Last visit was: 13 Jun 2024, 22:59 It is currently 13 Jun 2024, 22:59
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
SORT BY:
Date
Tags:
Show Tags
Hide Tags
User avatar
Senior Manager
Senior Manager
Joined: 25 Jun 2011
Status:Finally Done. Admitted in Kellogg for 2015 intake
Posts: 395
Own Kudos [?]: 16888 [232]
Given Kudos: 217
Location: United Kingdom
Concentration: International Business, Strategy
GMAT 1: 730 Q49 V45
GPA: 2.9
WE:Information Technology (Consulting)
Send PM
Most Helpful Reply
Math Expert
Joined: 02 Sep 2009
Posts: 93696
Own Kudos [?]: 631588 [142]
Given Kudos: 82279
Send PM
avatar
SVP
SVP
Joined: 27 Dec 2012
Status:The Best Or Nothing
Posts: 1559
Own Kudos [?]: 7264 [102]
Given Kudos: 193
Location: India
Concentration: General Management, Technology
WE:Information Technology (Computer Software)
Send PM
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6814
Own Kudos [?]: 30532 [2]
Given Kudos: 799
Location: Canada
Send PM
Re: The number 75 can be written as the sum of the squares of 3 different [#permalink]
1
Kudos
1
Bookmarks
Expert Reply
Top Contributor
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


We're looking for 3 DIFFERENT squares that add to 75

Here are the only squares we need to consider: 1, 4, 9, 16, 25, 36, 49, 64
Can you find 3 that add to 75?
After some fiddling, we may notice that 1 + 25 + 49
In other words, 1² + 5² + 7² = 75
We want the SUM of 1 + 5 + 7, which is 13

Answer: E

Cheers,
Brent
General Discussion
avatar
Manager
Manager
Joined: 26 Apr 2011
Posts: 191
Own Kudos [?]: 44 [12]
Given Kudos: 14
Send PM
Re: The number 75 can be written as the sum of the squares of 3 different [#permalink]
8
Kudos
4
Bookmarks
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
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4480
Own Kudos [?]: 28747 [6]
Given Kudos: 130
Re: need help with this PS question.... [#permalink]
5
Kudos
1
Bookmarks
Expert Reply
Hi, there. I'm happy to give my 2 cents on this. :)

First of all, this is a relatively difficult question for GMAT math. You would only see a question of this difficulty if you were already answering almost all of the math questions correctly.

I can't really suggest much other than trial-and-error. Since 25 is a factor of 75, I figured it might make sense if 25 were one of the three squares. That means the other two squares would have to add up to 50. Well, conveniently, 7^2 = 49, so 7^2 + 1^2 = 50, and 7^2 + 1^2 + 5^2 = 75. The three numbers are 1, 5, and 7, and those have a sum of 13. Answer = E.

Here, I was really just following my intuition for numbers, which is really just a notch above pure guess-and-check. I don't know the source of this question, but the real GMAT tends to give questions that admit of either a methodical approach or an elegant solution, whereas this more or less requires some guess & check, some poking around in the dark. That's just not the style of questions that the GMAC dishes out.

Please let me know if you have any questions on what I've said here.

