Find all School-related info fast with the new School-Specific MBA Forum

It is currently 18 Sep 2014, 08:05

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If x is the product of the positive integers from 1 to 8, in

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Manager
Manager
avatar
Joined: 17 Jul 2010
Posts: 126
Followers: 0

Kudos [?]: 24 [0], given: 43

If x is the product of the positive integers from 1 to 8, in [#permalink] New post 21 Jan 2013, 14:11
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

79% (02:08) correct 21% (02:21) wrong based on 66 sessions
If x is the product of the positive integers from 1 to 8, inclusive, and if i, k, m, and p are positive integers such that x = 2^i * 3^k * 5^m * 7^p, then i + k + m + p =

A. 4
B. 7
C. 8
D. 11
E. 12

The OG Guide and MGMAT Guide both have different solutions, a bit long. Can someone tell me if I'm doing this incorrectly.

If I'm plugging #'s in, I'm getting 2+3+4+5, = 14, but not all can be added, because not all are prime, and some numbers are repeated right, so if I take the sum of all primes in 2+3+4+5, without repeats I'll get 1+3+2+5, then I get 11? is this correct? I know 1 is not prime, and the first 2, and 4 share the same primes, so do I use 1 as a digit for 2, and use 2 as a prime # for 4? to end up with 1+3+2+5?
[Reveal] Spoiler: OA
Manhattan GMAT Discount CodesKaplan GMAT Prep Discount CodesKnewton GMAT Discount Codes
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29676
Followers: 3496

Kudos [?]: 26351 [0], given: 2710

Re: If x is the product of the positive integers from 1 to 8, in [#permalink] New post 21 Jan 2013, 14:29
Expert's post
If x is the product of the positive integers from 1 to 8, inclusive, and if i, k, m, and p are positive integers such that x = 2^i * 3^k * 5^m * 7^p, then i + k + m + p =

A. 4
B. 7
C. 8
D. 11
E. 12

Given that x=8!=2^7*3^2*5*7. Hence, x=2^7*3^2*5^1*7^1=2^i * 3^k * 5^m * 7^p, since i, k, m, and p are positive integers, then we can equate the exponents, so we have that i=7, k=2, m=1, and p=1.

Therefore, i + k + m + p=7+2+1+1=11.

Answer: D.

Hope it's clear.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Expert Post
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 4772
Location: Pune, India
Followers: 1114

Kudos [?]: 5051 [0], given: 164

Re: If x is the product of the positive integers from 1 to 8, in [#permalink] New post 21 Jan 2013, 19:56
Expert's post
laythesmack23 wrote:
If x is the product of the positive integers from 1 to 8, inclusive, and if i, k, m, and p are positive integers such that x = 2^i * 3^k * 5^m * 7^p, then i + k + m + p =

A. 4
B. 7
C. 8
D. 11
E. 12

The OG Guide and MGMAT Guide both have different solutions, a bit long. Can someone tell me if I'm doing this incorrectly.

If I'm plugging #'s in, I'm getting 2+3+4+5, = 14, but not all can be added, because not all are prime, and some numbers are repeated right, so if I take the sum of all primes in 2+3+4+5, without repeats I'll get 1+3+2+5, then I get 11? is this correct? I know 1 is not prime, and the first 2, and 4 share the same primes, so do I use 1 as a digit for 2, and use 2 as a prime # for 4? to end up with 1+3+2+5?


You cannot plug in numbers. You need to find the values of i, k, m and p.

x = 1*2*3*4*5*6*7*8 = 8!

x = 2^i*3^k*5^m*7^p

To get the value of i, you need to find the number of 2s in x i.e. 8! (including the 2s you get in 4, 6 and 8). You can quickly count - one from 2, two from 4, one from 6 and three from 8 = total seven 2s are there in 8!

