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Which of the following is equal to (2^k)(5^k − 1)?

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by Brent@GMATPrepNow » Mon Sep 11, 2017 1:22 pm
ahmedshafea wrote:Which of the following is equal to 2^k*5^(k-1)?

A. 2*10^(k-1)
B. 5*10^(k-1)
C. 10^k
D. 2*10^k )
E. 10^(2k-1)
There's a nice rule that says (x^k)(y^k) = (xy)^k
For example, (7^11)(10^11) = 70^11

Now recognize that 2^k = 2^1 * 2^(k-1)
So, we get....
2^k * 5^(k-1) = 2^1 * 2^(k-1) * 5^(k-1)
= 2^1 * 2^(k-1) * 5^(k-1)
= 2^1 * 10^(k-1)

Answer: A

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by [email protected] » Mon Sep 11, 2017 7:40 pm
Hi ahmedshafea,

This question can be solved by TESTing VALUES.

IF... K = 1, then (2^K)(5^[K-1]) =
(2^1)(5^0) =
(2)(1) =
2

So we're looking for an answer that equals 2 when you plug in K = 1. There's only one answer that matches.

Final Answer: A

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hi

by Scott@TargetTestPrep » Wed Sep 20, 2017 2:45 pm
ahmedshafea wrote:Which of the following is equal to 2^k*5^(k-1)?

A. 2*10^(k-1)
B. 5*10^(k-1)
C. 10^k
D. 2*10^k )
E. 10^(2k-1)
Let's simplify the given expression:

2^k * 5^(k-1) = 2^1 * 2^(k-1) * 5^(k-1) = 2 * (2*5)^(k-1) = 2 * 10^(k-1)

Answer: A

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