The numbers m, n, and K are all positive integers. Given that m is a factor of K

Question

The numbers m, n, and K are all positive integers. Given that m is a factor of K, that n is also a factor of K, and m < n, which of the following must also be a positive integer factor of K?

A. m + n
B. mn
C. n^2/m
D. K/m
E. K/(mn)

Answer: D
Source: Magoosh

Brent@GMATPrepNow · Answer

BTGModeratorVI wrote: ↑Sun Sep 27, 2020 7:07 am The numbers m, n, and K are all positive integers. Given that m is a factor of K, that n is also a factor of K, and m < n, which of the following must also be a positive integer factor of K? A. m + n B. mn C. n^2/m D. K/m E. K/(mn) Answer: D Source: Magoosh GIVEN: m is a factor of K This means that we can write: K = md for some integer d If m and d are both integers, then m and d are both factors of K Notice that, if K = md, then d = K/m, which means K/m is a factor of K Answer: D Cheers, Brent

Brent@GMATPrepNow · Answer

BTGModeratorVI wrote: ↑Sun Sep 27, 2020 7:07 am The numbers m, n, and K are all positive integers. Given that m is a factor of K, that n is also a factor of K, and m < n, which of the following must also be a positive integer factor of K? A. m + n B. mn C. n^2/m D. K/m E. K/(mn) Answer: D Source: Magoosh Different approach: The question asks "which of the following must also be a positive integer factor of K?" So, if we can find an answer choice that is NOT a factor of K we can ELIMINATE that answer choice. A. m + n If K = 12, then if COULD be the case that m = 4 and n = 6 In this case, m + n = 4 + 6 = 10, and 10 is NOT a factor of 12 ELIMINATE A B. mn If K = 12, then if COULD be the case that m = 4 and n = 6 In this case, mn = (4)(6) = 24, and 24 is NOT a factor of 12 ELIMINATE B C. n²/m If K = 12, then if COULD be the case that m = 4 and n = 6 In this case, n²/m = 6²/4 = 9, and 9 is NOT a factor of 12 ELIMINATE C D. K/m If K = 12, then if COULD be the case that m = 4 and n = 6 In this case, K/m = 12/4 = 3, and 3 IS a factor of 12 KEEP D (for now) E. K/(mn) If K = 12, then if COULD be the case that m = 4 and n = 6 In this case, K/(mn) = 12/(4)(6) = 1/2, and 1/2 is NOT a positive INTEGER factor of 12 ELIMINATE E By the process of elimination, the correct answer is D Cheers, Brent

swerve · Answer

BTGModeratorVI wrote: ↑Sun Sep 27, 2020 7:07 am The numbers m, n, and K are all positive integers. Given that m is a factor of K, that n is also a factor of K, and m < n, which of the following must also be a positive integer factor of K? A. m + n B. mn C. n^2/m D. K/m E. K/(mn) Answer: D Source: Magoosh If $K$ is a positive integer and $K$ is divided by one of its factors the result is always a factor of $K \Rightarrow$ K/m or K/n satisfies the rule. For example: $K = 100 \Rightarrow$ Factors of $K = 1, 2, 4, 5, 10, 20, 25, 50, 100$ Let $m = 10; n = 100$ A. $m + n \Rightarrow 110$ is not a factor of $K \Large{\color{red}\chi}$ B. $mn \Rightarrow 1000$ is not a factor of $K \Large{\color{red}\chi}$ C. $n^2/m \Rightarrow 1000$ is not a factor of $K \Large{\color{red}\chi}$ D. $K/m \Rightarrow 10$ is a factor of $K$ $\Large{\color{green}\checkmark}$ E. $K/(mn) \Rightarrow 0.1$ is not an integer $\Large{\color{red}\chi}$ Therefore, D

gentvenus · Answer

Brent@GMATPrepNow wrote: ↑Mon Sep 28, 2020 12:02 pm BTGModeratorVI wrote: ↑Sun Sep 27, 2020 7:07 am The numbers m, n, and K are all positive integers. Given that m is a factor of K, that n is also a factor of K, and m < n, which of the following must also be a positive integer factor of K? A. m + n B. mn C. n^2/m D. K/m E. K/(mn) Answer: D Source: Magoosh Different approach: The question asks "which of the following must also be a positive integer factor of K?" So, if we can find an answer choice that is NOT a factor of K we can ELIMINATE that answer choice. A. m + n If K = 12, then if COULD be the case that m = 4 and n = 6 In this case, m + n = 4 + 6 = 10, and 10 is NOT a factor of 12 ELIMINATE A B. mn If K = 12, then if COULD be the case that m = 4 and n = 6 In this case, mn = (4)(6) = 24, and 24 is NOT a factor of 12 ELIMINATE B C. n²/m If K = 12, then if COULD be the case that m = 4 and n = 6 In this case, n²/m = 6²/4 = 9, and 9 is NOT a factor of 12 ELIMINATE C D. K/m If K = 12, then if COULD be the case that m = 4 and n = 6 In this case, K/m = 12/4 = 3, and 3 IS a factor of 12 KEEP D (for now) E. K/(mn) If K = 12, then if COULD be the case that m = 4 and n = 6 In this case, K/(mn) = 12/(4)(6) = 1/2, and 1/2 is NOT a positive INTEGER factor of 12 ELIMINATE E By the process of elimination, the correct answer is D Cheers, Brent I like this approach

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The numbers m, n, and K are all positive integers. Given that m is a factor of K

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Re: The numbers m, n, and K are all positive integers. Given that m is a factor of K

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Re: The numbers m, n, and K are all positive integers. Given that m is a factor of K

Re: The numbers m, n, and K are all positive integers. Given that m is a factor of K

Re: The numbers m, n, and K are all positive integers. Given that m is a factor of K

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