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# Positive integers a and b each have exactly four factors. If a is a on

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Math Expert
Joined: 02 Sep 2009
Posts: 58453
Positive integers a and b each have exactly four factors. If a is a on  [#permalink]

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17 Dec 2018, 01:51
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Difficulty:

25% (medium)

Question Stats:

73% (01:22) correct 27% (01:18) wrong based on 42 sessions

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Positive integers a and b each have exactly four factors. If a is a one-digit number and b = a + 9, what is the value of b?

A. 13
B. 14
C. 15
D. 16
E. 17

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Re: Positive integers a and b each have exactly four factors. If a is a on  [#permalink]

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17 Dec 2018, 02:23
Bunuel wrote:
Positive integers a and b each have exactly four factors. If a is a one-digit number and b = a + 9, what is the value of b?

A. 13
B. 14
C. 15
D. 16
E. 17

To have four factors for a number, either it is a cube of a prime number or has only 2 prime numbers as its factor. Since a is a single digit number, it can either be 8(cube of 2) or 6 (with only 2 and 3 as its prime factors.)

For a=8, b=17, since it is given that b also has 4 prime factors. it can't 17 because it has only two factors.

For a=6, b=15, which has four factors with two distinct prime factors. (3&5) and total number of factors= 1,3,5,15.

Hence, b=15, IMO, Option C.
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Re: Positive integers a and b each have exactly four factors. If a is a on   [#permalink] 17 Dec 2018, 02:23
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# Positive integers a and b each have exactly four factors. If a is a on

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