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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, 09:50
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00:00

Difficulty:

55% (hard)

Question Stats:

59% (01:22) correct 41% (01:40) wrong based on 219 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
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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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08 Jun 2016, 10:11
1
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.

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Joined: 06 Nov 2014
Posts: 1877
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, 02:50
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
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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, 03:14
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

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

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, 06:59
2
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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Joined: 04 Jan 2015
Posts: 2568
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, 10:00
1
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
Joined: 08 Jul 2018
Posts: 62
Location: United Kingdom
Re: How many zeroes are there at the end of the number N, if N = 100! + 20  [#permalink]

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10 Jul 2018, 23:49
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 $$100! = \frac{100}{5} + \frac{20}{5} = 20 + 4 = 24$$

Math Expert
Joined: 02 Sep 2009
Posts: 52921
Re: How many zeroes are there at the end of the number N, if N = 100! + 20  [#permalink]

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10 Jul 2018, 23:54
1
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 $$100! = \frac{100}{5} + \frac{20}{5} = 20 + 4 = 24$$

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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Intern
Joined: 11 Oct 2018
Posts: 10
Re: How many zeroes are there at the end of the number N, if N = 100! + 20  [#permalink]

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19 Jan 2019, 15:45
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):

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

Re: How many zeroes are there at the end of the number N, if N = 100! + 20   [#permalink] 19 Jan 2019, 15:45
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