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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

0% (00:00) correct
0% (00:00) wrong based on 0 sessions

HideShow timer Statistics

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

I would solve it with playing with numbers.

1) integers cannot by grater than 8, because 9^2 = 81 > 75 2) write out all squares : 1, 4, 9, 16, 25, 36, 49 3) Do you see the answer? No? 4) 75 is a big integer, so let's one of integers is 7. 75-49=26 - for 2 squares. it is possible for 1+25 (1 and 5) 5) we could begin with 6. 75 - 36 = 39. 25+16=41, 25+9=34, others options are less than 39.
_________________

Re: An elegant way to solve this problem: [#permalink]

Show Tags

08 Jul 2009, 02:58

The number 75 can be written as the sum of the squares of 3 different positive integers. What is the sum of these integers:

75 is odd , and 75 must be made from squares of 3 different positive integers , the integers must be

Observations : 1.0 integer^2 = int X int so if int is odd then int^2 = odd , even , int^2 = even 2.0 Since 75 is odd then three integers must be { e,e,o} or {o,o,o} hence their sum must be odd

so then answer choices B and D are out ( B, D the sum is even)

3.0 We know that the largest of the 3 must be less than 9 ( 9^2 = 81) integers = { 1,2,3,4,5,6,7,8} integer squared (unit digit) = { 1,4,9,6,5,6,9,4}

there are three odd units( 1,5,9) and 2 even units (2,4)

Look at the unit digit of 75 , unit digit = 5 , so when we add the squares we must get 5 as the unit

From 2.0 check odd,odd,odd -----> 1+9+5 = 5; 5+5+5=5 , so it satisfies the unit place value , so the numbers could be 1,3,5 : 5,5,5 or 1,7,5 only 1,7,5 will satisfy the given condition (1,3,5 is too small and 5,5,5 is out because the integers must be different)

Re: An elegant way to solve this problem: [#permalink]

Show Tags

08 Jul 2009, 10:00

walker wrote:

I would solve it with playing with numbers.

1) integers cannot by grater than 8, because 9^2 = 81 > 75 2) write out all squares : 1, 4, 9, 16, 25, 36, 49 3) Do you see the answer? No? 4) 75 is a big integer, so let's one of integers is 7. 75-49=26 - for 2 squares. it is possible for 1+25 (1 and 5) 5) we could begin with 6. 75 - 36 = 39. 25+16=41, 25+9=34, others options are less than 39.

did exactly the same way
_________________

Las cualidades del agua...porque el agua no olvida que su destino es el mar, y que tarde o temprano deberá llegar a él.