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# Which of the following numbers is not prime ?

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

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Last edited by Bunuel on 03 May 2012, 00:19, edited 1 time in total.
Edited the question
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Re: Which of the following numbers is not prime ? [#permalink]  03 May 2012, 00:21
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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.

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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.

@ 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?
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Re: Which of the following numbers is not prime ? [#permalink]  03 May 2012, 08:38
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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.
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Re: Which of the following numbers is not prime ? [#permalink]  27 Nov 2012, 16:23
The added or subtracted terms, all but one of them, is a prime number itself, that should be a sort of red flag.
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Re: Which of the following numbers is not prime ? [#permalink]  27 Nov 2012, 16:40
+1 B

6! is multiple of 21 (= 3 * 7)
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Re: Which of the following numbers is not prime ? [#permalink]  12 Jun 2013, 04:25
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Bumping for review and further discussion*. Get a kudos point for an alternative solution!

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

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

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.
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Re: Which of the following numbers is not prime ? [#permalink]  16 Nov 2013, 20:35
any prime number greater than 3, can be written as either (6n+1) or (6n-1).
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Re: Which of the following numbers is not prime ? [#permalink]  12 Sep 2014, 01:03
The only pair having common factor except 1 and itself is 6!+21, they both divisible by 3. So their sum cannot be prime

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

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