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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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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  B
Joined: 31 Jan 2012
Posts: 69
Re: P is a prime number. If 6p is between 15 and 95  [#permalink]

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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.
Intern  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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Answer is B- of the prime numbers between 15 & 95, only 11 fits into one of the answer choices
Math Expert V
Joined: 02 Sep 2009
Posts: 58381
Re: P is a prime number. If 6p is between 15 and 95  [#permalink]

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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

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.

We should have 7p+2={answer choice} --> 7p={answer choice}-2;

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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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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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:

Let’s test each answer choice:

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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If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: P is a prime number. If 6p is between 15 and 95   [#permalink] 31 Oct 2018, 18:22
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P is a prime number. If 6p is between 15 and 95

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