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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8607
GMAT 1: 760 Q51 V42
GPA: 3.82
If m and n are positive integers, m=?  [#permalink]

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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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VP  D
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]

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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  B
Joined: 01 Nov 2017
Posts: 30
Re: If m and n are positive integers, m=?  [#permalink]

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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 V
Joined: 02 Sep 2009
Posts: 61538
Re: If m and n are positive integers, m=?  [#permalink]

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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.
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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8607
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: If m and n are positive integers, m=?  [#permalink]

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=>

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.

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: If m and n are positive integers, m=?  [#permalink]

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