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If n = 100! x 100!, what is the largest value of prime number t, such

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If n = 100! x 100!, what is the largest value of prime number t, such  [#permalink]

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New post 28 Jul 2017, 08:38
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

71% (01:15) correct 29% (01:15) wrong based on 124 sessions

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Re: If n = 100! x 100!, what is the largest value of prime number t, such  [#permalink]

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New post 28 Jul 2017, 09:21
1
Bunuel wrote:
If n = 100! x 100!, what is the largest value of prime number t, such that n/t is an integer?

A. 7
B. 19
C. 97
D. 99
E. 101


t can't be greater than 100. Eliminate E.

t can't be 99 since 99 isn't a prime.

Hence it's clear that C is the answer.
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Re: If n = 100! x 100!, what is the largest value of prime number t, such  [#permalink]

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New post 28 Jul 2017, 09:47
99 is not a prime. So out.
101 not possible.
97 should be the answer

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Re: If n = 100! x 100!, what is the largest value of prime number t, such  [#permalink]

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New post 28 Jul 2017, 13:25
Out of the given options prime numbers less than 100 can be correct.
99 is not a prime number.
97 can be considered.
option A and B have numbers less than 97 so the answer is C.
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If n = 100! x 100!, what is the largest value of prime number t, such  [#permalink]

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New post 28 Jul 2017, 20:24
We need to find the biggest prime number which is smaller than 100! and which will divide it to give an integer.

In this case, 97 is that number which when divides 100! will give us an integer (Option C)
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Re: If n = 100! x 100!, what is the largest value of prime number t, such  [#permalink]

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New post 28 Jul 2017, 20:48
100! * 100! = 1^2 * 2^2 * 3^2 * ..... * 96^2 * 97^2 * 98^2 * 99^2 * 100^2

101 is not possible.
99 is not prime.
Hence largest prime number that is the factor of 100!*100! is 97.

Answer : C
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Re: If n = 100! x 100!, what is the largest value of prime number t, such  [#permalink]

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New post 28 Jul 2017, 22:45
1
Bunuel wrote:
If n = 100! x 100!, what is the largest value of prime number t, such that n/t is an integer?

A. 7
B. 19
C. 97
D. 99
E. 101


We need to check the max prime no. available in 100! only.
So, it can't be 101 as it is greater than 100
99 is not a prime number.
97 is a prime number

Answer C
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Re: If n = 100! x 100!, what is the largest value of prime number t, such   [#permalink] 28 Jul 2017, 22:45
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