@n = product of even numbers between n and 2n.
@n must contain all even numbers.
for @k to have 17 as a prime factor, it must have 34 as one the numbers but should not include 38 included within k.

K = 9: @k will not include 34. not possible
k = 18; @k range from 20 - 34. possible
k = 32; @k range from 34-62. not possible because it includes 38 which shifts greater prime factor to be more than 17 to 31

ans: D

Since @n consist of the even number lies between n and 2n exclusive.
@k have 17 as the biggest prime number.
17 can't be the number itself because it's an odd number.
Therefore 34 is the number in the set.
@k = { .................34}
2K can be 36 or 38
Because even if 2k is 38 the largest no. will still be 17.
But 2k can't be 40. Because the greatest prime no. Will be 19 in that case.
2k = 36 or 38
K will be either 18 or 19
Only statement 2 is satisfying constraint
Therefore Answer should be B

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Ans is D .

@n = product of even numbers between n and 2n , exclusive n and 2n , and must contain all even numbers.

I. 9

-- @9 = 10 * 12 ......*16 [Max prime factor is 7 . so k = 9 not possible ]


II. 18

@18 = 20 * 22 ......*34 [Max prime factor is 17 . so k = 18 possible ]


III. 32
-- @32 = 34 * 12 ......*64 [Max prime factor is 31 . so k = 32 not possible ]

Hence ans is D
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The question is which cannot be the value of k

From your solution k can be 18 but cannot be 9 or 32

So the answer is D
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