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aayushagrawal
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How many zeroes are there at the end of the number N, if N = 100! + 20 08 Jun 2016, 10:50
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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55% (hard)

Question Stats:

59% (01:27) correct 41% (01:41) wrong based on 395 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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E
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EgmatQuantExpert
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How many zeroes are there at the end of the number N, if N = 100! + 20 31 Dec 2017, 11:00
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aayushagrawal
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
Show more


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.


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How many zeroes are there at the end of the number N, if N = 100! + 20 08 Jun 2016, 11:11
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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.

Answer: E
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How many zeroes are there at the end of the number N, if N = 100! + 20 09 Jun 2016, 03:50
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aayushagrawal
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
Show more

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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How many zeroes are there at the end of the number N, if N = 100! + 20 16 Dec 2016, 04:14
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aayushagrawal
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
Show more

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

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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How many zeroes are there at the end of the number N, if N = 100! + 20 16 Dec 2016, 07:59
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aayushagrawal
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
Show more

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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How many zeroes are there at the end of the number N, if N = 100! + 20 11 Jul 2018, 00:49
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aayushagrawal
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
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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?
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How many zeroes are there at the end of the number N, if N = 100! + 20 11 Jul 2018, 00:54
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aayushagrawal
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?
Show more


Theory on Trailing Zeros: https://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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How many zeroes are there at the end of the number N, if N = 100! + 20 19 Jan 2019, 16:45
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vitaliyGMAT
aayushagrawal
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 \(100! = 24\)
Show more

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
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How many zeroes are there at the end of the number N, if N = 100! + 20 04 Mar 2020, 04:17
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aayushagrawal
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
Show more

0s are made using 2s and 5s.
200! will have more 2s and 5s compared with 100!.
So 200! will certainly have more trailing 0s compared with 100!. Hence the 'big' number will have more trailing zeroes than the 'small' number.
Something like: 74653837000000 + 746638927364747560000000000000000
So all we need to do is find the number of trailing zeroes of the small number.
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