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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]  26 Dec 2011, 10:15
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Question Stats:

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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]  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]  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]  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.

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]  24 Jan 2012, 17:37
Thanks for a very clear explanation Bunuel.
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Re: Number 75 [#permalink]  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]  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]  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]  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]  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]  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]  30 Apr 2015, 01:02
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?
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?

just pick numbers

most of questions of math test us ability to pick numbers.

not easy one
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Re: The number 75 can be written as the sum of the squares of 3   [#permalink] 30 Apr 2015, 01:02
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