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# Which of the following numbers is the least positive integer that is

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Which of the following numbers is the least positive integer that is  [#permalink]

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20 Mar 2018, 01:01
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35% (medium)

Question Stats:

61% (01:09) correct 39% (00:55) wrong based on 100 sessions

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Which of the following numbers is the least positive integer that is not a prime and is not a factor of 15!

(A) 14
(B) 22
(C) 19
(D) 34
(E) 38

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Re: Which of the following numbers is the least positive integer that is  [#permalink]

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20 Mar 2018, 01:39
Bunuel wrote:
Which of the following numbers is the least positive integer that is not a prime and is not a factor of 15!

(A) 14
(B) 22
(C) 19
(D) 34
(E) 38

Since we're asked 'which of the following' we'll just use the answers!
This is an Alternative approach.

Starting with the least, 14. 14 is not a prime but it is a factor of 15!. NO
The next least: 19. 19 is a prime. NO
Next: 22 is not a prime and factors into 11*2. Then it is also a factor of 15!. NO
Next: 34 is not a prime and factors into 17*2. Then it is not a factor of 15!. YES

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Re: Which of the following numbers is the least positive integer that is  [#permalink]

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20 Mar 2018, 02:13
Bunuel wrote:
Which of the following numbers is the least positive integer that is not a prime and is not a factor of 15!

(A) 14
(B) 22
(C) 19
(D) 34
(E) 38

Using the principle of elimination - POE method. Since the question asks for not a prime & not a factor of 15! ... both the statements should hold true for a Correct answer however... even if one statement fails we can discard the answer choice

(A) 14 factor of 15!- discard
(B) 22 = 11*2 -> factors of 15! - discard
(D) 34 = 17*2 -> 2 is a factor but 17 is not... keep
(E) 38 = 19*2 -> same as above , 19 is not a factor of 15! ... keep

between 34 and 38 -> question is looking for the LEAST POSITIVE INT hence 38 is discarded.

Hence D.

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Which of the following numbers is the least positive integer that is  [#permalink]

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20 Mar 2018, 09:11
Bunuel wrote:
Which of the following numbers is the least positive integer that is not a prime and is not a factor of 15!

(A) 14
(B) 22
(C) 19
(D) 34
(E) 38

Option (C) can be ruled out easily, we are left with options (A), (B) , (D) and (E)

(A) 14 = 2*7 ( Factor of 15!)
(B) 22 = 2*11 ( Factor of 15!)
(D) 34 = 2 * 17 ( Not a Factor of 15!)
(E) 38 = 2 * 19 ( Not a Factor of 15!)

Thus the least positive integer that is not a prime and is not a factor of 15!, will be (D)
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Re: Which of the following numbers is the least positive integer that is  [#permalink]

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21 Mar 2018, 16:14
Bunuel wrote:
Which of the following numbers is the least positive integer that is not a prime and is not a factor of 15!

(A) 14
(B) 22
(C) 19
(D) 34
(E) 38

Remember that 15! = 15 x 14 x 13 x 12 x 11 x 10 x … x 2 x 1. Let’s consider each answer choice:

Choice A. We see that 14 is not a prime number, but it is a factor of 15!, so A is not correct.

Choice B. We see that 22 = 11 x 2, and both 11 and 2 are factors of 15!, so B is not correct.

Choice C. We see that 19 is NOT a factor of 15!. However, it is a prime number, so C is not correct.

Choice D. We see that 34 = 17 x 2, so 34 is not a prime. Furthermore, since 15! does not have a prime factor of 17, 34 cannot be a factor of 15!.

Thus, 34 is the least positive integer that is not a prime and is not a factor of 15!. Thus, choice D is correct.

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Re: Which of the following numbers is the least positive integer that is  [#permalink]

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26 Mar 2018, 00:38
Bunuel wrote:
Which of the following numbers is the least positive integer that is not a prime and is not a factor of 15!

(A) 14
(B) 22
(C) 19
(D) 34
(E) 38

(A) 14 = 2 * 7
(B) 22 = 2 * 11
(C) 19 = 1 * 19
(D) 34 = 2 * 17
(E) 38 = 2 * 19

Only number 17 and 19 are not the part of 15!

But we require least, therefore the number is "17"

Hence (D)
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Re: Which of the following numbers is the least positive integer that is   [#permalink] 26 Mar 2018, 00:38
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