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# If n is an integer and then which of the following could be

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Manager
Joined: 03 Sep 2005
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If n is an integer and then which of the following could be [#permalink]

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08 Sep 2005, 22:06
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If n is an integer and then which of the following could be the value of k?

n=(2*3*5*7*11*13)/77k

(A) 22
(B) 26
(C) 35
(D) 54
(E) 60

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Director
Joined: 13 Nov 2003
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09 Sep 2005, 01:43
it makes sense. Remove 7 and 11 from the product in the nominator, cause 77=7x11. Given that n is an integer, K should involve the numbers 2,3,5 and 13. Seems like K is 26

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Intern
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09 Sep 2005, 06:07
good answer ... with k = 26, n is still an integer

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Current Student
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09 Sep 2005, 06:09
K=26

remember N=(product of some primes)/77K

11*7, can divide 77...you are now left with (2*3*5*13)/k

K has to evenly divide....so try K=26...prime factors are 2*13....K=26....

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Manager
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09 Sep 2005, 11:34
Oh my gosh...I can't believe it. I <b>did</b> remove 7 and 11 from the denonimator, but for some reason none of those number divided evenly for me. Eeek, I feel like such a dumb dumb!

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Intern
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09 Sep 2005, 12:10
n=(2*3*5*7*11*13)/77k

n = (2*3*5*13)/k
K needs to be a number that will be divisible by the product of (2*3*5*13)
Plugging in all the numbers, we get the answer as 26.

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Intern
Joined: 05 May 2005
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10 Sep 2005, 10:24
trulyblessed wrote:
This problem makes no sense to me. I don't even think the answer choices are correct. Hmm...maybe this source I'm using is not very reliable?!

If n is an integer and then which of the following could be the value of k?

n=(2*3*5*7*11*13)/77k

(A) 22
(B) 26
(C) 35
(D) 54
(E) 60

note that 7*11 = 77 and rewrite the problem by crossing out the 77's on the numerator and demoninator:
n = (2*3*5*13)/k
i also noticed that from the answer choices b) 26 is also shown in the numerator as 2*13...
if k = 26 then 2*13 can be crossed out leaving you with 3*5 or in other words an integer.
no work was necessary in terms of dividing out the choices to see if n was an integer.

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Senior Manager
Joined: 15 Apr 2005
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13 Sep 2005, 01:37
Same reasoning as others, my answer is B - 26

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Intern
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16 Sep 2005, 01:37
n = (2*3*5*13)/k
so k could be =
2,3,5,13
6,10,26,
15,39
65

From this list we have ONLY 26

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16 Sep 2005, 01:37
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