Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 17 Jul 2019, 04:01

### 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

# Is C square of an Integer? 1) Sum of the factors of integer C is ODD

Author Message
TAGS:

### Hide Tags

CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2959
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Is C square of an Integer? 1) Sum of the factors of integer C is ODD  [#permalink]

### Show Tags

27 Apr 2018, 01:46
00:00

Difficulty:

75% (hard)

Question Stats:

51% (01:54) correct 49% (01:44) wrong based on 60 sessions

### HideShow timer Statistics

Is C square of an Integer?

1) Sum of the factors of integer C is ODD
2) Number of distinct factors of Integer C is ODD

Source: www.GMATinsight.com

_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
Manager
Joined: 05 Dec 2017
Posts: 53
Location: India
WE: Analyst (Commercial Banking)
Re: Is C square of an Integer? 1) Sum of the factors of integer C is ODD  [#permalink]

### Show Tags

27 Apr 2018, 02:06
GMATinsight wrote:
Is C square of an Integer?

1) Sum of the factors of integer C is ODD
2) Number of distinct factors of Integer C is ODD

Source: http://www.GMATinsight.com

St1 : Sum of the factors of integer C is ODD

Factors of 9 = 1, 3, 9; so sum : ODD
Factors of 8 = 1, 2, 4, 8 Sum : ODD

Hence statement 1 insuff

St2 : Number of distinct factors of Integer C is ODD
For a int N = $$x^ay^b..$$ the number of factors are $$(a+1)*(b+1)...$$
So if $$(a+1)*(b+1)...$$ is odd, this means each $$(a+1), (b+1),...$$ is odd

or A, B,... are even
Hence the number $$N = x^{even}*Y^{even}...$$

So We can say Number is square of number.

Hence Option B
Senior PS Moderator
Status: It always seems impossible until it's done.
Joined: 16 Sep 2016
Posts: 751
GMAT 1: 740 Q50 V40
GMAT 2: 770 Q51 V42
Re: Is C square of an Integer? 1) Sum of the factors of integer C is ODD  [#permalink]

### Show Tags

27 Apr 2018, 03:34
GMATinsight wrote:
Is C square of an Integer?

1) Sum of the factors of integer C is ODD
2) Number of distinct factors of Integer C is ODD

Source: http://www.GMATinsight.com

Let us try to solve this by trying numbers :

let n = 4. we know n is a square of integer 2.

1) Sum of the factors of integer C is ODD. Not sufficient 1 + 2 + 4 = 7 ( true for 4) 1 + 2 + 3 + 4 + 6 + 9 + 12 + 18 + 36 = 91 ( true for 36) 1 + 17 + 289 ( true for 289 ).
Although it is true for perfect squares, it is also true for other which are not perfect squares

ex. 1 + 2 + 4 + 8 = 15 ( also true for 8)

2) Number of distinct factors of Integer C is ODD Suff this is a property which is easily seen to be true. all the factors will pair out and the perfect square will remain. look at the factors of 36 to verify this

Hence Option (B) is our answer.

Best,
_________________
Regards,

“Do. Or do not. There is no try.” - Yoda (The Empire Strikes Back)
Intern
Joined: 16 Aug 2018
Posts: 28
Concentration: General Management, Strategy
Schools: Guanghua"21 (A)
GMAT 1: 700 Q49 V36
Re: Is C square of an Integer? 1) Sum of the factors of integer C is ODD  [#permalink]

### Show Tags

22 Aug 2018, 17:55
statement 1:
we can only infer that no. of odd prime factors is odd but we don't know the no. of even prime factor (2):
eg. 3^2*2^3 has 3 odd factors and 9 even factors but the sum of the factors is odd
3^2*2^4 has 3 odd factors and 12 even factors but the sum of the factors is still odd
statement 2:
assume C=A^a*B^b*E^e
no. of factors: (a+1)(b+1)(c+1)
a,b,e all have to be even no. to have odd no. of distince factors. hence C is a squre
Re: Is C square of an Integer? 1) Sum of the factors of integer C is ODD   [#permalink] 22 Aug 2018, 17:55
Display posts from previous: Sort by