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Source:MGMAT CAT For any integer k > 1, the term length

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Source:MGMAT CAT For any integer k > 1, the term length  [#permalink]

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New post 02 Nov 2008, 08:29
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Source:MGMAT CAT

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?

5
6
15
16
18

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Re: PS : length of an integer  [#permalink]

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New post 02 Nov 2008, 09:13
since the prime factors need not necessarily be distinct in order to be counted for the length, would start working using 2 and solve for values of x and y which satisfy the given equation

For getting the max of length of x, let's go with 512 for x (2^9).

Then try solving for y, which should be < 488. It works out ~ 2^7 or 128.

Now plugging this back in the equation
512 + 3 x 128 < 1000
512 + 384 < 1000 (which is satisfied)

So max of sums of length of x , y = 9 + 7 = 16. Answer D
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Re: PS : length of an integer  [#permalink]

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New post 02 Nov 2008, 09:53
i get 17..

2^9 + 3*2^7 =9+1+7 =17

hmm i guess if i had to choose 16 would be it..but i think they messed up on the ans choices
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Re: PS : length of an integer  [#permalink]

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New post 02 Nov 2008, 13:56
LiveStronger wrote:
Source:MGMAT CAT

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?

5
6
15
16
18



TO GET THE MAX NUMBER OF PRIMES LOOK FOR 2

2^9 = 512 ( WE CAN RAISE 2 TO HIGHER POWERS OR IT WILL EXCEED 1000

3*2^7 = 384

9+7+1 = 17
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Re: PS : length of an integer  [#permalink]

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New post 02 Nov 2008, 15:35
OA is D - 16

yezz and fresinha12:
512 :9
384 --> y= 128:7

9+7=16

Question asks for length of y, not 3y
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Re: PS : length of an integer  [#permalink]

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New post 02 Nov 2008, 15:57
yezz wrote:
LiveStronger wrote:
Source:MGMAT CAT

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?

5
6
15
16
18



TO GET THE MAX NUMBER OF PRIMES LOOK FOR 2

2^9 = 512 ( WE CAN RAISE 2 TO HIGHER POWERS OR IT WILL EXCEED 1000

3*2^7 = 384

9+7+1 = 17



why are you adding 1 from 3.

the question is asking for the prime factors of x and y, and 3 is not a prime factor of neither x nor y..
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Re: PS : length of an integer  [#permalink]

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New post 02 Nov 2008, 21:21
:beat :beat :wall my bad

thanks folks :punk .........16 is the answer

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Re: PS : length of an integer &nbs [#permalink] 02 Nov 2008, 21:21
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Source:MGMAT CAT For any integer k > 1, the term length

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