Mike :)
User avatar
Senior Manager
Senior Manager
Joined: 25 Jun 2011
Status:Finally Done. Admitted in Kellogg for 2015 intake
Posts: 395
Own Kudos [?]: 16888 [0]
Given Kudos: 217
Location: United Kingdom
Concentration: International Business, Strategy
GMAT 1: 730 Q49 V45
GPA: 2.9
WE:Information Technology (Consulting)
Send PM
Re: The number 75 can be written as the sum of the squares of 3 different [#permalink]
Thanks for a very clear explanation Bunuel.
User avatar
Manager
Manager
Joined: 23 Feb 2012
Posts: 195
Own Kudos [?]: 87 [5]
Given Kudos: 22
Location: India
Concentration: Finance, Entrepreneurship
Schools: Said
GMAT 1: 710 Q44 V44
GPA: 2.9
WE:Marketing (Computer Software)
Send PM
Re: The number 75 can be written as the sum of the squares of 3 different [#permalink]
4
Kudos
1
Bookmarks
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.
User avatar
Manager
Manager
Joined: 27 Oct 2011
Posts: 85
Own Kudos [?]: 925 [1]
Given Kudos: 4
Location: United States
Concentration: Finance, Strategy
GPA: 3.7
WE:Account Management (Consumer Products)
Send PM
Re: The number 75 can be written as the sum of the squares of 3 different [#permalink]
1
Kudos
thanks for the solution... was hoping for another solution other than just brute calculation. bunel you rock tho.
avatar
Manager
Manager
Joined: 07 Jun 2014
Posts: 69
Own Kudos [?]: 9 [0]
Given Kudos: 42
Re: The number 75 can be written as the sum of the squares of 3 different [#permalink]
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.
User avatar
Manager
Manager
Joined: 11 Oct 2013
Posts: 70
Own Kudos [?]: 287 [2]
Given Kudos: 137
Concentration: Marketing, General Management
GMAT 1: 600 Q41 V31
Send PM
Re: The number 75 can be written as the sum of the squares of 3 different [#permalink]
2
Bookmarks
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?


Bunuel's bruteforce using odd and even looks promising! I'd also like to add that you could eliminate some answer options using the same approach.
Since 75 is an odd number. The squares must be of the form -
\(Odd^2 + Odd^2 + Odd^2\) OR
\(Even^2 + Even^2 + Odd^2\)

Alternatively -
\(Odd + Odd + Even\) OR \(Even + Even + Odd\). Thus, the sum of these numbers must be ODD. Eliminate answer option B and C.
Breaking 13, 15, and 17 using further bruteforce. We get \(7^2 + 1^2 + 5^2\). 7 + 1 + 5 = 13. Answer Option A

Bunuel - Please correct me I am wrong, but if this is a general question that appears on the exam, we can conclude -
Sum of squares equal to a number?
* If the number is odd --> Correct answer option will be Odd.
* If the number is even --> Correct answer option will be Even
GMAT Club Legend
GMAT Club Legend
Joined: 19 Dec 2014
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Posts: 21843
Own Kudos [?]: 11720 [6]
Given Kudos: 450
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Send PM
Re: The number 75 can be written as the sum of the squares of 3 different [#permalink]
5
Kudos
1
Bookmarks
Expert Reply
Hi All,

This question can be solved with a bit of 'brute force' arithmetic, but the speed with which you solve it will likely depend on how quickly you can write everything down and how you do the work.

We're asked to find the three positive integers, whose squares add up to 75. To start, we should write down the list of possible squares:

1
4
9
16
25
36
49
64

We're limited to these 8 numbers. To work efficiently, we should work from 'greatest to least'..

If we use 64, then the other two numbers have to add up to 11....but there's NO WAY to make that happen (so 64 is NOT one of the numbers we need).

Next, let's try 49... then the other two numbers have to add up to 26....25 and 1 'fit', so the three numbers are 49, 25 and 1 (7, 5 and 1 --> that sum = 13).

Final Answer:

GMAT assassins aren't born, they're made,
Rich
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 19013
Own Kudos [?]: 22400 [3]
Given Kudos: 286
Location: United States (CA)
Send PM
Re: The number 75 can be written as the sum of the squares of 3 different [#permalink]
1
Kudos
2
Bookmarks
Expert Reply
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


If the sum of 3 different perfect squares is 75, each must be less than 75. So, we want to start by writing out the perfect squares that are less than 75:

1, 4, 9, 16, 25, 36, 49, 64

In this problem, there is no shortcut to determining which 3 squares add up to 75; however, it is strategic to start with the largest one, 64, and move down the list if it doesn’t work:

64 + 11 = 75

There is no way 11 can be written as a sum of two squares. So, we move down to 49:

49 + 26 = 75

We see that 26 can be written as the sum of 25 and 1; that is:

49 + 25 + 1 = 75

We have found the three perfect squares that sum to 75. In other words:

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

The sum of 7, 5, and 1 is 7 + 5 + 1 = 13.

