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# P is a prime number. If 6p is between 15 and 95

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Intern
Joined: 18 Feb 2011
Posts: 33
GPA: 3.91
P is a prime number. If 6p is between 15 and 95  [#permalink]

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05 Feb 2012, 23:33
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Question Stats:

85% (01:56) correct 15% (01:55) wrong based on 153 sessions

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P is a prime number. If 6p is between 15 and 95, which of the following can be a value of 7p + 2?

A. 15
B. 79
C. 121
D. 65
E. 21
Manager
Joined: 31 Jan 2012
Posts: 69
Re: P is a prime number. If 6p is between 15 and 95  [#permalink]

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06 Feb 2012, 01:18
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[3,5,7,11,13] are prime numbers that fits this equation 15< 6X <95. Afterwards subtract 2 from all the answer n see if it's divisible by 7. Therefore A and E are out. Leaves out with B C D.
B =11
C =17
D = 9
Only 11 is the set of prime numbers that fit between 15 and 95. Therefore 79 is the answer.
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Joined: 05 Jan 2012
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Re: P is a prime number. If 6p is between 15 and 95  [#permalink]

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06 Feb 2012, 01:51
Answer is B- of the prime numbers between 15 & 95, only 11 fits into one of the answer choices
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Posts: 58381
Re: P is a prime number. If 6p is between 15 and 95  [#permalink]

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06 Feb 2012, 01:58
nafishasan60 wrote:
P is a prime number. If 6p is between 15 and 95, which of the following can be a value of 7p + 2?

A. 15
B. 79
C. 121
D. 65
E. 21

15<6p<95 --> the minimum value of prime number p is 3 (6*3=18>15) and the maximum value is 13 (6*13=84<95 and 6*17>95). So, possible values of p are: 3, 5, 7, 11, and 13.

Answer choices which are multiples of 7 after we subtract 2 are 79 (B), 121 (C) and 65 (D) but only (79-2)/7 yields a prime number from our range: 11. 121 also yields a prim number 17, (121-2)/7=17=prime, but 17 is out of our range.

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Re: P is a prime number. If 6p is between 15 and 95  [#permalink]

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06 Feb 2012, 02:10
2
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nafishasan60 wrote:
P is a prime number. If 6p is between 15 and 95, which of the following can be a value of 7p + 2?

A. 15
B. 79
C. 121
D. 65
E. 21

Even though you already have the solution, let me point out the takeaway from this question.

"which of the following can be..." questions are generally best done by using the options. Use the options to find the one which satisfies all conditions.

We see that the format we are looking for is 7p + 2.
When you subtract 2 from option A, you get 13 - not a multiple of 7. Ignore.
When you subtract 2 from option B, you get 77. It is a multiple of 7. Let's check it. p = 11 which is prime. Good. 6p = 66 which is between 15 and 95. Very good. All conditions satisfied so answer is (b)
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Re: P is a prime number. If 6p is between 15 and 95  [#permalink]

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31 Oct 2018, 18:22
nafishasan60 wrote:
P is a prime number. If 6p is between 15 and 95, which of the following can be a value of 7p + 2?

A. 15
B. 79
C. 121
D. 65
E. 21

If p is 3, then 6p is 18.

If p is 13, then 6p is 78.

So p must be between 3 and 13, inclusive, and thus 7p + 2 must be between 23 and 93, inclusive. We see that both answer choices B 79 and D 65 are between 23 and 93.

If 7p + 2 = 79, then 7p = 77 and p = 11.

If 7p + 2 = 65, then 7p = 63 and p = 9.

Since p = 11 is a prime (and p = 9 is not a prime), then 7p + 2 = 79.

Alternate Solution:

A) 7p + 2 = 15

If 7p + 2 = 15, then 7p = 13 and p is not an integer.

B) 7p + 2 = 79

If 7p + 2 = 79, then 7p = 77 and p = 11. We see that 6p = 66 is between 15 and 95; therefore B is the correct choice.

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Re: P is a prime number. If 6p is between 15 and 95   [#permalink] 31 Oct 2018, 18:22
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