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# For positive integer m and n, is 2m/3n an integer?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 7597
GMAT 1: 760 Q51 V42
GPA: 3.82
For positive integer m and n, is 2m/3n an integer?  [#permalink]

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26 Feb 2018, 02:33
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Difficulty:

35% (medium)

Question Stats:

74% (01:09) correct 26% (00:53) wrong based on 58 sessions

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[GMAT math practice question]

For positive integer $$m$$ and $$n$$, is $$\frac{2m}{3n}$$ an integer?

1) $$m$$ is a multiple of $$3$$
2) $$n$$ is a multiple of $$2$$

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Retired Moderator Joined: 07 Jan 2016 Posts: 1090 Location: India GMAT 1: 710 Q49 V36 Re: For positive integer m and n, is 2m/3n an integer? [#permalink] ### Show Tags 26 Feb 2018, 04:13 MathRevolution wrote: [GMAT math practice question] For positive integer $$m$$ and $$n$$, is $$\frac{2m}{3n}$$ an integer? 1) $$m$$ is a multiple of $$3$$ 2) $$n$$ is a multiple of $$2$$ only if n= 2 will the above value be an integer m= 6 n=4 2x6 / 2x4 not int n=3 n=2 int using both statements the value of n=2 CBD (E) imo Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7597 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: For positive integer m and n, is 2m/3n an integer? [#permalink] ### Show Tags 28 Feb 2018, 01:27 => 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. Since we have 2 variables (m and n) and 0 equations, C is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first. Conditions 1) & 2): $$m = 3, n = 2$$: $$\frac{2m}{3n} = \frac{6}{6} = 1$$ is an integer. $$m = 3, n= 4$$: $$\frac{2m}{3n} = \frac{6}{12} = \frac{1}{2}$$ is not an integer. Since we don’t have a unique solution, both conditions together are not sufficient. Therefore, E is the answer. Answer: E 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. _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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Re: For positive integer m and n, is 2m/3n an integer?   [#permalink] 28 Feb 2018, 01:27
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