GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 22 Oct 2019, 22:16

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

The number 75 can be written as the sum of the squares of 3 different

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Senior Manager
Senior Manager
avatar
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 439
Location: United Kingdom
Concentration: International Business, Strategy
GMAT 1: 730 Q49 V45
GPA: 2.9
WE: Information Technology (Consulting)
The number 75 can be written as the sum of the squares of 3 different  [#permalink]

Show Tags

New post 26 Dec 2011, 11:15
12
1
67
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

80% (01:32) correct 20% (01:48) wrong based on 650 sessions

HideShow timer Statistics

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

_________________
Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
GMAT ==> 730
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58430
The number 75 can be written as the sum of the squares of 3 different  [#permalink]

Show Tags

New post 19 Jan 2012, 19:19
50
37
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.

Answer: E.
_________________
Most Helpful Community Reply
SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1747
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: The number 75 can be written as the sum of the squares of 3 different  [#permalink]

Show Tags

New post 08 Aug 2014, 01:23
79
1
11
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
_________________
Kindly press "+1 Kudos" to appreciate :)
General Discussion
Manager
Manager
avatar
Joined: 26 Apr 2011
Posts: 201
GMAT ToolKit User Reviews Badge
Re: The number 75 can be written as the sum of the squares of 3 different  [#permalink]

Show Tags

New post 27 Dec 2011, 03:53
8
3
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
User avatar
G
Joined: 28 Dec 2011
Posts: 4472
Re: need help with this PS question....  [#permalink]

Show Tags

New post 20 Jan 2012, 12:37
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 :)
_________________
Mike McGarry
Magoosh Test Prep


Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)
Senior Manager
Senior Manager
avatar
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 439
Location: United Kingdom
Concentration: International Business, Strategy
GMAT 1: 730 Q49 V45
GPA: 2.9
WE: Information Technology (Consulting)
Re: The number 75 can be written as the sum of the squares of 3 different  [#permalink]

Show Tags

New post 24 Jan 2012, 18:37
Thanks for a very clear explanation Bunuel.
_________________
Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
GMAT ==> 730
Manager
Manager
User avatar
Joined: 23 Feb 2012
Posts: 197
Location: India
Concentration: Finance, Entrepreneurship
Schools: Said
GMAT 1: 710 Q44 V44
GPA: 2.9
WE: Marketing (Computer Software)
Re: The number 75 can be written as the sum of the squares of 3 different  [#permalink]

Show Tags

New post 12 Mar 2012, 23:59
4
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.
_________________
If you like it, Kudo it!

"There is no alternative to hard work. If you don't do it now, you'll probably have to do it later. If you didn't need it now, you probably did it earlier. But there is no escaping it."

710 Debrief. Crash and Burn
Manager
Manager
User avatar
Joined: 27 Oct 2011
Posts: 117
Location: United States
Concentration: Finance, Strategy
GPA: 3.7
WE: Account Management (Consumer Products)
Re: The number 75 can be written as the sum of the squares of 3 different  [#permalink]

Show Tags

New post 18 Apr 2012, 20:11
1
thanks for the solution... was hoping for another solution other than just brute calculation. bunel you rock tho.
_________________
DETERMINED TO BREAK 700!!!
Manager
Manager
avatar
Joined: 07 Jun 2014
Posts: 69
GMAT 1: 600 Q42 V27
GPA: 3.55
WE: Engineering (Other)
GMAT ToolKit User
Re: The number 75 can be written as the sum of the squares of 3 different  [#permalink]

Show Tags

New post 29 Jun 2014, 20:12
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.
Senior Manager
Senior Manager
User avatar
B
Joined: 14 Jul 2013
Posts: 275
Location: India
Concentration: Marketing, Strategy
GMAT 1: 690 Q49 V34
GMAT 2: 670 Q49 V33
GPA: 3.6
WE: Brand Management (Retail)
GMAT ToolKit User Reviews Badge
Re: The number 75 can be written as the sum of the squares of 3 different  [#permalink]

Show Tags

New post 09 Aug 2014, 08:31
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
_________________
Manager
Manager
avatar
Joined: 21 Sep 2008
Posts: 170
Concentration: Strategy, Economics
GMAT Date: 07-17-2015
GPA: 3.57
GMAT ToolKit User
Re: The number 75 can be written as the sum of the squares of 3 different  [#permalink]

Show Tags

New post 12 Jun 2015, 00:34
Yeah I misread this question and thought it was asking for factors so I had 5 5 3 which also add up to 13

Oh God.
_________________
Life with the GMAT:

Jerome: Ben, c'est 20 secondes de plus qu'hier sur le meme parcours! C'etait bien le meme parcours la, non?!
Gigi: Mais t'enerve pas, Jerome, je crois que t'as accroche une porte.
Jerome: *$&#(*%&(*#%&
Intern
Intern
avatar
Joined: 13 Aug 2014
Posts: 23
GMAT 1: 750 Q51 V39
Re: The number 75 can be written as the sum of the squares of 3 different  [#permalink]

Show Tags

New post 10 Jul 2015, 16:48
1
FatRiverPuff wrote:
Yeah I misread this question and thought it was asking for factors so I had 5 5 3 which also add up to 13

Oh God.


