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# If a = 15! + 13, which of the following are factors of a?

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Math Expert
Joined: 02 Sep 2009
Posts: 56272
If a = 15! + 13, which of the following are factors of a?  [#permalink]

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23 Sep 2018, 23:07
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Difficulty:

35% (medium)

Question Stats:

66% (00:58) correct 34% (01:04) wrong based on 79 sessions

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If a = 15! + 13, which of the following are factors of a?

I. 13
II. 14
III. 26

A. I only
B. I and II only
C. I and III only
D. I, II, and III only
E. None of the above

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Re: If a = 15! + 13, which of the following are factors of a?  [#permalink]

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23 Sep 2018, 23:24
f a = 15! + 13, which of the following are factors of a?

I. 13
II. 14
III. 26

A. I only
B. I and II only
C. I and III only
D. I, II, and III only
E. None of the above

IMO only option A would be correct..
from the given expression a=15!+13
we can get : 13((15*14*12!)+1)
by which we can say that for factors of a would be 13 so option 1 is correct.

Coming to 2nd option 14: factor 7*2 so no

and 3rd option 26= 13*2,
for the expression 13((15*14*12!)+1) , though 13 would get cancelled out but for the rest of expression the outcome would be an odd no. so 26 wont be factor of the expression..

This is my take of the question, let me know if i have done any error..
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Re: If a = 15! + 13, which of the following are factors of a?  [#permalink]

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23 Sep 2018, 23:49
Bunuel wrote:
If a = 15! + 13, which of the following are factors of a?

I. 13
II. 14
III. 26

A. I only
B. I and II only
C. I and III only
D. I, II, and III only
E. None of the above

a = 15! + 13 = 13xEven+13 = 13(Even+1) = 13xOdd number

Hence, only 13 will be factor of a out of gievn three numbers

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Re: If a = 15! + 13, which of the following are factors of a?  [#permalink]

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24 Sep 2018, 02:03
Bunuel wrote:
If a = 15! + 13, which of the following are factors of a?

I. 13
II. 14
III. 26

A. I only
B. I and II only
C. I and III only
D. I, II, and III only
E. None of the above

$$a = 15! + 13 = 13 * (1*2*3..12*14*15 + 1)$$

Note the two factors of a - "13" and "1 more than a number that has all other primes till 15"
Hence, this second factor will have none of these primes (2, 3, 5, 7, 11)

I. 13
13 is a factor of a.

II. 14
2 and 7 are not factors of a.

III. 26
2 is not a factor of a.

Check:
https://www.veritasprep.com/blog/2011/0 ... c-or-math/
https://www.veritasprep.com/blog/2011/0 ... h-part-ii/
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Re: If a = 15! + 13, which of the following are factors of a?   [#permalink] 24 Sep 2018, 02:03
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