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M60-20

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Math Revolution GMAT Instructor
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GMAT 1: 760 Q51 V42
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M60-20  [#permalink]

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New post 11 Jun 2018, 06:45
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

71% (00:37) correct 29% (00:30) wrong based on 7 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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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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Math Revolution GMAT Instructor
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Joined: 16 Aug 2015
Posts: 7766
GMAT 1: 760 Q51 V42
GPA: 3.82
Re M60-20  [#permalink]

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New post 11 Jun 2018, 06:46
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.



Therefore, E is the 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.

Answer: E
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Re: M60-20  [#permalink]

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New post 01 Aug 2019, 23:47
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?
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Re: M60-20  [#permalink]

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New post 11 Aug 2019, 15:08
If x= 90 then its divisible by both 6 and 10 but not by 60.
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Re: M60-20   [#permalink] 11 Aug 2019, 15:08
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