GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Positive integers a and b each have exactly four factors. If
[#permalink]
12 Aug 2018, 15:24
12 Aug 2018, 15:24
1
Expert Reply
5
Bookmarks
00:00
Question Stats:
79% (01:09) correct
20% (01:36) wrong based on 53 sessions
Hide Show timer Statistics
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?
Show: :: OA
6
Re: Positive integers a and b each have exactly four factors. If
[#permalink]
15 Aug 2018, 05:21
15 Aug 2018, 05:21
1
Expert Reply
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.
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.
Re: Positive integers a and b each have exactly four factors. If
[#permalink]
30 Apr 2021, 00:25
30 Apr 2021, 00:25
1
I'm aware that prime numbers have only 2 factors, but in the question they didn't mention that a and b are a prime numbers there they mentioned that they are "positive integers". Why can't I assume that 2 has factors -1, -2, 1 and 2? I know that this sounds wierd but sounds possible.
Posted from my mobile device
Posted from my mobile device
