 It is currently 13 Aug 2020, 18:02 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. # Let M = 10! and let N = M3. If a is the greatest integer val  Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:
Founder  Joined: 18 Apr 2015
Posts: 12642
Followers: 268

Kudos [?]: 3171 , given: 11677

Let M = 10! and let N = M3. If a is the greatest integer val [#permalink]
Expert's post 00:00

Question Stats: 87% (01:43) correct 12% (02:14) wrong based on 8 sessions
Let $$M = 10!$$ and let $$N = M^3$$. If a is the greatest integer value of x such that $$2^x$$ is a factor of N, and b is the greatest integer value of y such that $$3^y$$ is a factor of N, then what is the value of a + b?

A. 18

B. 24

C. 33

D. 36

E. 54
[Reveal] Spoiler: OA

_________________

Need Practice? 20 Free GRE Quant Tests available for free with 20 Kudos
GRE Prep Club Members of the Month: Each member of the month will get three months free access of GRE Prep Club tests.

Intern Joined: 19 Jan 2020
Posts: 44
Followers: 0

Kudos [?]: 25 , given: 50

Re: Let M = 10! and let N = M3. If a is the greatest integer val [#permalink]
M = 10! will have 2^8 and 3^4 along with other factors.
N = M^3, N will have 2^24 and 3^12 along with other factors.
Since a and b are greatest integer. a = 24 and b= 12.
Senior Manager  Joined: 10 Feb 2020
Posts: 384
Followers: 1

Kudos [?]: 86 , given: 227

Re: Let M = 10! and let N = M3. If a is the greatest integer val [#permalink]
Didnt understand this
_________________

Ever Tried? Ever Failed? No Matter. Try Again. Fail Again. Fail Better!!

Intern Joined: 10 Aug 2019
Posts: 19
Followers: 0

Kudos [?]: 7 , given: 2

Re: Let M = 10! and let N = M3. If a is the greatest integer val [#permalink]
Prime factorization of 10! will give us 2 to the power 8 and 3 to the power 4.

Hence, a cube of 10! will have 2 to the power of 24 and 3 to the power of 12.

so, a=24 and b=12.

a+b = 36.

Option D.
Manager Joined: 22 Jan 2020
Posts: 77
Followers: 0

Kudos [?]: 52 , given: 8

Re: Let M = 10! and let N = M3. If a is the greatest integer val [#permalink]
M=10!=10*9*8*7*6*5*4*3*2*1

N=M^3= (10*9*8*7*6*5*4*3*2*1)^3 = 10^3 * 9^3 * 8^3 * 7^3 * 6^3 * 5^3 * 4^3 * 3^3 * 2^3 * 1^3

The greatest value of x such that 2^x is a factor of N is the number of times 2 appears as a factor in N
Therefore from N we get:

10^3=(2*5)^3= 2^3 * 5^3 -->3 two's
8^3= (2^3)^3 = 2^9 -->9 two's
6^3= (2*3)^3 = 2^3 * 3^3 -->3 two's
4^3= (2^2)^3 = 2^6 -->6 two's
2^3 -->3 two's

Total: 24 two's
a=24

We repeat the same process in order to look for b the max number that 3 appears as a factor in N

9^3= (3^2)^3= 3^6 -->6 three's
6^3= (2*3)^3 = 2^3 * 3^3 -->3 three's
3^3 -->3 three's

Total: 12 three's
b=12

a+b=24+12=36 Re: Let M = 10! and let N = M3. If a is the greatest integer val   [#permalink] 03 Aug 2020, 01:49
Display posts from previous: Sort by

# Let M = 10! and let N = M3. If a is the greatest integer val  Question banks Downloads My Bookmarks Reviews Important topics Powered by phpBB © phpBB Group Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.