GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 20 Jan 2020, 06:56

### 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

# A number N^2 has 35 factors. How many factors can N have?

Author Message
TAGS:

### Hide Tags

Retired Moderator
Status: The best is yet to come.....
Joined: 10 Mar 2013
Posts: 484
A number N^2 has 35 factors. How many factors can N have?  [#permalink]

### Show Tags

20 Oct 2017, 05:07
3
16
00:00

Difficulty:

45% (medium)

Question Stats:

62% (01:41) correct 38% (01:36) wrong based on 142 sessions

### HideShow timer Statistics

A number $$N^2$$ has 35 factors. How many factors can $$N$$ have?

A. 6 or 10 factors
B. 8 or 14 factors
C. 10 or 16 factors
D. 12 or 18 factors
E. 14 or 20 factors

_________________
Hasan Mahmud
Manager
Joined: 01 Aug 2017
Posts: 220
Location: India
GMAT 1: 500 Q47 V15
GPA: 3.4
WE: Information Technology (Computer Software)
A number N^2 has 35 factors. How many factors can N have?  [#permalink]

### Show Tags

20 Oct 2017, 05:27
1
Lets take an example 12. Factors of 12 are 2- 2time and 3- 1 time. Total no of factor - (2+1) * (1+1) =6.
For 12*12 - it has 2 - 4times and 3 - 2 timed. Total no of factor - 5*3=15

Case 1 :-

N=x.y
For N*N
Trying reverse approach. 35 = 5*7.
Factors are x - 4times and y- 6times.
FOR N - x -2 times and y- 3 times.
Total no of factor is (2+1)*(3+1)=12

Case 2:-

If N^2 is raised to the power of 34.
N^2 will have 34 factors.
And hence for N we have 17 factors.
Hence total no of factor as 17+1 = 18

Ans is D
Math Expert
Joined: 02 Aug 2009
Posts: 8344
A number N^2 has 35 factors. How many factors can N have?  [#permalink]

### Show Tags

20 Oct 2017, 06:22
Mahmud6 wrote:
A number $$N^2$$ has 35 factors. How many factors can $$N$$ have?

A. 6 or 10 factors
B. 8 or 14 factors
C. 10 or 16 factors
D. 12 or 18 factors
E. 14 or 20 factors

Hi...

Factors of 35 are 1,5,7,35 .. 35 = 1*35= 5*7..

So we can look for two cases..

1) where N or $$N^2$$ contains ONLY one type of prime factor, a, that is $$N=a^x$$
Number of factors =(power of factor +1)=35.......
In this case power of the prime factor will be TWO times that of N as
$$N^2=a^2x....... So 2x+1=35....x=17.. N=a^17$$
So factor of N =17+1=18

2) where N^2 contains TWO prime factors...a and b.
So $$N=a^x*b^y..........N^2=a^2x*b^2y..$$
Number of factors=$$(2x+1)(2y+1)=35=5*7$$.....
Only possibility is when 2x+1=5....x=2
And $$2y+1=7...y=3$$
So $$N=a^2*b^3$$..
Number of factors=(2+1)(3+1)=3*4=12

Ans 12 and 18
D
_________________
Intern
Joined: 30 May 2017
Posts: 7
Re: A number N^2 has 35 factors. How many factors can N have?  [#permalink]

### Show Tags

20 Oct 2017, 09:28
1
1
Case 1: N^2 is composed by two different primes
A number with 35 factors = a^6*b^4 (to count the number of factors we must add one to the power and multiply them, for instance, (6+1)*(4+1) = 7*5 = 35 factors.

So N = a^3*b^2. The number of factors of N can be obtained in the same way that we obtained the 35 factors of N^2.
Number of factors of N =(3+1)*(2+1) = 12 factors

Case 2: N^2 is composed by one prime
Using the same rule to count factors mentioned above, N^2 = a^34
so N = a^17 then N has 18 factors

Manager
Joined: 06 Aug 2017
Posts: 77
GMAT 1: 570 Q50 V18
GMAT 2: 610 Q49 V24
GMAT 3: 640 Q48 V29
A number N^2 has 35 factors. How many factors can N have?  [#permalink]

### Show Tags

21 Oct 2017, 04:59
Mahmud6 wrote:
A number $$N^2$$ has 35 factors. How many factors can $$N$$ have?

A. 6 or 10 factors
B. 8 or 14 factors
C. 10 or 16 factors
D. 12 or 18 factors
E. 14 or 20 factors

D is the answer as follows.

Sometime in GMAT where we have time crunch we have to consider specific case based on the answer options provided.

Here, particularly in this question just by considering a single prime factor will be sufficient to answer the question.

Lets assume $$a^p = N^2$$ => since it has 35 factors including N^2, hence p = 34
For N the number of factors will be 17 ($$\frac{34}{2}$$). Considering N as one of the factor the number of factors will become 18.

Only D satisfies the condition, hence no need to consider the case of multiple prime factors.

Hope, I am clear.
Non-Human User
Joined: 09 Sep 2013
Posts: 13988
Re: A number N^2 has 35 factors. How many factors can N have?  [#permalink]

### Show Tags

22 Nov 2019, 22:44
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: A number N^2 has 35 factors. How many factors can N have?   [#permalink] 22 Nov 2019, 22:44
Display posts from previous: Sort by