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

 It is currently 10 Dec 2018, 17:09

### 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

## Events & Promotions

###### Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
• ### Free lesson on number properties

December 10, 2018

December 10, 2018

10:00 PM PST

11:00 PM PST

Practice the one most important Quant section - Integer properties, and rapidly improve your skills.
• ### Free GMAT Prep Hour

December 11, 2018

December 11, 2018

09:00 PM EST

10:00 PM EST

Strategies and techniques for approaching featured GMAT topics. December 11 at 9 PM EST.

# If x represents the number of positive factors of integer y, is x odd

Author Message
TAGS:

### Hide Tags

Manager
Joined: 03 Jul 2013
Posts: 89
Schools: ISB '17 (A), IIMC (A)
GMAT 1: 660 Q48 V32
If x represents the number of positive factors of integer y, is x odd  [#permalink]

### Show Tags

02 Oct 2014, 19:39
3
18
00:00

Difficulty:

55% (hard)

Question Stats:

53% (00:55) correct 47% (00:39) wrong based on 377 sessions

### HideShow timer Statistics

If x represents the number of positive factors of integer y, is x odd?

(1) y = n! where n is a positive integer greater than 1
(2) y = m^2 − 1 where m is a positive integer greater than 1

_________________

Sometimes standing still can be, the best move you ever make......

Math Expert
Joined: 02 Sep 2009
Posts: 51072
Re: If x represents the number of positive factors of integer y, is x odd  [#permalink]

### Show Tags

02 Oct 2014, 23:59
5
17
If x represents the number of positive factors of integer y, is x odd?

The question asks whether the number of factors of y is odd. The number of distinct factors of a perfect square is ALWAYS ODD. The reverse is also true: if a number has the odd number of distinct factors then it's a perfect square. So, the question asks whether y is a perfect square.

(1) y = n! where n is a positive integer greater than 1. Among factorials, only 0! and 1! are perfect squares. So, y is not. Sufficient.

(2) y = m^2 − 1 where m is a positive integer greater than 1 --> y is 1 less, than a perfect square, so not a perfect square (two positive consecutive integers cannot both be prefect squares). Sufficient.

_________________
##### General Discussion
Manager
Joined: 03 Jul 2013
Posts: 89
Schools: ISB '17 (A), IIMC (A)
GMAT 1: 660 Q48 V32
Re: If x represents the number of positive factors of integer y, is x odd  [#permalink]

### Show Tags

02 Oct 2014, 19:42
1
My Aprproach:

Statement 1)

when n=2, y=2, factors of 2 are 1,2 so x=2
when n=3, y=6, factors of 6 are 1,2,3,6 so x=4
n=4,y=24, factors of y are 1,2,3,4,6,8,12,24 x= 8

hence x can never be odd. Sufficient.

Statement 2)

m=2, y=1, factors of y =1, so x=1
m=3, y=8, factors of y=1,2,4,8 x=4

Insufficient as x can be even or odd.

_________________

Sometimes standing still can be, the best move you ever make......

Manager
Joined: 02 Jul 2012
Posts: 189
Location: India
Schools: IIMC (A)
GMAT 1: 720 Q50 V38
GPA: 2.6
WE: Information Technology (Consulting)
Re: If x represents the number of positive factors of integer y, is x odd  [#permalink]

### Show Tags

02 Oct 2014, 22:48
1
1
If x represents the number of positive factors of integer y, is x odd?

y=n! where n is a positive integer greater than 1

y=m^2−1 where m is a positive integer greater than 1

a) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
b) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
c) Both statements (1) and (2) TOGETHER are sufficient to answer the question asked; but NEITHER statement ALONE is sufficient
e) Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed

Y = n! = Since n > 1, What ever be the number, the number of factors of n! will always be even. Here's how:

For any number n, n! = 1 * 2 * 3 * 4.... n

No. of factors of 1 = 1 i.e 1
No. of factors of 2 = 2 i.e 1, 2
No. of factors of 3 = 2 i.e 1, 3
etc. etc.

