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# If m and n are positive integers, m+n=?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6639
GMAT 1: 760 Q51 V42
GPA: 3.82
If m and n are positive integers, m+n=?  [#permalink]

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25 Jun 2018, 05:54
00:00

Difficulty:

35% (medium)

Question Stats:

62% (01:11) correct 38% (01:25) wrong based on 61 sessions

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[GMAT math practice question]

If $$m$$ and $$n$$ are positive integers, $$m+n=$$?

1) $$m-n=-1$$
2) $$n^2<5$$

_________________

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 $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Math Expert Joined: 02 Aug 2009 Posts: 7108 Re: If m and n are positive integers, m+n=? [#permalink] ### Show Tags 25 Jun 2018, 06:24 MathRevolution wrote: [GMAT math practice question] If $$m$$ and $$n$$ are positive integers, $$m+n=$$? 1) $$m-n=-1$$ 2) $$n^2<5$$ 1) m-n=-1 So n-m=1... Or n and m are consecutive positive integers and n>m>0 n and m can take any values.. 3&4 or 10&11 Insufficient 2) $$n^2<5$$.. So n can be 1 or 2, nothing about m Insufficient.. Combined n>m>0 and n can be 1 or 2.. If n is 1, m becomes 0 but m>0, so only value of n is 2 and m is 1 n+m=1+2=3 Sufficient C _________________ 1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html GMAT online Tutor Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6639 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If m and n are positive integers, m+n=? [#permalink] ### Show Tags 27 Jun 2018, 00:57 => 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) Since $$0 < n^2<5$$, we must have $$n = 1$$ or $$n = 2.$$ Case 1: $$n = 1$$ Since $$m – n = m – 1 = -1$$, we have $$m = 0$$, which is not positive. So, $$n$$ is not equal to $$1$$. Case 2: $$n = 2$$ Since $$m – n = m – 2 = -1$$, we have $$m = 1$$. Thus $$m + n = 1 + 2 = 3.$$ Because we have a unique solution, both conditions together are sufficient. Since this question is an integer question (one of the key question areas), CMT (Common Mistake Type) 4(A) of the VA (Variable Approach) method tells us that we should also check answers A and B. Condition 1) If $$m = 1$$ and $$n = 2$$, then $$m + n = 3.$$ If $$m = 2$$ and $$n = 3$$, then $$m + n = 5.$$ Since we don’t have a unique solution, condition 1) is not sufficient. Condition 2) Since we don’t have any information about m, condition 2) is not sufficient. Therefore, C is the answer. Answer: C 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$99 for 3 month Online Course"
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Re: If m and n are positive integers, m+n=? &nbs [#permalink] 27 Jun 2018, 00:57
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