Answer: E
Intern
Intern
Joined: 05 Feb 2019
Posts: 1
Own Kudos [?]: 0 [0]
Given Kudos: 1
Location: United States
Schools: HSG SIM "22
Send PM
Re: The number 75 can be written as the sum of the squares of 3 different [#permalink]
I got this question on a practice test I took via GMAC.

Oddly enough, if you prime factorize 75 (15->5 and 3 and 5), you will get 5+5+3= 13. Is that a coincidence or is there actually something behind it?

I know that the question is not asking for this, but I found it a bit strange. Any insight on this would be helpful! Thank you
GMAT Club Legend
GMAT Club Legend
Joined: 19 Dec 2014
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Posts: 21843
Own Kudos [?]: 11720 [0]
Given Kudos: 450
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Send PM
Re: The number 75 can be written as the sum of the squares of 3 different [#permalink]
Expert Reply
Hi MTLGMAT514,

Since you can't actually get to MOST integers by adding up three squares of integers, this result is just a coincidence.

GMAT assassins aren't born, they're made,
Rich
Intern
Intern
Joined: 24 Jan 2020
Posts: 8
Own Kudos [?]: 0 [0]
Given Kudos: 3
Location: United States (NY)
GMAT 1: 710 Q47 V41
GPA: 3.51
Send PM
Re: The number 75 can be written as the sum of the squares of 3 different [#permalink]
mikemcgarry wrote:
Hi, there. I'm happy to give my 2 cents on this. :)

First of all, this is a relatively difficult question for GMAT math. You would only see a question of this difficulty if you were already answering almost all of the math questions correctly.

I can't really suggest much other than trial-and-error. Since 25 is a factor of 75, I figured it might make sense if 25 were one of the three squares. That means the other two squares would have to add up to 50. Well, conveniently, 7^2 = 49, so 7^2 + 1^2 = 50, and 7^2 + 1^2 + 5^2 = 75. The three numbers are 1, 5, and 7, and those have a sum of 13. Answer = E.

Here, I was really just following my intuition for numbers, which is really just a notch above pure guess-and-check. I don't know the source of this question, but the real GMAT tends to give questions that admit of either a methodical approach or an elegant solution, whereas this more or less requires some guess & check, some poking around in the dark. That's just not the style of questions that the GMAC dishes out.

Please let me know if you have any questions on what I've said here.

Mike :)


newish here - how come this is labeled sub 600 if it's tough? I found this on a official practice gmat
GMAT Club Legend
GMAT Club Legend
Joined: 19 Dec 2014
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Posts: 21843
Own Kudos [?]: 11720 [1]
Given Kudos: 450
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Send PM
Re: The number 75 can be written as the sum of the squares of 3 different [#permalink]
1
Kudos
Expert Reply
Hi maxraxstax,

As far as the 'knowledge' and the 'skills' needed to answer this question are concerned, this is not a particularly difficult question (at its core, you're just adding some 1-digit and 2-digit numbers together - and that's low level Arithmetic). As such, the sub-600 'label' is appropriate.

GMAT assassins aren't born, they're made,
Rich
Intern
Intern
Joined: 21 Aug 2020
Posts: 17
Own Kudos [?]: 6 [0]
Given Kudos: 57
Location: India
Send PM
Re: The number 75 can be written as the sum of the squares of 3 different [#permalink]
­Thanks Bunel for the approach
GMAT Club Bot
Re: The number 75 can be written as the sum of the squares of 3 different [#permalink]
Moderator:
Math Expert
93696 posts