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# Is the positive integer x divisible by 60?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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GPA: 3.82
Is the positive integer x divisible by 60? [#permalink]

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02 Feb 2018, 00:59
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Difficulty:

45% (medium)

Question Stats:

49% (00:31) correct 51% (00:34) wrong based on 61 sessions

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[GMAT math practice question]

Is the positive integer $$x$$ divisible by $$60$$?

1) $$x$$ is divisible by $$6$$
2) $$x$$ is divisible by $$10$$
[Reveal] Spoiler: OA

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Re: Is the positive integer x divisible by 60? [#permalink]

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02 Feb 2018, 01:07
E
1. X may be 12, 18 and statement can hold. X can be 60 and both statement and question stem hold. Insufficient

2. X may be 10, 20 and statement can hold. X can be 60 and both statement and question stem hold. Insufficient
Combining,

X can be 30 and both statements can hold but not the question stem. When x is 60 both statements and question stem can hold.
Clearly both statements are insufficient

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Re: Is the positive integer x divisible by 60? [#permalink]

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02 Feb 2018, 07:34
MathRevolution wrote:
[GMAT math practice question]

Is the positive integer $$x$$ divisible by $$60$$?

1) $$x$$ is divisible by $$6$$
2) $$x$$ is divisible by $$10$$

If a positive integer N is divisible by positive integers:- x, y, z etc. then it is also divisible by the LCM of (x, y, z..)
So if a number is divisible by both 6 and 10 then it must also be divisible by the LCM of 6 & 10, which is '30'

Individual statements are not sufficient because a multiple of 6 might or might not be a multiple of 60 and similarly a multiple of 10 might or might not be a multiple of 60. Combining the two statements, x will be divisible by 30. But a multiple of 30 might or might not be a multiple of 60 (90 is not, but 120 is). So not sufficient.

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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GPA: 3.82
Re: Is the positive integer x divisible by 60? [#permalink]

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04 Feb 2018, 17:10
=>

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.

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Re: Is the positive integer x divisible by 60?   [#permalink] 04 Feb 2018, 17:10
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# Is the positive integer x divisible by 60?

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