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Composite numbers and tens digit

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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Wed Apr 08, 2015 7:55 am
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 .
Target question: Is n composite?

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

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Brent
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by [email protected] » Wed Apr 08, 2015 8:10 pm
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

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Rich
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