To get the value of k, you need to find the number of 3s in 8!. There are two 3s in 8! (one from 3 and another from 6)
It is easy to see that there is only one 5 and one 7 in 8!.

x = 2^7*3^2*5^1*7^1

So 7 + 2 + 1 + 1 = 11

Check this post for more on powers in factorials: http://www.veritasprep.com/blog/2011/06 ... actorials/
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Senior Manager
Senior Manager
avatar
Joined: 16 Feb 2012
Posts: 260
Concentration: Finance, Economics
Followers: 4

Kudos [?]: 65 [0], given: 111

GMAT ToolKit User
If x is the product of the positive integers from 1 to 8, in [#permalink] New post 11 Aug 2013, 00:44
If x is the product of the positive integers from 1 to 8, inclusive, and if i, k, m and p are positive integers such that x = 2^i3^k5^m7^p, then i + k + m + p =
A 4
B 7
C 8
D 11
E 12
_________________

Kudos if you like the post!

Failing to plan is planning to fail.

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29676
Followers: 3496

Kudos [?]: 26351 [0], given: 2710

Re: If x is the product of the positive integers from 1 to 8, in [#permalink] New post 11 Aug 2013, 00:48
Expert's post
Stiv wrote:
If x is the product of the positive integers from 1 to 8, inclusive, and if i, k, m and p are positive integers such that x = 2^i3^k5^m7^p, then i + k + m + p =
A 4
B 7
C 8
D 11
E 12


Merging similar topics. Please refer to the solutions above.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Current Student
User avatar
Joined: 14 Dec 2012
Posts: 838
Location: India
Concentration: General Management, Operations
GMAT 1: 700 Q50 V34
GPA: 3.6
Followers: 37

Kudos [?]: 585 [0], given: 197

GMAT ToolKit User
Re: If x is the product of the positive integers from 1 to 8, in [#permalink] New post 11 Aug 2013, 00:51
Stiv wrote:
If x is the product of the positive integers from 1 to 8, inclusive, and if i, k, m and p are positive integers such that x = 2^i3^k5^m7^p, then i + k + m + p =
A 4
B 7
C 8
D 11
E 12


X= 1*2*3*4*5*6*7*8 OR =1*2*3*2^2*5*(2*3)*7*2^3 =1*2^7*3^2*5*7
THEREFORE i + k + m + p = 7+2+1+1 = 11

HENCE D
_________________

When you want to succeed as bad as you want to breathe ...then you will be successfull....

GIVE VALUE TO OFFICIAL QUESTIONS...



GMAT RCs VOCABULARY LIST: vocabulary-list-for-gmat-reading-comprehension-155228.html
learn AWA writing techniques while watching video : http://www.gmatprepnow.com/module/gmat- ... assessment
: http://www.youtube.com/watch?v=APt9ITygGss

Intern
Intern
avatar
Status: Preparation
Joined: 03 Apr 2012
Posts: 8
Location: India
GMAT 1: 700 Q50 V34
GPA: 2.9
Followers: 0

Kudos [?]: 6 [0], given: 10

Re: If x is the product of the positive integers from 1 to 8, in [#permalink] New post 11 Aug 2013, 01:40
If given any factorial .Then the maximum power of a prime number in that factorial can be obtained by using the following formula.

If given n! then the maximum power of a prime number p in that factorial is obtained by

[n/p] + [n/p^2] + [n/p^3] + ......

where [x] is a step function and gives the greatest integer less than or equal to X.

We have to continue the above formula until we get the value of some term zero.

For example take 8!.

To find the power of 2 in 8!. We apply this formula.

[8/2] + [8/4] + [8/8] + [8/16] +....

= 4 + 2 + 1 + 0 + 0 + ..... = 7
Re: If x is the product of the positive integers from 1 to 8, in   [#permalink] 11 Aug 2013, 01:40
    Similar topics Author Replies Last post
Similar
Topics:
2 If x is the product of the positive integers from 1 to 8, albany09 2 07 Oct 2008, 09:28
If x is the product of the positive integers from 1 to 8, goalsnr 3 06 Jul 2008, 19:54
If x is the product of the positive integers from 1 to 8, goalsnr 1 01 Jun 2008, 12:56
If x is the product of the positive integers from 1 to 8 puma 4 15 May 2008, 10:48
If x is the product of the positive integers from 1 to 8, JyotiBharadwaj 11 25 Apr 2007, 21:50
Display posts from previous: Sort by

If x is the product of the positive integers from 1 to 8, in

  Question banks Downloads My Bookmarks Reviews Important topics  


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

Powered by phpBB © phpBB Group and phpBB SEO

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®.