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For any integer k > 1, the term “length of an integer” refers to the n

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Re: For any integer k > 1, the term “length of an integer” refers to the n  [#permalink]

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New post 01 Dec 2017, 08:42
Aneko wrote:
ajit257 wrote:
For any integer k > 1, the term “length of an integer” refers to the number of positive prime factors, not necessarily distinct, whose product is equal to k. For example, if k = 24, the length of k is equal to 4, since 24 = 2 × 2 × 2 × 3. If x and y are positive integers such that x > 1, y > 1, and x + 3y < 1000, what is the maximum possible sum of the length of x and the length of y?

A. 5
B. 6
C. 15
D. 16
E. 18


Hi everyone, I have read all comments below the problem but still cannot understand why the max. possible sum is 16.
We all agree that x=512=2^9 so length of x is 9, great!
Now, we are left with 3*y that could be 3*2^7=3*128=384. So, still 512+384<1000, right?. BUT length of y is 8, am i wrong? 384=2x2x2x2x2x2x2x3 8 primes!
so max. possible sum appears to be 9+8=17 which is not in the list of answer choices, so I guess I would go whatever the other choice I have but why everyone is posting that length of y is 7?
Maybe I miss something after sleepless night, doing math test whole night, I don't know :roll:
Thanks



Because you are counting 3 as a prime factor, when 3 is just additional integer which has nothing to do with x and y. Hope it helps
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Re: For any integer k > 1, the term “length of an integer” refers to the n  [#permalink]

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New post 08 Jan 2020, 22:49
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Re: For any integer k > 1, the term “length of an integer” refers to the n   [#permalink] 08 Jan 2020, 22:49

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