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# |m-n|=?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 7590
GMAT 1: 760 Q51 V42
GPA: 3.82

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10 Jul 2018, 02:37
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Difficulty:

35% (medium)

Question Stats:

63% (00:48) correct 37% (00:41) wrong based on 50 sessions

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[GMAT math practice question]

|m-n|=?

1) m and n are integers
2) mn=13

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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" SVP Joined: 26 Mar 2013 Posts: 2283 |m-n|=? [#permalink] ### Show Tags 10 Jul 2018, 03:20 MathRevolution wrote: [GMAT math practice question] |m-n|=? 1) m and n are integers 2) mn=13 1) m and n are integers Clearly any integers could plugged in m=2 & n=1........|m-n|=1 m=10 & n=1........|m-n|=9 m=2 & n=8........|m-n|=6 Insufficient 2) mn=13 m=13 & n=1........|m-n|=12 m=1 & n=13........|m-n|=12 m=26 & n=$$\frac{1}{2}$$........|m-n|=25.5 Insufficient Combine 1 & 2 From 2: 13 is a prime number From 1: m & n are integers so either (m=13 & n=1) or (m=1 & n=13). In both cases.........|m-n|=12 Sufficient Answer: C Senior Manager Joined: 04 Aug 2010 Posts: 434 Schools: Dartmouth College Re: |m-n|=? [#permalink] ### Show Tags 10 Jul 2018, 04:47 MathRevolution wrote: [GMAT math practice question] |m-n|=? 1) m and n are integers 2) mn=13 {m-n| = the distance between m and n. Question stem, rephrased: What is the distance between m and n? Statement 1: Clearly INSUFFICIENT. Statement 2: Case 1: m=13 and n=1, with the result that the distance between m and n is 12 Case 2: m=100 and n=13/100, with the result that the distance between m and n is about 100 Since the distance can be different values, INSUFFICIENT. Statements combined: Only four cases are possible: m=13, n=1 m=-13, n=-1 m=1, n=13 m=-1, n=-13 In every case, the distance between m and n is 12. SUFFICIENT. _________________ GMAT and GRE Tutor Over 1800 followers GMATGuruNY@gmail.com New York, NY If you find one of my posts helpful, please take a moment to click on the "Kudos" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7590 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: |m-n|=? [#permalink] ### Show Tags 12 Jul 2018, 01:05 => 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 m and n are integers, the pairs of solutions of the equation $$mn=13$$ are $$m = 1, n = 13; m = 13, n = 1; m = -1, n = -13$$; and $$m = -13, n = -1.$$ If $$m = 1, n = 13,$$ then $$| m – n | = | 1 – 13 | = 12.$$ If $$m = 13, n = 1$$, then $$| m – n | = | 13 – 1 | = 12.$$ If $$m = -1, n = -13,$$ then $$| m – n | = | -1 – (-13) | = 12.$$ If $$m = -13, n = -1,$$ then $$| m – n | = | -13 – (-1) | = 12.$$ Since this question is an absolute value 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) Since we don’t have enough information, condition 1) is not sufficient. Condition 2) If $$m = 1, n = 13,$$ then $$| m – n | = | 1 – 13 | = 12.$$ If $$m = 2, n = \frac{13}{2}$$, then $$| m – n | = | 2 – \frac{13}{2} | = \frac{9}{2}$$. Since we don’t have a unique solution, 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$79 for 1 month Online Course"
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Re: |m-n|=?   [#permalink] 12 Jul 2018, 01:05
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