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If m and n are positive integers, m=?

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

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New post 28 Jun 2018, 02:33
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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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Re: If m and n are positive integers, m=?  [#permalink]

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New post 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.
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Re: If m and n are positive integers, m=?  [#permalink]

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New post 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

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

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New post 28 Jun 2018, 19:37
Math Revolution GMAT Instructor
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Re: If m and n are positive integers, m=?  [#permalink]

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New post 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.
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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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