Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 18 Jul 2019, 14:42 ### 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.  # What is the value of N? (1) 10^N is the least positive integer which

Author Message
TAGS:

### Hide Tags

Retired Moderator P
Joined: 22 Aug 2013
Posts: 1435
Location: India
What is the value of N? (1) 10^N is the least positive integer which  [#permalink]

### Show Tags 00:00

Difficulty:   35% (medium)

Question Stats: 71% (01:43) correct 29% (01:49) wrong based on 102 sessions

### HideShow timer Statistics What is the value of N?

(1) 10^N is the least positive integer which is divisible by both 5^8 and 4^4.

(2) N is the least positive integer such that product of all integers from 1 to N, inclusive, is divisible by 128.
Manager  G
Joined: 30 Mar 2017
Posts: 130
GMAT 1: 200 Q1 V1 What is the value of N? (1) 10^N is the least positive integer which  [#permalink]

### Show Tags

I think it's D.

Statement 1
5^8 and 4^4 have to both divide 10^N, where N is minimized. We can find N (i.e. there exists a smallest N such that 10^N is divisible by both 5^8 and 4^4). Sufficient.

Statement 2
128 has to divide N!, where N is minimized. We can find N (i.e. there exists a smallest number N such that N! is div by 128). Sufficient.
Manager  G
Joined: 19 Apr 2017
Posts: 129
Concentration: General Management, Sustainability
Schools: ESSEC '22
GPA: 3.9
WE: Operations (Hospitality and Tourism)
What is the value of N? (1) 10^N is the least positive integer which  [#permalink]

### Show Tags

2
What is the value of N?

(1) $$10^N$$ is the least positive integer which is divisible by both $$5^8$$ and $$4^4.$$

$$10^N/(5^8*4^4)$$ can be written as $$10^N/(5^8*2^8) = 10^N/(10^8)$$ N has to be 8?

(2) N is the least positive integer such that product of all integers from 1 to N, inclusive, is divisible by 128.

$$128=2^7$$

N! has to contain at least 7 2's to be divisible by $$128 => N!/128 =N!/2^7$$

IF N = 7 then $$N! = {1*2*3*4*5*6*7} = {1*2*3*(2^2)*5*(2*3)*7}$$ this contains only 4 2's we need three more 2
if N = 8 then $$N! = {1*2*3*4*5*6*7*8} = {1*2*3*(2^2)*5*(2*3)*7*(2^3)}$$ this contains 7 twos so N= 8

Sufficient So D What is the value of N? (1) 10^N is the least positive integer which   [#permalink] 27 Sep 2018, 12:55
Display posts from previous: Sort by

# What is the value of N? (1) 10^N is the least positive integer which  