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Which of the following numbers is not prime ? [#permalink]
03 May 2012, 00:14

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Difficulty:

25% (medium)

Question Stats:

68% (01:55) correct
32% (01:07) wrong based on 242 sessions

Which of the following numbers is not prime? (Hint: avoid actually computing these numbers.)

A. 6!-1 B. 6!+21 C. 6!+41 D. 7!-1 E. 7!+11

Could please someone expalin the logic behind this ? Even though I picked the right answer while solving I am not pretty clear about the underlying concept?

Re: Which of the following numbers is not prime ? [#permalink]
03 May 2012, 00:21

1

This post received KUDOS

Expert's post

abhi47 wrote:

Which of the following numbers is not prime? (Hint: avoid actually computing these numbers.)

A. 6!-1 B. 6!+21 C. 6!+41 D. 7!-1 E. 7!+11

Could please someone expalin the logic behind this ? Even though I picked the right answer while solving I am not pretty clear about the underlying concept?

Thanks, Abhi

Notice that we can factor out 3 out of 6!+21 --> 6!+21=3*(2*4*5*6+7), which means that this number is not a prime.

Re: Which of the following numbers is not prime ? [#permalink]
03 May 2012, 00:36

Bunuel wrote:

abhi47 wrote:

Which of the following numbers is not prime? (Hint: avoid actually computing these numbers.)

A. 6!-1 B. 6!+21 C. 6!+41 D. 7!-1 E. 7!+11

Could please someone expalin the logic behind this ? Even though I picked the right answer while solving I am not pretty clear about the underlying concept?

Thanks, Abhi

Notice that we can factor out 3 out of 6!+21 --> 6!+21=3*(2*4*5*6+7), which means that this number is not a prime.

Answer: B.

@ Bunuel - what inference does 'factor out 3' make? can we say that the second part of the options (11,41) are prime so resultant could be a prime? but 1. could u pls explain?

Re: Which of the following numbers is not prime ? [#permalink]
03 May 2012, 08:38

3

This post received KUDOS

Expert's post

abhi47 wrote:

Which of the following numbers is not prime? (Hint: avoid actually computing these numbers.)

A. 6!-1 B. 6!+21 C. 6!+41 D. 7!-1 E. 7!+11

Could please someone expalin the logic behind this ? Even though I picked the right answer while solving I am not pretty clear about the underlying concept?

Thanks, Abhi

A prime number has only two factors - 1 and itself.

Without calculating, we cannot say whether 6!-1 or 6!+41 will be prime.

But, I can say that 6!+21 will not be prime. The reason is that 6!+21 = 3(1*2*4*5*6 + 7) (taking 3 common). This means that whatever, the value of 6!+21, it can be written as the product of two numbers: 3 and something else. Hence, this number, 6!+21, definitely has 3 as a factor and hence it cannot be prime. Since a PS question can have only one correct answer, we don't have to worry about the other options. We can say with certainty that they must be prime. _________________

Re: Which of the following numbers is not prime ? [#permalink]
12 Jun 2013, 14:26

Prime numbers are of the form 6n+1 or 6n-1. The first part of each of the terms contains a 6,and hence is a multiple of 6. We only need to factor out 6's from the 2nd part of each option. If you're left with a number greater than one, then that's the answer . In this case, that would be B.

Re: Which of the following numbers is not prime ? [#permalink]
12 Jun 2013, 14:43

1

This post received KUDOS

Expert's post

v1gnesh wrote:

Prime numbers are of the form 6n+1 or 6n-1. The first part of each of the terms contains a 6,and hence is a multiple of 6. We only need to factor out 6's from the 2nd part of each option. If you're left with a number greater than one, then that's the answer . In this case, that would be B.

Don't get your solution...

The property you are referring to is: any prime number \(p\) greater than 3 could be expressed as \(p=6n+1\) or \(p=6n+5\) (\(p=6n-1\)), where \(n\) is an integer >1.

That's because any prime number \(p\) greater than 3 when divided by 6 can only give remainder of 1 or 5 (remainder can not be 2 or 4 as in this case \(p\) would be even and remainder can not be 3 as in this case \(p\) would be divisible by 3).

But: Note that, not all number which yield a remainder of 1 or 5 upon division by 6 are primes, so vise-versa of above property is not correct. For example 25 (for \(n=4\)) yields a remainder of 1 upon division by 6 and it's not a prime number. _________________

Re: Which of the following numbers is not prime ? [#permalink]
12 Jun 2013, 17:52

Bunuel wrote:

Don't get your solution...

The property you are referring to is: any prime number \(p\) greater than 3 could be expressed as \(p=6n+1\) or \(p=6n+5\) (\(p=6n-1\)), where \(n\) is an integer >1.

That's because any prime number \(p\) greater than 3 when divided by 6 can only give remainder of 1 or 5 (remainder can not be 2 or 4 as in this case \(p\) would be even and remainder can not be 3 as in this case \(p\) would be divisible by 3).

But: Note that, not all number which yield a remainder of 1 or 5 upon division by 6 are primes, so vise-versa of above property is not correct. For example 25 (for \(n=4\)) yields a remainder of 1 upon division by 6 and it's not a prime number.

Thank you! Glad I can correct my understanding now rather than later.

Re: Which of the following numbers is not prime ? [#permalink]
17 Sep 2014, 11:19

I got it really fast 6! is not a prime, so in order to get a non-prime number, we have to add a non-prime number. 21 is not a prime number, therefore 6!+21 is not prime.

gmatclubot

Re: Which of the following numbers is not prime ?
[#permalink]
17 Sep 2014, 11:19

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