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# Note the following problem and explanation: Which of the

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Note the following problem and explanation: Which of the [#permalink]

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20 May 2008, 11:34
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Note the following problem and explanation:

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

4(10^[k − 1])
10k
10^[k − 1]
2(10^[k − 1])
2(5^[k+1])

We are asked to convert the equation (2^[k+1])(5^[k − 1]) into another form.

Though here the bases are dissimilar, the exponents can be matched up by observing that 2^[k-1] divided by 2 is equal to 2^k , or 2^[k+1] divided by 4 is equal to 2^[k-1].

By making use of the common exponent, we can convert the terms into terms with the same exponents:

(2^[k+1])(5^[k − 1])

4 (2^[k-1])(5^[k − 1]) <---- My question is here. We can just multiply one term by 4 here? Doesn't seem like proper math??? Can someone elaborate?

4 (10^[k-1])

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Posts: 81
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Re: Interesting ManhattanGMAT Problem and Explanation. [#permalink]

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20 May 2008, 14:53
jimmyjamesdonkey wrote:
Note the following problem and explanation:

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

4(10^[k − 1])
10k
10^[k − 1]
2(10^[k − 1])
2(5^[k+1])

We are asked to convert the equation (2^[k+1])(5^[k − 1]) into another form.

Though here the bases are dissimilar, the exponents can be matched up by observing that 2^[k-1] divided by 2 is equal to 2^k , or 2^[k+1] divided by 4 is equal to 2^[k-1].

By making use of the common exponent, we can convert the terms into terms with the same exponents:

(2^[k+1])(5^[k − 1])

4 (2^[k-1])(5^[k − 1]) <---- My question is here. We can just multiply one term by 4 here? Doesn't seem like proper math??? Can someone elaborate?

4 (10^[k-1])

The term 4 is there because 2^(k+1) = 4 [2^(k-1)]
Re: Interesting ManhattanGMAT Problem and Explanation.   [#permalink] 20 May 2008, 14:53
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