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Intern  B
Joined: 01 Nov 2015
Posts: 18
How many zeroes are there at the end of the number N, if N = 100! + 20  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 60% (01:24) correct 40% (01:40) wrong based on 228 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
Marshall & McDonough Moderator D
Joined: 13 Apr 2015
Posts: 1684
Location: India
Re: How many zeroes are there at the end of the number N, if N = 100! + 20  [#permalink]

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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  B
Joined: 06 Nov 2014
Posts: 1873
Re: How many zeroes are there at the end of the number N, if N = 100! + 20  [#permalink]

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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  B
Joined: 13 Oct 2016
Posts: 359
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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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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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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 V
Joined: 04 Jan 2015
Posts: 3074
Re: How many zeroes are there at the end of the number N, if N = 100! + 20  [#permalink]

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1
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
Quant Expert
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Manager  B
Joined: 08 Jul 2018
Posts: 73
Location: United States
Re: How many zeroes are there at the end of the number N, if N = 100! + 20  [#permalink]

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EgmatQuantExpert wrote:
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
Quant Expert

I don't understand this part here

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

Can someone please explain?
Math Expert V
Joined: 02 Sep 2009
Posts: 58391
Re: How many zeroes are there at the end of the number N, if N = 100! + 20  [#permalink]

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jackjones wrote:
EgmatQuantExpert wrote:
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
Quant Expert

I don't understand this part here

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

Can someone please explain?

Theory on Trailing Zeros: http://gmatclub.com/forum/everything-ab ... 85592.html

For more check Trailing Zeros Questions and Power of a number in a factorial questions in our Special Questions Directory.

Hope this helps.
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Joined: 11 Oct 2018
Posts: 21
Location: Germany
Re: How many zeroes are there at the end of the number N, if N = 100! + 20  [#permalink]

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vitaliyGMAT wrote:
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 $$100! = 24$$

If the expression in the parentheses would end with 1 as units digit, then how can the whole expression have any trailing zeros?

Example:

$$100! < 200!$$

So small number + big number (with 1 as units digit):

$$200 + 200001=200201 -> no trailing zeros.$$

Can you please explain? vitaliyGMAT Re: How many zeroes are there at the end of the number N, if N = 100! + 20   [#permalink] 19 Jan 2019, 16:45
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