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# How many zeroes are there at the end of the number N, if N = 100! + 20

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Intern
Joined: 01 Nov 2015
Posts: 20
How many zeroes are there at the end of the number N, if N = 100! + 20 [#permalink]

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08 Jun 2016, 10:50
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Difficulty:

55% (hard)

Question Stats:

64% (00:47) correct 36% (01:03) wrong based on 118 sessions

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How many zeroes are there at the end of the number N, if N = 100! + 200! ?

A) 73
B) 49
C) 20
D) 48
E) 24
[Reveal] Spoiler: OA
SC Moderator
Joined: 13 Apr 2015
Posts: 1616
Location: India
Concentration: Strategy, General Management
WE: Analyst (Retail)
Re: How many zeroes are there at the end of the number N, if N = 100! + 20 [#permalink]

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08 Jun 2016, 11:11
1
KUDOS
There are 24 trailing zeros in 100! and 49 trailing zeros in 200!

Addition of 100! and 200! will result in only 24 trailing zeros.

SVP
Joined: 06 Nov 2014
Posts: 1891
Re: How many zeroes are there at the end of the number N, if N = 100! + 20 [#permalink]

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09 Jun 2016, 03:50
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aayushagrawal wrote:
How many zeroes are there at the end of the number N, if N = 100! + 200! ?

A) 73
B) 49
C) 20
D) 48
E) 24

The number of zeroes at the end of 100! will be less than the number of zeroes at the end of 200!
Hence it would be sufficient to calculate the number of zeroes at the end of 100!

Number of zeroes = [100/5] + [100/25] + [100/125] = 20 + 4 + 0 = 24

Correct Option: E
Senior Manager
Joined: 13 Oct 2016
Posts: 367
GPA: 3.98
Re: How many zeroes are there at the end of the number N, if N = 100! + 20 [#permalink]

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16 Dec 2016, 04:14
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aayushagrawal wrote:
How many zeroes are there at the end of the number N, if N = 100! + 200! ?

A) 73
B) 49
C) 20
D) 48
E) 24

$$100! + 200! = 100! (1 + 101*102*103* … *200)$$

Expression in the parenthesis will have $$1$$ as its units digit. Hence we need to know only the number of trailing zeros at the end of $$100! = 24$$
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Re: How many zeroes are there at the end of the number N, if N = 100! + 20 [#permalink]

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16 Dec 2016, 07:59
2
KUDOS
aayushagrawal wrote:
How many zeroes are there at the end of the number N, if N = 100! + 200! ?

A) 73
B) 49
C) 20
D) 48
E) 24

No of zeroes in the 100! + 200! will be the numebr of zeroes in 100!..

100! has 24 zeroes ..

100/5 = 20
20/5 = 4

So, the correct answer will be (E) 24

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e-GMAT Representative
Joined: 04 Jan 2015
Posts: 1001
Re: How many zeroes are there at the end of the number N, if N = 100! + 20 [#permalink]

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31 Dec 2017, 11:00
aayushagrawal wrote:
How many zeroes are there at the end of the number N, if N = 100! + 200! ?

A) 73
B) 49
C) 20
D) 48
E) 24

While adding two numbers, the numbers of zeros will depend on the number with lesser number of zeros.

For example, 200 + 2000 will have only 2 trailing zeros and the number of zeros is limited by 200 which has 2 only zeros. [200 + 2000 = 2200]

So, instead of wasting time in finding the number of zeros of 200!, we can simply find the number of zeros in 100! and mark the answer.

The number of zeros in $$100! = \frac{100}{5} + \frac{20}{5} = 20 + 4 = 24$$

Hence the correct answer is Option E.

Regards,
Saquib
e-GMAT
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Re: How many zeroes are there at the end of the number N, if N = 100! + 20   [#permalink] 31 Dec 2017, 11:00
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