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

 It is currently 18 Jun 2019, 00:28

### 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

# What is the total number of positive factors of a?

Author Message
TAGS:

### Hide Tags

Intern
Joined: 01 Dec 2017
Posts: 14
Location: India
GMAT 1: 520 Q42 V22
GMAT 2: 490 Q47 V13
GPA: 2.4
What is the total number of positive factors of a?  [#permalink]

### Show Tags

Updated on: 25 Dec 2018, 08:40
2
00:00

Difficulty:

85% (hard)

Question Stats:

33% (02:21) correct 67% (01:46) wrong based on 38 sessions

### HideShow timer Statistics

What is the total number of positive factors of a?

(1) 2a is a multiple of 50.

(2) a/9 is an integer and has exactly 3 positive factors.

Originally posted by kiran1213 on 24 Dec 2018, 11:02.
Last edited by chetan2u on 25 Dec 2018, 08:40, edited 1 time in total.
Corrected the OA
Math Expert
Joined: 02 Aug 2009
Posts: 7752
Re: What is the total number of positive factors of a?  [#permalink]

### Show Tags

25 Dec 2018, 08:39
3
What is the total number of positive factors of a?

(1) 2a is a multiple of 50.
We do not know what is 2a..
It can be 50, that is 2a=50...a=25=5^2....prime factors is (2+1)=3
Say 2a is 100, that is 2a=100....$$a=50=2*5^2$$. Factors is (1+1)(2+1)=2*3=6
Insufficient.

(2) a/9 is an integer and has exactly 3 positive factors.
This means a/9 is square of a prime number..
Let $$\frac{a}{9}=9.....a=81=3^4$$.. factors =(4+1)=5
Let $$\frac{a}{9}=4.....a=36=3^2*2^2$$.. factors =(2+1)(2+1)=3*3=9

Combined..
a is a multiple of 25.. but $$\frac{√a}{3}$$ is a prime number..
So only possible value is 25*9..
Factors of $$5^23^2$$ are (2+1)(2+1)=9..
C

OA given is wrong..
_________________
##### General Discussion
Manager
Joined: 08 Oct 2018
Posts: 64
Location: India
GPA: 4
WE: Brand Management (Health Care)
Re: What is the total number of positive factors of a?  [#permalink]

### Show Tags

25 Dec 2018, 04:52
kiran1213 wrote:
What is the total number of positive factors of a?

(1) 2a is a multiple of 50.

(2) a/9 is an integer and has exactly 3 positive factors.

Statement (1): 2a is a multiple of 50
Therefore a is a multiple of 50/2 = 25.
if a is a multiple of 25, a can be 25, 50, 75....so on.
Each of these numbers will have different numbers of positive factors.
Hence insufficient.

Statement (2): a/9 is an integer and has exactly 3 positive factors.
We can write this as a=9k, where k is an integer.
Or a=3^2 x k^m
It says that 'a' has exactly 3 positive factors. Therefore a=3^2 x 1 = 3^2 (because if 'k' is anything >1, then a will not have exactly 3 factors, but will have more than 3 factors)
Sufficient.

Hence, B.

I don't understand why OA is D.
_________________
We learn permanently when we teach,
We grow infinitely when we share.
Math Expert
Joined: 02 Aug 2009
Posts: 7752
Re: What is the total number of positive factors of a?  [#permalink]

### Show Tags

25 Dec 2018, 08:41
Darshi04 wrote:
kiran1213 wrote:
What is the total number of positive factors of a?

(1) 2a is a multiple of 50.

(2) a/9 is an integer and has exactly 3 positive factors.

Statement (1): 2a is a multiple of 50
Therefore a is a multiple of 50/2 = 25.
if a is a multiple of 25, a can be 25, 50, 75....so on.
Each of these numbers will have different numbers of positive factors.
Hence insufficient.

Statement (2): a/9 is an integer and has exactly 3 positive factors.
We can write this as a=9k, where k is an integer.
Or a=3^2 x k^m
It says that 'a' has exactly 3 positive factors. Therefore a=3^2 x 1 = 3^2 (because if 'k' is anything >1, then a will not have exactly 3 factors, but will have more than 3 factors)
Sufficient.

Hence, B.

I don't understand why OA is D.

Statement II will not be sufficient..
_________________
Manager
Joined: 08 Oct 2018
Posts: 64
Location: India
GPA: 4
WE: Brand Management (Health Care)
Re: What is the total number of positive factors of a?  [#permalink]

### Show Tags

25 Dec 2018, 09:02
chetan2u wrote:
What is the total number of positive factors of a?

(1) 2a is a multiple of 50.
We do not know what is 2a..
It can be 50, that is 2a=50...a=25=5^2....prime factors is (2+1)=3
Say 2a is 100, that is 2a=100....$$a=50=2*5^2$$. Factors is (1+1)(2+1)=2*3=6
Insufficient.

(2) a/9 is an integer and has exactly 3 positive factors.
This means a/9 is square of a prime number..
Let $$\frac{a}{9}=9.....a=81=3^4$$.. factors =(4+1)=5
Let $$\frac{a}{9}=4.....a=36=3^2*2^2$$.. factors =(2+1)(2+1)=3*3=9

Combined..
a is a multiple of 25.. but $$\frac{√a}{3}$$ is a prime number..
So only possible value is 25*9..
Factors of $$5^23^2$$ are (2+1)(2+1)=9..
C

OA given is wrong..

This was a much needed clarification. Thank you chetan2u
I've also understood why B won't be sufficient. Many thanks again!
_________________
We learn permanently when we teach,
We grow infinitely when we share.
Re: What is the total number of positive factors of a?   [#permalink] 25 Dec 2018, 09:02
Display posts from previous: Sort by