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# If j is an integer, is k an integer?

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Re: If j is an integer, is k an integer? [#permalink]
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rohit8865
Bunuel
If j is an integer, is k an integer?

(1) j – 2k is an integer.
(2) 5k – j is an integer.

let j=10
(1) then, if k=1 then yes
k=1/2 No ....insuff

(2) k=1 then yes
k=1/5 then No...insuff..

combined k must be ineteger....suff

Ans C

Questions asks if k is an integer? J is already integer. (it can be positive or negative).

A) is quite clear, its is INSUFFICIENT

in B if, k = 0.2 (which is 1/5) --> 5(0.2) - j (the integer) --> 1 - 2 = -1 there fore k is NOT integer.(is j is 2, 3, 4.. since answer is an integer, so answer can be negative or positive).
On the other hand, if k =1 --> then 5 - 4 (if j = 4) --> 1 or 5 - (-2) --> 7. Again K is Integer.
So both are INSUFFICIENT.
Hence E

How is C the answer? Could you give me a little detail into the solving? Thank you, it would be highly appreciated
Hi,

There is no single non-integer which can be multiplied by either 2 or 5, and still results in an integer. So since the number results in an integer when multiplied by either 2 or 5, it must be an integer. Hope this helps!

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Re: If j is an integer, is k an integer? [#permalink]
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(1) j-2k
k could be 1 or 1/2
Insufficient information

(2) 5k-j
If k=1 then yes
k=1/2 then insufficient information

combine them and we know k times 2 or k times 5 is an integer and therefore sufficient.
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If j is an integer, is k an integer? [#permalink]
1 and 2 alone are clearly not sufficient

Now, If we combine 1 and 2:

2K is an integer, and 5K is integer
for 5K to be integer, k = 0.2, 0.4, 0.6, 0.8, 1.0, 1.2....and so on...
but 2K cannot be an integer if k = 0.2, 0.4, 0.6, 0.8, 1.0, 1.2.

So K has to be an integer if 2k and 5k are integer.

1 and 2 combined are sufficient to answer the question
If j is an integer, is k an integer? [#permalink]
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