It is currently 21 Oct 2017, 02:15

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

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

  post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
Manager
Manager
avatar
Joined: 05 Aug 2008
Posts: 91

Kudos [?]: 47 [0], given: 0

Schools: McCombs Class of 2012
The number 75 can be written as the sum of the squares [#permalink]

Show Tags

New post 24 Dec 2008, 17:23
1
This post was
BOOKMARKED
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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

Attachment:
Q1.JPG
Q1.JPG [ 15.13 KiB | Viewed 784 times ]

Kudos [?]: 47 [0], given: 0

SVP
SVP
User avatar
Joined: 07 Nov 2007
Posts: 1792

Kudos [?]: 1062 [0], given: 5

Location: New York
Re: Sum of squares [#permalink]

Show Tags

New post 24 Dec 2008, 21:22
smarinov wrote:
Attachment:
Q1.JPG


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

Ans = 1+5+7=13

E
_________________

Your attitude determines your altitude
Smiling wins more friends than frowning

Kudos [?]: 1062 [0], given: 5

Manager
Manager
avatar
Joined: 05 Aug 2008
Posts: 91

Kudos [?]: 47 [0], given: 0

Schools: McCombs Class of 2012
Re: Sum of squares [#permalink]

Show Tags

New post 24 Dec 2008, 21:26
x2suresh,

that is the correct answer, was there an approach you took to get to this answer, or did you just plug numbers and used your intuition/knowledge to see that 5^2 + 7^2 + 1 would give you 75?

thanks

Kudos [?]: 47 [0], given: 0

Intern
Intern
avatar
Joined: 26 Dec 2008
Posts: 1

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

Re: Sum of squares [#permalink]

Show Tags

New post 26 Dec 2008, 02:24
1 4 9 16 25 36 49

75 is an odd number, so:
a) 2 of 3 our numbers must be even and one odd (3 cases: 4,16; 4;36; 16;36)
b) 3 of our numbers must be odd (4 cases: 1,9,25; 1,25,49; 1,9,49; 9,25,49)

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

Intern
Intern
avatar
Joined: 26 Dec 2008
Posts: 10

Kudos [?]: 6 [0], given: 0

Schools: Thunderbird
Re: Sum of squares [#permalink]

Show Tags

New post 27 Dec 2008, 00:28
2, 3, 8 also works. There has to be a formula behind this.

Can anyone come up with it? :?:

Kudos [?]: 6 [0], given: 0

Intern
Intern
avatar
Joined: 27 Nov 2008
Posts: 5

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

Re: Sum of squares [#permalink]

Show Tags

New post 27 Dec 2008, 04:21
Both 7,5,1 and 8,3,2 add up to 13.
So it doesn't really matter which set you come up with.

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

SVP
SVP
User avatar
Joined: 07 Nov 2007
Posts: 1792

Kudos [?]: 1062 [0], given: 5

Location: New York
Re: Sum of squares [#permalink]

Show Tags

New post 27 Dec 2008, 07:30
amopk wrote:
Both 7,5,1 and 8,3,2 add up to 13.
So it doesn't really matter which set you come up with.


Anyway 64+9+4 = 77 not equal to 75
_________________

Your attitude determines your altitude
Smiling wins more friends than frowning

Kudos [?]: 1062 [0], given: 5

Intern
Intern
avatar
Joined: 26 Dec 2008
Posts: 10

Kudos [?]: 6 [0], given: 0

Schools: Thunderbird
Re: Sum of squares [#permalink]

Show Tags

New post 27 Dec 2008, 10:35
...ugh... :roll:

Kudos [?]: 6 [0], given: 0

Expert Post
GMAT Tutor
avatar
B
Joined: 24 Jun 2008
Posts: 1339

Kudos [?]: 1954 [0], given: 6

Re: Sum of squares [#permalink]

Show Tags

New post 27 Dec 2008, 20:02
It's possibly overkill to do any analysis here, since there aren't many possibilities regardless, but if 75 were a larger number, we could at least cut down on the number of cases by doing a bit of math. As wkeeper points out, there are two cases:

* two evens, one odd
* three odds

The first case is mathematically impossible, because 75 doesn't have the right remainder when you divide by 4. Even squares are always multiples of 4, and odd squares are always 1 greater than multiples of 4 (actually, than multiples of 8, but we don't need that here). So, if you add two even squares and an odd square, you'll get a number with a remainder of 1 when you divide by 4. That's not true of 75, so we must be adding three odd squares here, and after we see that, there really aren't many possibilities to check.
_________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

Kudos [?]: 1954 [0], given: 6

Re: Sum of squares   [#permalink] 27 Dec 2008, 20:02
Display posts from previous: Sort by

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

  post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.