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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8987
GMAT 1: 760 Q51 V42
GPA: 3.82

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Difficulty:   25% (medium)

Question Stats: 78% (00:33) correct 22% (00:30) wrong based on 9 sessions

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Is the positive integer x divisible by 60?

1) x is divisible by 6

2) x is divisible by 10

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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8987
GMAT 1: 760 Q51 V42
GPA: 3.82

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Official Solution:

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question, and then recheck the question.

The question asks if x = 60t for some integer t.

$$x = 60t$$

⇔ $$x = 2^2*3*5*t$$

Conditions 1) ($$x = 2*3m$$ for some integer $$m$$) and 2) ($$x = 2*5n$$ for some integer n) do not tell us whether $$2^2$$ is a factor of $$x$$. So, they are not sufficient, when taken together. For example, if

$$x = 60$$, then the answer is 'yes', but if

$$x = 30$$, then the answer is 'no'.

Both conditions together are not sufficient, as the question does not have a unique answer.

Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.

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Intern  Joined: 12 Jun 2019
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Why do we need a unique answer, when clearly, the type of question is binary, either a yes or a no.

If x=60t,
S1 -> x = 6t
S2 -> x = 10t

Both of which are divisible if x = 60t. Hence, D.

But maybe I'm wrong. If yes, can somebody explain?
Intern  B
Joined: 01 Feb 2019
Posts: 1

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If x= 90 then its divisible by both 6 and 10 but not by 60.
Intern  Joined: 13 Apr 2020
Posts: 3

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Right, nos like 90, 150 etc make option 'C' not a right choice. E is the answer Re: M60-20   [#permalink] 13 Apr 2020, 22:23

# M60-20

Moderators: chetan2u, Bunuel  