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After the reduction of 245 - k270 to its lowest terms, the numerator is a multiple of 3. What is the minimum of the pos

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by Max@Math Revolution » Wed Jun 17, 2020 12:53 am

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[GMAT math practice question]

After the reduction of 245 - k/270 to its lowest terms, the numerator is a multiple of 3. What is the minimum of the positive integer k?

A. 1
B. 2
C. 3
D. 4
E. 5
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Re: After the reduction of 245 - k270 to its lowest terms, the numerator is a multiple of 3. What is the minimum of the

by Max@Math Revolution » Thu Jun 18, 2020 11:32 pm
=>

Since 245 - k/270 = 245 - k/2*3^3*5 is a multiple of 3, we have 245 - k = 3^4*a.
3^4*(a – k) is a maximum with 0 < 3^4·a < 245 in order for k to be a minimum.
Then we have a = 3 and k = 2.

Therefore, B is the answer.
Answer: B
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