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Integer Properties question from the little green book

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Integer Properties question from the little green book

by hutch27 » Sat Apr 13, 2013 4:08 pm
I know this question was posted before but I didn't really understand it and I have a question too.

115) is the positive integer n a multiple of 24

1) n is a multiple of 4
2) n is a multiple of 6

oa is e

So the way that I tried to answer this question was I first rephrased the target question to: is n a multiple of 24, is 24 a divisor of n, is the prime factorization of 24 hiding in n, ect... that help me start out

so i prime factorized 24 and got 2^3 x 3

saw statement 1... obviously insufficient. dont need help with that
statement 2.. same thing. im good with this.

combined I see that the prime factors of 4 are 2 and 2, and the prime factors of 6 are 2 and 3... so I just saw that both statements shared the same prime factors as 24.
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by Brent@GMATPrepNow » Sat Apr 13, 2013 5:00 pm
hutch27 wrote:I know this question was posted before but I didn't really understand it and I have a question too.

115) is the positive integer n a multiple of 24

1) n is a multiple of 4
2) n is a multiple of 6

oa is e

So the way that I tried to answer this question was I first rephrased the target question to: is n a multiple of 24, is 24 a divisor of n, is the prime factorization of 24 hiding in n, ect... that help me start out

so i prime factorized 24 and got 2^3 x 3

saw statement 1... obviously insufficient. dont need help with that
statement 2.. same thing. im good with this.

combined I see that the prime factors of 4 are 2 and 2, and the prime factors of 6 are 2 and 3... so I just saw that both statements shared the same prime factors as 24.
I like your approach. Here's the same approach carried through to the end.

Target question: Is n a multiple of 24?

Aside: For questions involving multiples, we can say:
If N is a multiple of k, then k is "hiding" within the prime factorization of N
Examples:
12 is a multiple of 3 <--> 12 = (2)(2)(3)
70 is a multiple of 5 <--> (2)(5)(7)
330 is a multiple of 6 <--> 330 = (2)(3)(5)(11)

Since 24 = (2)(2)(2)(3), we can rephrase the target question...

Rephrased target question: Are there three 2's and a 3 hiding in the prime factorization of n?

Statement 1: n is a multiple of 4
Since 4 = (2)(2), this statement is telling us that there are two 2's hiding in the prime factorization of n.
This is not enough information to determine whether or not there are three 2's and a 3 hiding on the prime factorization of n
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: n is a multiple of 6
Since 6 = (2)(3), this statement is telling us that there's one 2 and one 3 hiding in the prime factorization of n.
This is not enough information to determine whether or not there are three 2's and a 3 hiding on the prime factorization of n
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined:
Statement 1 tells us that there are two 2's hiding in the prime factorization of n.
Statement 2 tells us that there's one 2 and one 3 hiding in the prime factorization of n.
So, all we can conclude is that there are two 2's hiding and one 3 hiding in the prime factorization of n.
This is not enough information to determine whether or not there are three 2's and a 3 hiding on the prime factorization of n
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer = E

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by Brent@GMATPrepNow » Sat Apr 13, 2013 5:06 pm
hutch27 wrote:I know this question was posted before but I didn't really understand it and I have a question too.

115) is the positive integer n a multiple of 24

1) n is a multiple of 4
2) n is a multiple of 6

oa is e
Here's a different (bare bones) approach.

Target question: Is n a multiple of 24?

Statement 1: n is a multiple of 4
Some possible values of n are: 4, 8, 12, 16, 20, 24, 28, etc
As we can see, some values of n are multiples of 24, and some are not.
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: n is a multiple of 6
Some possible values of n are: 6, 12, 18, 24, 30, 36 etc
As we can see, some values of n are multiples of 24, and some are not.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined:
So n is a multiple of 4 AND a multiple of 6.
Some possible values of n are: 12, 24, 36 etc
As we can see, some values of n are multiples of 24, and some are not.
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer = E

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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