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

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

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28 Jun 2018, 02:33
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Difficulty:

15% (low)

Question Stats:

75% (00:53) correct 25% (01:17) wrong based on 79 sessions

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[GMAT math practice question]

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

$$1) 7^m11^n=847$$
$$2) n=2$$

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"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" VP Joined: 31 Oct 2013 Posts: 1491 Concentration: Accounting, Finance GPA: 3.68 WE: Analyst (Accounting) Re: If m and n are positive integers, m=? [#permalink] ### Show Tags 28 Jun 2018, 03:11 MathRevolution wrote: [GMAT math practice question] If $$m$$ and $$n$$ are positive integers, $$m=$$? $$1) 7^m11^n=847$$ $$2) n=2$$ Note: m and n are positive integers we have to find out what is the value of m statement 1: $$7^m$$ $$11^n$$ = 847 $$7^n$$$$11^n$$ =$$7 ^1$$ $$11^2$$ Note: m and n are the exponents of the the prime. So, prime factorization is needed here. So, m = 1 . sufficient. Statement 2: n = 2 clearly not stuff. Thus the best answer is A. Intern Joined: 01 Nov 2017 Posts: 30 Re: If m and n are positive integers, m=? [#permalink] ### Show Tags 28 Jun 2018, 10:38 1 1 Why is statement 2 not true? 1) n = 2 2) 7^m * 11^2 = 847 3) 7^m * 121 = 847 4) 7^m = 7^1 5) m = 1 ? Math Expert Joined: 02 Sep 2009 Posts: 61538 Re: If m and n are positive integers, m=? [#permalink] ### Show Tags 28 Jun 2018, 19:37 surfingpirate wrote: Why is statement 2 not true? 1) n = 2 2) 7^m * 11^2 = 847 3) 7^m * 121 = 847 4) 7^m = 7^1 5) m = 1 ? You are using info given in (1), which says that 7^m * 11^2 = 847, to evaluate (2), which only says that n = 2. When evaluate a statement we should use only the info given in the stem and in that statement only. _________________ Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8607 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If m and n are positive integers, m=? [#permalink] ### Show Tags 01 Jul 2018, 17:06 => 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 $$847 = 7^1*11^2$$, we must have $$m = 1$$ and $$n = 2.$$ 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) Since $$847 = 7^1*11^2$$, we must have $$m = 1$$ and $$n = 2$$. Thus, condition 1) is sufficient. Condition 2) Since condition 2) gives us no information about m, it is not sufficient. For condition 2), we should consider CMT3. We should forget everything about condition 1), since conditions 1) and 2) are independent. Therefore, A is the answer. Answer: A 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: If m and n are positive integers, m=?  [#permalink]

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22 Jan 2020, 00:22
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Re: If m and n are positive integers, m=?   [#permalink] 22 Jan 2020, 00:22
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