Composite numbers and tens digit
This topic has expert replies
-
- Master | Next Rank: 500 Posts
- Posts: 107
- Joined: Tue Oct 07, 2014 3:50 am
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Target question: Is n composite?An integer greater than 1 that is not prime is called composite. If the two digit integer n is greater than 20 , is n composite ?
1) The tens digit of n is a factor of the units digit of n .
2) The tens digit of n is 2 .
Given: n > 20
Statement 1: The tens digit of n is a factor of the units digit of n
It doesn't take long to list the 2-digit numbers that satisfy this condition:
22, 24, 26, 28
33, 36, 39
44, 48
55
66
77
88
99
ALL of these possible values of n are composite, so n must be composite.
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: The tens digit of n is 2.
There are several values of n that meet this condition. Here are two:
Case a: n = 21, in which case n is composite
Case b: n = 23, in which case n is not composite
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Answer = A
Cheers,
Brent
GMAT/MBA Expert
- [email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
Hi Mallika,
Brent's approach to solving this problem is spot-on, so I won't rehash any of that work here. Instead, I'll point out the Number Property patterns that occur in this prompt.
First, we're told that N is a 2-digit integer greater than 20. We're asked if N is composite (is it non-prime?)?
Fact 1 tells us that the ten's digit of N is a factor of the unit's digit of N.
With this information, we know we'll be dealing with lots of multiples of 11 (re: 22, 33, 44, 55, etc.) and none of those are prime (since they're all divisible by 11.
The other numbers all have to be less than 50.
The ones in the 20s: 22, 24, 26, 28 are all even, so they're not prime
The ones in the 30s: 33, 36, 39 are all divisible by 3 (the rule of 3)
The ones in the 40s: 44, 48 are both even as well.
So none of them are prime. This is a consistent situation, so Fact 1 is SUFFICIENT
GMAT assassins aren't born, they're made,
Rich
Brent's approach to solving this problem is spot-on, so I won't rehash any of that work here. Instead, I'll point out the Number Property patterns that occur in this prompt.
First, we're told that N is a 2-digit integer greater than 20. We're asked if N is composite (is it non-prime?)?
Fact 1 tells us that the ten's digit of N is a factor of the unit's digit of N.
With this information, we know we'll be dealing with lots of multiples of 11 (re: 22, 33, 44, 55, etc.) and none of those are prime (since they're all divisible by 11.
The other numbers all have to be less than 50.
The ones in the 20s: 22, 24, 26, 28 are all even, so they're not prime
The ones in the 30s: 33, 36, 39 are all divisible by 3 (the rule of 3)
The ones in the 40s: 44, 48 are both even as well.
So none of them are prime. This is a consistent situation, so Fact 1 is SUFFICIENT
GMAT assassins aren't born, they're made,
Rich