It is currently 17 Jun 2019, 20:56

### 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

# The number of zeros at the end of m when written in integer

Author Message
TAGS:
Founder
Joined: 18 Apr 2015
Posts: 6885
Followers: 114

Kudos [?]: 1338 [0], given: 6306

The number of zeros at the end of m when written in integer [#permalink]  16 Sep 2017, 10:35
Expert's post
00:00

Question Stats:

60% (00:42) correct 40% (00:49) wrong based on 50 sessions

$$m=2^{16}3^{17}4^{18}5^{19}$$

$$n=2^{19}3^{18}4^{17}5^{16}$$

 Quantity A Quantity B The number of zeros at the end of m whenwritten in integer form The number of zeros at the end of n whenwritten in integer form

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

_________________
Director
Joined: 03 Sep 2017
Posts: 520
Followers: 1

Kudos [?]: 356 [0], given: 66

Re: The number of zeros at the end of m when written in integer [#permalink]  21 Sep 2017, 08:41
Any help with this one?
Intern
Joined: 06 Sep 2017
Posts: 1
Followers: 0

Kudos [?]: 1 [1] , given: 0

Re: The number of zeros at the end of m when written in integer [#permalink]  05 Oct 2017, 18:01
1
KUDOS
can be written as
m = 2^16 3^17 4^17 5^16 4 5^3
n = 2^16 3^17 4^17 5^16 3 2^3
now we see in first 4 terms are same for both m and n but it m we see 5^3 * 4 that means two more zeroes
thats why quantity a is greater
Intern
Joined: 16 Sep 2017
Posts: 3
Followers: 0

Kudos [?]: 3 [1] , given: 2

Re: The number of zeros at the end of m when written in integer [#permalink]  09 Oct 2017, 22:17
1
KUDOS
the number of zeroes will be determined by the number of 5s and 2s. since 5*2 gives us one zero, the number of zeroes will be the number of (5*2) that we get. So in first case it is 19 and in second case it is 16. Hence A is greater than B.
Intern
Joined: 08 Dec 2017
Posts: 40
Followers: 1

Kudos [?]: 43 [1] , given: 70

Re: The number of zeros at the end of m when written in integer [#permalink]  22 Feb 2018, 04:05
1
KUDOS
m=2^{16}3^{17}4^{18}5^{19}

n=2^{19}3^{18}4^{17}5^{16}
We can rewrite it as following:

m= 2^{16}..2^{36}...5^{19} = 2^{52}..5^{19} = 19 zeroes
n= 2^{19}..2^{34}...5^{16} = 2^{53}..5^{16} = 16 zeroes

So A is greater.
Intern
Joined: 24 Feb 2018
Posts: 15
Followers: 0

Kudos [?]: 1 [0], given: 0

Re: The number of zeros at the end of m when written in integer [#permalink]  24 Feb 2018, 17:23
A
Manager
Joined: 26 Jun 2017
Posts: 104
Followers: 0

Kudos [?]: 41 [0], given: 38

Re: The number of zeros at the end of m when written in integer [#permalink]  04 Mar 2018, 02:48
Can someone explain this in detail?
_________________

What you think, you become.

Manager
Joined: 22 Feb 2018
Posts: 163
Followers: 2

Kudos [?]: 114 [0], given: 22

Re: The number of zeros at the end of m when written in integer [#permalink]  21 Mar 2018, 12:12
The parameters that can produce 0 are 2 and 5.
n= 2^19 * 3^18 * 4^17 * 5^16 = 2^16 * 5^16 * 3^18 * 4^17 (there are 16 2s and 16 5s, we didn’t consider 4 because there are only 16 5s, if there were more than 19 5s we used 4s after 2s. So there are 16 zeros in the end of n)
m= 2^16 * 3^17 * 4 ^18 * 5^19= 5^19 * 2^52 * 3^17 = 5^19 * 2^19 * 2^33 * 3^17 (there are 19 multiplication of 2 with 5. So there are 19 zeros in the end of m)
So the number of zeros in m are more than n. And the answer is A.

_________________

Re: The number of zeros at the end of m when written in integer   [#permalink] 21 Mar 2018, 12:12
Display posts from previous: Sort by