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If 5m=25^{2n}, what is the value of m, in terms of n?

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by Max@Math Revolution » Mon May 07, 2018 1:13 am

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[GMAT math practice question]

If 5m=25^{2n}, what is the value of m, in terms of n?

A. m=5^{3n-2}
B. m=25n
C. m=5^{4n-1}
D. m=5^{2n-1}
E. m=5n
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by GMATGuruNY » Mon May 07, 2018 2:15 am
Max@Math Revolution wrote:[GMAT math practice question]

If 5m=25^{2n}, what is the value of m, in terms of n?

A. m=5^{3n-2}
B. m=25n
C. m=5^{4n-1}
D. m=5^{2n-1}
E. m=5n
Let n = 1/2.
Substituting n = 1/2 into 5m = 25^(2n), we get:
5m = 25¹
m = 5.

The question stem asks for the value of m (5).
Now plug n = 1/2 into the answers to see which yields the target value of 5.
Only C works:
m = 5^(4n-1) = 5¹ = 5.

The correct answer is C.
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by Brent@GMATPrepNow » Mon May 07, 2018 5:35 am
Max@Math Revolution wrote:[GMAT math practice question]

If 5m=25^{2n}, what is the value of m, in terms of n?

A. m=5^{3n-2}
B. m=25n
C. m=5^{4n-1}
D. m=5^{2n-1}
E. m=5n
Given: 5m = 25^(2n)
Rewrite 25 as 5² to get: 5m = (5²)^(2n)
Apply power of a power law to get: 5m = 5^(4n)
Divide both sides by 5 to get: m = [5^(4n)]/5
Since 5 = 5¹, we get: : m = [5^(4n)]/(5¹)
Apply quotient law to get: m = 5^(4n - 1)

Answer: C

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by Scott@TargetTestPrep » Tue May 08, 2018 10:38 am
Max@Math Revolution wrote:[GMAT math practice question]

If 5m=25^{2n}, what is the value of m, in terms of n?

A. m=5^{3n-2}
B. m=25n
C. m=5^{4n-1}
D. m=5^{2n-1}
E. m=5n
Simplifying the equation we have:

5m = 25^2n

5m = 5^4n

m = 5^4n/5

m = 5^(4n - 1)

Answer: C

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by Max@Math Revolution » Wed May 09, 2018 2:13 am
=>
$$5m=25^{2n}$$
=> $$5m=\left(5^2\right)^{2n}=5^{4n}$$
=> $$m=5^{4n-1}$$

Therefore, C is the answer.

Answer C
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