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

 It is currently 15 Aug 2018, 13:56

### 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

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

# Which of the following CANNOT be expressed as the sum of squares of tw

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 47920
Which of the following CANNOT be expressed as the sum of squares of tw  [#permalink]

### Show Tags

12 Jul 2018, 01:16
00:00

Difficulty:

15% (low)

Question Stats:

91% (01:11) correct 9% (01:09) wrong based on 34 sessions

### HideShow timer Statistics

Which of the following CANNOT be expressed as the sum of squares of two integer?

A 13
B 17
C 21
D 29
E 34

_________________
examPAL Representative
Joined: 07 Dec 2017
Posts: 553
Re: Which of the following CANNOT be expressed as the sum of squares of tw  [#permalink]

### Show Tags

12 Jul 2018, 01:54
Bunuel wrote:
Which of the following CANNOT be expressed as the sum of squares of two integer?

A 13
B 17
C 21
D 29
E 34

As we don't have that many options, we'll test them all.
This is an Alternative approach.

We only need to look at the squares up to 5^2 (as 6^2 = 36 is larger than our largest value).
So there are a total of 5 choose 2 = 10 options.
1 + 4 = 5
1 + 9 = 10
1 + 16 = 17 **
1 + 25 = 26
4 + 9 = 13 **
4 + 16 = 20
4 + 25 = 29 **
9 + 16 = 25
9 + 25 = 34 **
16 + 25 = 41

_________________

David
Senior tutor at examPAL
Signup for a free GMAT course

We won some awards:

Save up to \$250 on examPAL packages (special for GMAT Club members)

Director
Joined: 20 Feb 2015
Posts: 511
Concentration: Strategy, General Management
Re: Which of the following CANNOT be expressed as the sum of squares of tw  [#permalink]

### Show Tags

12 Jul 2018, 02:30
Bunuel wrote:
Which of the following CANNOT be expressed as the sum of squares of two integer?

A 13
B 17
C 21
D 29
E 34

13=2^2+3^2
17=4^2+1^2
21=Cannot be expressed
29=5^2+2^2
34=5^2+3^2

C
Senior Manager
Joined: 31 Oct 2013
Posts: 477
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
Re: Which of the following CANNOT be expressed as the sum of squares of tw  [#permalink]

### Show Tags

12 Jul 2018, 03:53
Bunuel wrote:
Which of the following CANNOT be expressed as the sum of squares of two integer?

A 13
B 17
C 21
D 29
E 34

A bit tricky question. Number testing is the way to get the answer.

$$3^2$$ + $$2^2$$ = 13
$$4^2$$ + $$1^1$$ = 17
$$5^2$$+ $$2^2$$ = 29
$$5^2$$ + $$3^2$$ = 34

Now , option C is left. That's our answer. Try different number less than 21. There is a reason. 21 = 3*7 or 21*1. See none of the factors are square of an integer except 1. Thus it is also impossible to express 21 as a sum of the square of the 2 integers.

Senior Manager
Status: Asst. Manager
Joined: 01 Oct 2017
Posts: 475
Location: India
Concentration: Operations, Entrepreneurship
GPA: 4
WE: Supply Chain Management (Energy and Utilities)
Re: Which of the following CANNOT be expressed as the sum of squares of tw  [#permalink]

### Show Tags

12 Jul 2018, 13:59
1
Bunuel wrote:
Which of the following CANNOT be expressed as the sum of squares of two integer?

A 13
B 17
C 21
D 29
E 34

Every prime of the form (4k+1) can be expressed as the sum of two squares..
Among the answer options 13,17, and 29 are prime and they can be written in the form (4k+1). So, eliminate A,B, and D.

when the number is not prime:- If each of the factors of the integer can be written as the sum of two squares is itself expressible as the sum of two squares.
Prime factorization of 34=2*17, ($$2=1^2+1^2$$ & 17 is in the form of 4k+1. So, both 2 & 17 are perfect squares)
Therefore, 34 is a sum of squares of two integer.So, eliminate E.

Ans. (C)
_________________

Regards,

PKN

Rise above the storm, you will find the sunshine

Re: Which of the following CANNOT be expressed as the sum of squares of tw &nbs [#permalink] 12 Jul 2018, 13:59
Display posts from previous: Sort by

# Events & Promotions

 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®.