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gmatprep1 question

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Senior Manager
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Joined: 11 Dec 2008
Posts: 477

Kudos [?]: 234 [0], given: 12

Location: United States
GMAT 1: 760 Q49 V44
GPA: 3.9
gmatprep1 question [#permalink]

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New post 06 Aug 2009, 11:17
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The number 75 can be written as the sum of squares of 3 different positive integers. What is the sum of these integers?

17
16
15
14
13

Any method of doing this besides blindly picking 3 numbers?

Kudos [?]: 234 [0], given: 12

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Manager
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Kudos [?]: 113 [1], given: 37

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Re: gmatprep1 question [#permalink]

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New post 06 Aug 2009, 11:29
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i used iterative method....see if it helps....

1) list all sqrs from 1 to 8 ...( upto 8 bcoz 9x9=81 crossing 75.....all sqrs should be below 75)
2) start from max value and start negating one by one....say a,b,c are those numbers then a=8 ....so 75-64 = 11 ...b^2+c^2 = 11....from all options from 1 to7 its not possible...hence negate 8

3) move to a=7....75-49 = 26...Hurrey! :-D possible....as b=1 c=25.....but now the question is are there any more possible combinations......but since question asks unique answer it should be the only one possibility.....otherwise question would have been find max or min type...since it is not we can be rest assure it is the only combination

if u lik my post...consider it for Kudos :wink:
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Bhushan S.
If you like my post....Consider it for Kudos :-D

Kudos [?]: 113 [1], given: 37

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Senior Manager
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Joined: 17 Jul 2009
Posts: 286

Kudos [?]: 44 [1], given: 9

Concentration: Nonprofit, Strategy
GPA: 3.42
WE: Engineering (Computer Hardware)
Re: gmatprep1 question [#permalink]

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New post 06 Aug 2009, 13:28
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i would start doing this by thinking .... if 75 is smaller than 9^2. thus we can only have 1~8 as our numbers. and we have to have 3 different numbers here, 8 doesn't work because 75-64 = 11 etc.
as for 7, we have 75-49 = 26 = 5 + 1
7 + 5 + 1 = 13.
etc...

i am not sure if there is an easier way to do it

Kudos [?]: 44 [1], given: 9

Senior Manager
Senior Manager
User avatar
Joined: 11 Dec 2008
Posts: 477

Kudos [?]: 234 [0], given: 12

Location: United States
GMAT 1: 760 Q49 V44
GPA: 3.9
Re: gmatprep1 question [#permalink]

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New post 06 Aug 2009, 14:23
sprtng wrote:
i would start doing this by thinking .... if 75 is smaller than 9^2. thus we can only have 1~8 as our numbers. and we have to have 3 different numbers here, 8 doesn't work because 75-64 = 11 etc.
as for 7, we have 75-49 = 26 = 5 + 1
7 + 5 + 1 = 13.
etc...

i am not sure if there is an easier way to do it


i like that method... kudos 8-)

Kudos [?]: 234 [0], given: 12

CEO
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Re: gmatprep1 question [#permalink]

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New post 06 Aug 2009, 15:00
bipolarbear wrote:
The number 75 can be written as the sum of squares of 3 different positive integers. What is the sum of these integers?

17
16
15
14
13

Any method of doing this besides blindly picking 3 numbers?


I just picked numbers. Seems to be the quickest. But here is where you can shave even more time.

There needs to be a 5 in this so 5^2 is a must. Now its just picking two other numbers. 7^2 and 1^2 are the only two that fit.

So E it is.

Kudos [?]: 500 [0], given: 0

Senior Manager
Senior Manager
avatar
Joined: 17 Jul 2009
Posts: 286

Kudos [?]: 44 [0], given: 9

Concentration: Nonprofit, Strategy
GPA: 3.42
WE: Engineering (Computer Hardware)
Re: gmatprep1 question [#permalink]

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New post 06 Aug 2009, 16:53
GMATBLACKBELT wrote:
bipolarbear wrote:
The number 75 can be written as the sum of squares of 3 different positive integers. What is the sum of these integers?

17
16
15
14
13

Any method of doing this besides blindly picking 3 numbers?


I just picked numbers. Seems to be the quickest. But here is where you can shave even more time.

There needs to be a 5 in this so 5^2 is a must. Now its just picking two other numbers. 7^2 and 1^2 are the only two that fit.

So E it is.


nice observation about a 5 being needed in this case. which made me think in this kind of questions, since couldn't we just analyze via the last digit? such as this one, the last digits of the squares from 1 to 8 are: 1 4 9 6 5 6 9 4, and from these we need to pick 3 to get a 5...easier than adding the 25s and 36s i think

Kudos [?]: 44 [0], given: 9

Re: gmatprep1 question   [#permalink] 06 Aug 2009, 16:53
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