This would mean that what ever be the numbers ahead and what ever be their number of factors (Even / Odd), they would always be multiplied by an even number. Since the number of factors are calculated by multiplying the number of factors of each prime factor.

Now the correct answer to this question will either be A or D. To analyze it, lets look at choice B.

y=m^2−1 m>1

y = (m + 1) (m - 1)
This too will always lead to an even choice since either of m + 1 and m - 1 will have even number of factors.

Therefore, this can be answered by using either of choices.

Ans. D
_________________

Give KUDOS if the post helps you...

Intern
Joined: 12 Sep 2014
Posts: 3
Re: If x represents the number of positive factors of integer y, is x odd  [#permalink]

### Show Tags

03 Oct 2014, 11:07
Bunuel wrote:
If x represents the number of positive factors of integer y, is x odd?

The question asks whether the number of factors of y is odd. The number of distinct factors of a perfect square is ALWAYS ODD. The reverse is also true: if a number has the odd number of distinct factors then it's a perfect square. So, the question asks whether y is a perfect square.

(1) y = n! where n is a positive integer greater than 1. Among factorials, only 0! and 1! are perfect squares. So, y is not. Sufficient.

(2) y = m^2 − 1 where m is a positive integer greater than 1 --> y is 1 less, than a perfect square, so not a perfect square (two positive consecutive integers cannot both be prefect squares). Sufficient.

That's a nice explaination .
Manager
Joined: 03 Jul 2013
Posts: 89
Schools: ISB '17 (A), IIMC (A)
GMAT 1: 660 Q48 V32
Re: If x represents the number of positive factors of integer y, is x odd  [#permalink]

### Show Tags

03 Oct 2014, 11:24
Bunuel wrote:
If x represents the number of positive factors of integer y, is x odd?

The question asks whether the number of factors of y is odd. The number of distinct factors of a perfect square is ALWAYS ODD. The reverse is also true: if a number has the odd number of distinct factors then it's a perfect square. So, the question asks whether y is a perfect square.

(1) y = n! where n is a positive integer greater than 1. Among factorials, only 0! and 1! are perfect squares. So, y is not. Sufficient.

(2) y = m^2 − 1 where m is a positive integer greater than 1 --> y is 1 less, than a perfect square, so not a perfect square (two positive consecutive integers cannot both be prefect squares). Sufficient.

Thanks bunuel but could you please tell me what was the issue with my approach so that ill be careful on exam day
_________________

Sometimes standing still can be, the best move you ever make......

Math Expert
Joined: 02 Sep 2009
Posts: 51072
If x represents the number of positive factors of integer y, is x odd  [#permalink]

### Show Tags

03 Oct 2014, 11:26
2
My Aprproach:

Statement 1)

when n=2, y=2, factors of 2 are 1,2 so x=2
when n=3, y=6, factors of 6 are 1,2,3,6 so x=4
n=4,y=24, factors of y are 1,2,3,4,6,8,12,24 x= 8

hence x can never be odd. Sufficient.

Statement 2)

m=2, y=1, factors of y =1, so x=1
m=3, y=8, factors of y=1,2,4,8 x=4

Insufficient as x can be even or odd.

(2) y = m^2 − 1 where m is a positive integer greater than 1

If m = 2, then y = 2^2 - 1 = 3, not 1. Factors of 3 are 1 and 3.
_________________
Manager
Joined: 03 Jul 2013
Posts: 89
Schools: ISB '17 (A), IIMC (A)
GMAT 1: 660 Q48 V32
Re: If x represents the number of positive factors of integer y, is x odd  [#permalink]

### Show Tags

03 Oct 2014, 11:27
Bunuel wrote:
My Aprproach:

Statement 1)

when n=2, y=2, factors of 2 are 1,2 so x=2
when n=3, y=6, factors of 6 are 1,2,3,6 so x=4
n=4,y=24, factors of y are 1,2,3,4,6,8,12,24 x= 8

hence x can never be odd. Sufficient.

Statement 2)

m=2, y=1, factors of y =1, so x=1
m=3, y=8, factors of y=1,2,4,8 x=4

Insufficient as x can be even or odd.

