If a positive integer n is divisible by both 5 and 7

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M7MBA: Moderator; Posts: 2058; Joined: Sun Oct 29, 2017 4:24 am; Thanked: 1 times; Followed by:5 members

If a positive integer n is divisible by both 5 and 7

by M7MBA » Mon Apr 15, 2019 1:27 am

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If a positive integer "n" is divisible by both 5 and 7, then "n" must also be divisible by which of the following?

I. 12
II. 35
III. 70

(A) None
(B) I only
(C) II only
(D) I and II
(E) II and III

[spoiler]OA=C[/spoiler]

Source: Official Guide

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Source: Beat The GMAT — Problem Solving | Mon Apr 15, 2019 1:27 am

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Wed Apr 17, 2019 5:46 pm

M7MBA wrote:If a positive integer "n" is divisible by both 5 and 7, then "n" must also be divisible by which of the following?

I. 12
II. 35
III. 70

(A) None
(B) I only
(C) II only
(D) I and II
(E) II and III

[spoiler]OA=C[/spoiler]

Source: Official Guide

Since n is divisible by both 5 and 7 it MUST be divisible by the least common multiple of 5 and 7, which is 35. If we take n = 35, we see that n is not necessarily divisible neither by 12 nor by 70.

Answer: C

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