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

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GMAT Club Legend
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Joined: 07 Jun 2014
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GRE 1: Q167 V156
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Positive integers a and b each have exactly four factors. If [#permalink] New post 12 Aug 2018, 15:24
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100% (00:40) correct 0% (00:00) wrong based on 6 sessions
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 a?

[Reveal] Spoiler: OA
6

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Sandy
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GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jun 2014
Posts: 4749
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 93

Kudos [?]: 1653 [0], given: 396

CAT Tests
Re: Positive integers a and b each have exactly four factors. If [#permalink] New post 15 Aug 2018, 05:21
Expert's post
Explanation

Start by considering integer a, which is the most constrained variable. It is a positive one-digit number (between 1 and 9, inclusive) and it has four factors. Prime numbers have exactly two factors:

themselves and one, so only look at non-prime one-digit positive integers. That’s a short enough list:

1 has just one factor

4 has three factors: 1, 2, and 4

6 has four factors: 1, 2, 3, and 6

8 has four factors: 1, 2, 4, and 8

9 has three factors: 1, 3, and 9

So the two possibilities for a are 6 and 8. Now apply the two constraints for b. It is 9 greater than a, and it has exactly four factors. Check the possibilities:

If a = 6, then b = 15, which has four factors: 1, 3, 5, and 15.

If a = 8, then b = 17, which is prime, so it has only has two factors: 1 and 17.

Only b = 15 works, so a must be 6.
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Re: Positive integers a and b each have exactly four factors. If   [#permalink] 15 Aug 2018, 05:21
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Positive integers a and b each have exactly four factors. If

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