(2) y = m^2 − 1 where m is a positive integer greater than 1

If m = 2, then y = 2^2 - 1 = 3, not 1. Factors of 3 are 1 and 3.

Ohh god I feel so stupid now. Thanks a ton man.
_________________

Sometimes standing still can be, the best move you ever make......

Intern
Joined: 24 Aug 2015
Posts: 22
Location: Israel
GMAT 1: 740 Q49 V41
GPA: 3.32
Re: If x represents the number of positive factors of integer y, is x odd  [#permalink]

### Show Tags

30 Aug 2015, 06:16
Bunuel wrote:
If x represents the number of positive factors of integer y, is x odd?

The question asks whether the number of factors of y is odd. The number of distinct factors of a perfect square is ALWAYS ODD. The reverse is also true: if a number has the odd number of distinct factors then it's a perfect square. So, the question asks whether y is a perfect square.

(1) y = n! where n is a positive integer greater than 1. Among factorials, only 0! and 1! are perfect squares. So, y is not. Sufficient.

(2) y = m^2 − 1 where m is a positive integer greater than 1 --> y is 1 less, than a perfect square, so not a perfect square (two positive consecutive integers cannot both be prefect squares). Sufficient.

Sorry guys, I just don't get it.
Take 36 for example - 36= 2^2*3^2.
Two prime, distinct factors.

It must be some weird terminology issue, I would be glad if someone could explain this to me (Taking the GMAT on wednsday!)

CEO
Joined: 20 Mar 2014
Posts: 2633
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
If x represents the number of positive factors of integer y, is x odd  [#permalink]

### Show Tags

30 Aug 2015, 06:29
3
1
goidelg wrote:
Bunuel wrote:
If x represents the number of positive factors of integer y, is x odd?

The question asks whether the number of factors of y is odd. The number of distinct factors of a perfect square is ALWAYS ODD. The reverse is also true: if a number has the odd number of distinct factors then it's a perfect square. So, the question asks whether y is a perfect square.

(1) y = n! where n is a positive integer greater than 1. Among factorials, only 0! and 1! are perfect squares. So, y is not. Sufficient.

(2) y = m^2 − 1 where m is a positive integer greater than 1 --> y is 1 less, than a perfect square, so not a perfect square (two positive consecutive integers cannot both be prefect squares). Sufficient.

Sorry guys, I just don't get it.
Take 36 for example - 36= 2^2*3^2.
Two prime, distinct factors.

It must be some weird terminology issue, I would be glad if someone could explain this to me (Taking the GMAT on wednsday!)

Look below:

For any given number, N, the number of factors of N are as follows:

N = a^p * b^q * c^r .... Where a,b,c are prime number (=2,3,5,7,11...) and p,q,r are integers. This should always be the first step.

Writing N in terms of its prime factors is known as prime factorization.

Once you have done the prime factorization, the number of factors of N= (p+1)(q+1)(r+1)... (Please note that the formula for number of factors include 1 and the number itself as well.)

What you are confusing is the definition of

1. Prime factors
2. Positive factors

You are correct that 36 has 2 prime factors but for positive factors, you need to use the formula mentioned above.

So once you write 36 = $$2^2$$*$$3^2$$, you need to take the powers of the prime factors (2 and 3 in this case) and calculate (power of 2 +1)(power of 3 +1) = (2+1)(2+1) = 3*3 = 9, an odd number.

By counting, the factors of 36 are:
1 36
2 18
3 12
4 9
6 6 (so in all you have 9 factors, with 6 only counted ONCE).

The above property of total factors to be odd are especially true for perfect squares. The reverse is true as well.

Thus, for a perfect square, the total number of positive factors will always be ODD while number with ODD number of positive factors will ALWAYS be perfect squares (25,36,49, etc)

Hope this helps.
Non-Human User
Joined: 09 Sep 2013
Posts: 9097
Re: If x represents the number of positive factors of integer y, is x odd  [#permalink]

### Show Tags

08 Dec 2018, 22:38
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: If x represents the number of positive factors of integer y, is x odd &nbs [#permalink] 08 Dec 2018, 22:38
Display posts from previous: Sort by