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

It is currently 21 Aug 2018, 19:02

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

There are 3 ways to make the number 12 using products of two positive

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6046
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
There are 3 ways to make the number 12 using products of two positive  [#permalink]

Show Tags

New post 24 Jul 2018, 01:26
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

37% (01:16) correct 63% (01:53) wrong based on 100 sessions

HideShow timer Statistics

[Math Revolution GMAT math practice question]

There are 3 ways to make the number 12 using products of two positive integers. These are 1*12, 2*6, and 3*4. In how many ways can 2700 be written as the product of two positive integers?

A. 6
B. 12
C. 15
D. 18
E. 36

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Math Revolution Discount CodesEconomist GMAT Tutor Discount CodesOptimus Prep Discount Codes
Director
Director
User avatar
S
Joined: 20 Feb 2015
Posts: 546
Concentration: Strategy, General Management
Premium Member CAT Tests
There are 3 ways to make the number 12 using products of two positive  [#permalink]

Show Tags

New post 24 Jul 2018, 02:24
1
MathRevolution wrote:
[Math Revolution GMAT math practice question]

There are 3 ways to make the number 12 using products of two positive integers. These are 1*12, 2*6, and 3*4. In how many ways can 2700 be written as the product of two positive integers?

A. 6
B. 12
C. 15
D. 18
E. 36


2700 = (2^2 × 3^3 × 5^2)
total number of factors are (2+1)(3+1)(2+1)=36 including 1 and itself
no of ways 2700 can be written as product of two positive int = 36/2=18
Manager
Manager
avatar
S
Joined: 04 Aug 2010
Posts: 243
Schools: Dartmouth College
Re: There are 3 ways to make the number 12 using products of two positive  [#permalink]

Show Tags

New post 24 Jul 2018, 03:57
2
1
MathRevolution wrote:
[Math Revolution GMAT math practice question]

There are 3 ways to make the number 12 using products of two positive integers. These are 1*12, 2*6, and 3*4. In how many ways can 2700 be written as the product of two positive integers?

A. 6
B. 12
C. 15
D. 18
E. 36


To count the factors of a positive integer:
1. Prime-factorize the integer
2. Write the prime-factorization in the form \((a^p)(b^q)(c^r)\)...
3. The number of factors = \((p+1)(q+1)(r+1)\)...

\(2700 = 2^2 * 3^3 * 5^2\)

Adding 1 to each exponent and multiplying, we get:
Total number of factors = \((2+1)(3+1)(2+1) = 36\)

These 36 factors can be used to form 18 FACTOR PAIRS, as follows:
1*2700
2*1350
3*300
And so on.


_________________

GMAT and GRE Tutor
Over 1800 followers
Click here to learn more
GMATGuruNY@gmail.com
New York, NY
If you find one of my posts helpful, please take a moment to click on the "Kudos" icon.
Available for tutoring in NYC and long-distance.
For more information, please email me at GMATGuruNY@gmail.com.

Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 6561
There are 3 ways to make the number 12 using products of two positive  [#permalink]

Show Tags

New post 24 Jul 2018, 04:28
2
1
MathRevolution wrote:
[Math Revolution GMAT math practice question]

There are 3 ways to make the number 12 using products of two positive integers. These are 1*12, 2*6, and 3*4. In how many ways can 2700 be written as the product of two positive integers?

A. 6
B. 12
C. 15
D. 18
E. 36



Most of us by now know how to find factors. But even after knowing this, you can go wrong if you miss out on "pair of factors" and mark "number of factors"

1) Prime factorise 2700..
\(2700=3^3*10^2=3^3*2^2*5^2\)
2) number of factors ..
(3+1)(2+1)(2+1)=4*3*3=36..

But we are looking for pairs so 35/2=18 as product of two factors say 1*2700=10*270=2*1350...

Some extra points
If a number is a square, the number of factors will be ODD
For example say it was 8100..
\(8100=3^4*2^2*5^2.....5*3*3=45\)
So now 45/2 is not an integer...so what does one do..
Two cases..
1) if question asks you pair of factors then add 1 as \(90*90 =8100\)
So \(\frac{(45+1)}{2}=23\)
2) but if question asks you pair of different factors then subtract one as 90*90 will not be included so \((\frac{45-1)}{2}=22\)
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

VP
VP
User avatar
P
Status: Learning
Joined: 20 Dec 2015
Posts: 1218
Location: India
Concentration: Operations, Marketing
GMAT 1: 670 Q48 V36
GRE 1: Q157 V157
GPA: 3.4
WE: Engineering (Manufacturing)
Reviews Badge CAT Tests
Re: There are 3 ways to make the number 12 using products of two positive  [#permalink]

Show Tags

New post 24 Jul 2018, 10:08
chetan2u wrote:
MathRevolution wrote:
[Math Revolution GMAT math practice question]

There are 3 ways to make the number 12 using products of two positive integers. These are 1*12, 2*6, and 3*4. In how many ways can 2700 be written as the product of two positive integers?

