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

 It is currently 19 Oct 2018, 06:23

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

In how many ways can the integer 48 be expressed as a product of two

Author Message
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 50001
In how many ways can the integer 48 be expressed as a product of two  [#permalink]

Show Tags

18 Aug 2015, 02:15
2
5
00:00

Difficulty:

35% (medium)

Question Stats:

61% (01:01) correct 39% (01:12) wrong based on 204 sessions

HideShow timer Statistics

In how many ways can the integer 48 be expressed as a product of two different positive integers?

A. 10
B. 8
C. 5
D. 4
E. 2

Kudos for a correct solution.

_________________
Director
Joined: 21 May 2013
Posts: 651
Re: In how many ways can the integer 48 be expressed as a product of two  [#permalink]

Show Tags

18 Aug 2015, 03:25
Bunuel wrote:
In how many ways can the integer 48 be expressed as a product of two different positive integers?

A. 10
B. 8
C. 5
D. 4
E. 2

Kudos for a correct solution.

48=(2^4)*3
No of factors=5*2=10
Since 48 is not a perfect square, no of ways=5
Manager
Joined: 08 Sep 2012
Posts: 61
Location: India
Concentration: Social Entrepreneurship, General Management
WE: Engineering (Investment Banking)
Re: In how many ways can the integer 48 be expressed as a product of two  [#permalink]

Show Tags

18 Aug 2015, 04:25
1
3
Bunuel wrote:
In how many ways can the integer 48 be expressed as a product of two different positive integers?

A. 10
B. 8
C. 5
D. 4
E. 2

Kudos for a correct solution.

Method 1: Listing all multiples since given number is small
48 = 1*48, 2*24, 3*16, 4*12, 6*8 => 5 ways

Method 2: Express given number as prime factors
48 = 6*8 = 2*3 * 2^3 = 2^4 * 3
Total number of factors = (4+1)(1+1) = 5*2 = 10
Since the given number is not a perfect square, there will be exact 5 pairs possible of the given 10 factors => 5 ways

Option C
_________________

+1 Kudos if you liked my post! Thank you!

Manager
Joined: 22 Feb 2015
Posts: 56
Location: United States
Concentration: Finance, Operations
GMAT Date: 04-01-2015
GPA: 3.98
Re: In how many ways can the integer 48 be expressed as a product of two  [#permalink]

Show Tags

18 Aug 2015, 07:05
1
48 = 2^4 * 3^1

No of factors = (4+1) (1+1) = 10

So there are exactly 5 pairs
_________________

Click +1 KUDOS , You can make me happy with just one click! Thanks

CEO
Joined: 08 Jul 2010
Posts: 2548
Location: India
GMAT: INSIGHT
WE: Education (Education)
In how many ways can the integer 48 be expressed as a product of two  [#permalink]

Show Tags

18 Aug 2015, 07:15
1
2
Bunuel wrote:
In how many ways can the integer 48 be expressed as a product of two different positive integers?

A. 10
B. 8
C. 5
D. 4
E. 2

Kudos for a correct solution.

CONCEPT:

The No. of ways of writing a (Non-Perfect Square) Number as product of two different Positive integers = Number of Factors /2
The No. of ways of writing a (Perfect Square) Number as product of two different Positive integers = (Number of Factors+1) /2

48 = 16x3 = 2^4*3^1

No. of Factors of 48 = (4+1)*(1+1) = 10

The No. of ways of writing a (Non-Perfect Square) 48 as product of two different Positive integers = Number of Factors /2 = 10/2 = 5

(1*48)
(2*24)
(3*16)
(4*12)
(6*8)

_________________

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: 10 Jun 2015
Posts: 118
Re: In how many ways can the integer 48 be expressed as a product of two  [#permalink]

Show Tags

18 Aug 2015, 07:28
Bunuel wrote:
In how many ways can the integer 48 be expressed as a product of two different positive integers?

A. 10
B. 8
C. 5
D. 4
E. 2

Kudos for a correct solution.

48=2^4*3^1
the number of divisors are 5*2=10
(10/2)=5 pairs
Manager
Joined: 14 Mar 2014
Posts: 147
GMAT 1: 710 Q50 V34
Re: In how many ways can the integer 48 be expressed as a product of two  [#permalink]

Show Tags

19 Aug 2015, 00:13
1
Bunuel wrote:
In how many ways can the integer 48 be expressed as a product of two different positive integers?

A. 10
B. 8
C. 5
D. 4
E. 2

Kudos for a correct solution.

IMO: C

If N = $$p_1^a * p_2 ^b * p_3^c ...$$

Then No. of factors of N = (a+1)(b+1)(c+1)....

No. of ways of representing as a product of two different positive integers(If N is not a perfect square) = Total No. of factors/2

Thus 48 = $$2^4 * 3^1$$

48 be expressed as a product of two different positive integers = (4+1)(1+1)/2
= 5
_________________

I'm happy, if I make math for you slightly clearer
And yes, I like kudos
¯\_(ツ)_/¯

Manager
Joined: 27 Aug 2016
Posts: 91
Location: India
Schools: HEC Montreal '21
GMAT 1: 670 Q47 V37
GPA: 3
WE: Engineering (Energy and Utilities)
Re: In how many ways can the integer 48 be expressed as a product of two  [#permalink]

Show Tags

15 Jan 2017, 09:47
Bunuel wrote:
In how many ways can the integer 48 be expressed as a product of two different positive integers?

A. 10
B. 8
C. 5
D. 4
E. 2

Kudos for a correct solution.

IMHO:
prime factorization of 48=2x2x2x2x3
so the prob be comes in how many ways can 2,2,2,2,3 be arranged which is similar to arrangement of letters so i went via this route 5!/4!=5....Am I right...
Non-Human User
Joined: 09 Sep 2013
Posts: 8464
Re: In how many ways can the integer 48 be expressed as a product of two  [#permalink]

Show Tags

02 Apr 2018, 10:18
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: In how many ways can the integer 48 be expressed as a product of two &nbs [#permalink] 02 Apr 2018, 10:18
Display posts from previous: Sort by