The number 75 can be written as the sum of the squares of 3 [#permalink] New post 09 Aug 2014, 07:31
I Seriously cannot believe I got this one wrong. I forgot to take into consideration square of 1 is 1 and guessed an answer. Still managed to get a score of 48 on this GMATprep, undeserved if I commit such silly mistakes. Good method Paresh
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Re: The number 75 can be written as the sum of the squares of 3   [#permalink] 09 Aug 2014, 07:31
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