A. 6
B. 12
C. 15
D. 18
E. 36



Most of us by now know how to find factors. But even after knowing this, you can go wrong if you miss out on "pair of factors" and mark "number of factors"

1) Prime factorise 2700..
\(2700=3^3*10^2=3^3*2^2*5^2\)
2) number of factors ..
(3+1)(2+1)(2+1)=4*3*3=36..

But we are looking for pairs so 35/2=18 as product of two factors say 1*2700=10*270=2*1350...

Some extra points
If a number is a square, the number of factors will be ODD
For example say it was 8100..
8100=3^4*2^2*5^2.....5*3*3=45
So now 45/2 is not an integer...so what does one do..
Two cases..
1) if question asks you pair of factors then add 1 as 900*900 =8100
So (45+1)/2=23
2) but if question asks you pair of different factors then subtract one as 900*900 will not be included so (45-1)/2=22


Hi chetan2u,
I the question asks about the sum of the factors then how to go about that?
_________________

Please give kudos if you found my answers useful

Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6046
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
Re: There are 3 ways to make the number 12 using products of two positive  [#permalink]

Show Tags

New post 26 Jul 2018, 01:45
=>

\(2700 = 2^2*3^3*5^2\)
The number of distinct factors of \(2700\) is \((2+1)(3+1)(2+1) = 36.\)
Since the order of multiplication does not matter (i.e. \(30 * 90 = 90*30\)), the number of pairs of positive integers that multiply to give \(2700\) is \(\frac{36}{2} = 18.\)

Therefore, the answer is D.
Answer: D
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 6561
Re: There are 3 ways to make the number 12 using products of two positive  [#permalink]

Show Tags

New post 27 Jul 2018, 23:37
arvind910619 wrote:
chetan2u wrote:
MathRevolution wrote:
[Math Revolution GMAT math practice question]

There are 3 ways to make the number 12 using products of two positive integers. These are 1*12, 2*6, and 3*4. In how many ways can 2700 be written as the product of two positive integers?

A. 6
B. 12
C. 15
D. 18
E. 36



Most of us by now know how to find factors. But even after knowing this, you can go wrong if you miss out on "pair of factors" and mark "number of factors"

1) Prime factorise 2700..
\(2700=3^3*10^2=3^3*2^2*5^2\)
2) number of factors ..
(3+1)(2+1)(2+1)=4*3*3=36..

But we are looking for pairs so 35/2=18 as product of two factors say 1*2700=10*270=2*1350...

Some extra points
If a number is a square, the number of factors will be ODD
For example say it was 8100..
8100=3^4*2^2*5^2.....5*3*3=45
So now 45/2 is not an integer...so what does one do..
Two cases..
1) if question asks you pair of factors then add 1 as 900*900 =8100
So (45+1)/2=23
2) but if question asks you pair of different factors then subtract one as 900*900 will not be included so (45-1)/2=22


Hi chetan2u,
I the question asks about the sum of the factors then how to go about that?


hi..
not likely you will such a question in actual, it will limit to number of factors and not sum of factors ..
but formula for it is ..
1) Prime factorise 2700..
\(2700=3^3*10^2=3^3*2^2*5^2\)
    a) number of factors ..
    \((3+1)(2+1)(2+1)=4*3*3=36..\)
    b) sum of factors ..
    for \(a^x*b^y*c^z\), it is \(\frac{a^{(x+1)}-1}{a-1}*\frac{b^{(y+1)}-1}{b-1}*\frac{c^{(z+1)}-1}{c-1}\)..
    \(\frac{2^{(2+1)}-1}{2-1}*\frac{3^{(3+1)}-1}{3-1}*\frac{5^{(2+1)}-1}{5-1}=7*\frac{3^4-1}{2}*\frac{5^3-1}{4}=7*40*31=8680\)

_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

Re: There are 3 ways to make the number 12 using products of two positive &nbs [#permalink] 27 Jul 2018, 23:37
Display posts from previous: Sort by

There are 3 ways to make the number 12 using products of two positive

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  

Events & Promotions

PREV
NEXT


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.