Um...the sum of factors of 75 = 1 + 3 + 5 + 15 + 25 + 75. You just got catastrophically lucky!

Oh God indeed.
Manager
Manager
User avatar
Joined: 11 Oct 2013
Posts: 98
Concentration: Marketing, General Management
GMAT 1: 600 Q41 V31
GMAT ToolKit User
Re: The number 75 can be written as the sum of the squares of 3 different  [#permalink]

Show Tags

New post 29 Nov 2015, 01:31
1
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
_________________
Its not over..
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15310
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: The number 75 can be written as the sum of the squares of 3 different  [#permalink]

Show Tags

New post 29 Nov 2015, 11:05
3
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
_________________
Contact Rich at: Rich.C@empowergmat.com
Image


The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Board of Directors
User avatar
D
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4774
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
GMAT ToolKit User
Re: The number 75 can be written as the sum of the squares of 3 different  [#permalink]

Show Tags

New post 29 Nov 2015, 11:14
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?


1^2 = 1
2^2 = 4
3^2 = 9
4^2 = 16
5^2 = 25
6^2 = 36
7^2 = 49
8^2 = 64


9^2 = 81
10^2 = 100


Quote:
The sum of the squares of 3 different positive integers is 75


Start from 8^2 = 64

75 - 64 = 11 ; we need 2 other squares to add upto 11 - No possibility

Then 7^2 = 49

75 - 49 = 26 ; we need 2 other squares to add upto 26 - Possibile squares are 25 , 1

So, the required numbers are 7 , 5 and 1

Hence the numbers are 1,5,7

_________________
Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
SVP
SVP
avatar
B
Joined: 06 Nov 2014
Posts: 1873
Re: The number 75 can be written as the sum of the squares of 3 different  [#permalink]

Show Tags

New post 26 Jun 2016, 22:18
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?

75 = a^2 + b^2 + c^2

1^2 = 1
2^2 = 4
3^2 = 9
4^2 = 16
5^2 = 25
6^2 = 36
7^2 = 49
8^2 = 64

We need to put in the values of a,b and c from the above list of values and see which ones satisfy.
71 = 49 + 25 + 1 = 7^2 + 5^2 + 1^2
Hence (a,b,c) = (7,5,1)
a+b+c = 7+5+1 = 13

Correct Option: E
Target Test Prep Representative
User avatar
D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8137
Location: United States (CA)
Re: The number 75 can be written as the sum of the squares of 3 different  [#permalink]

Show Tags

New post 26 Jul 2017, 16:43
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
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Manager
Manager
User avatar
S
Joined: 09 Jun 2018
Posts: 93
GMAT 1: 610 Q42 V33
GMAT 2: 620 Q40 V35
GMAT 3: 660 Q41 V40
GPA: 3.32
Re: The number 75 can be written as the sum of the squares of 3 different  [#permalink]

Show Tags

New post 30 Apr 2019, 09:34
I began by breaking down 75 and all the squares that go into 75.
1^2 = 1
2^2 = 4
3^2 = 9
4^2 = 16
5^2 = 25
6^2 = 36
7^2 = 49
8^2 = 64

Now, 75 is an odd number so the squares that add up to it have to be odd+odd+odd=odd or even+even+odd=odd

Starting with the even+even+odd=odd option, we can select a number of options from our list of numbers but none add to 75.

With a bit of number sense, I could see that 1+49=50 and 50+25=75.

This leads to 1+7+5=13

The trick here is to not rule out 1 as a square that goes into 75.

Answer choice E.

Please give kudos if this helped you in any way!
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58430
Re: The number 75 can be written as the sum of the squares of 3 different  [#permalink]

Show Tags

New post 07 Oct 2019, 08:01
Intern
Intern
avatar
Joined: 05 Feb 2019
Posts: 1
Re: The number 75 can be written as the sum of the squares of 3 different  [#permalink]

Show Tags

New post 14 Oct 2019, 13:05
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 Bot
Re: The number 75 can be written as the sum of the squares of 3 different   [#permalink] 14 Oct 2019, 13:05

Go to page    1   2    Next  [ 22 posts ] 

Display posts from previous: Sort by

The number 75 can be written as the sum of the squares of 3 different

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





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