It is given that factors of k are: 1, 3, 7 and k. We need to find the value of k.
Since 3 and 7 are factors of k, so 21 should also be a factor of k.
So, now we have 4 factors of k: 1, 3, 7, 21 and k
(1) 3^2 is a factor of k implies 9 is also a factor of k.
So, now we know 5 factors of k: 1, 3, 7, 9, 21 and k
Hence, k = 3*3*7 = 63
So, (1) is SUFFICIENT.
(2) 7^2 is not a factor of k, which means one 7 is the prime factor of k.
Now, the remaining factor is to be found by the factor 3, so 3^2 = 9 is the factor of k.
Hence, k = 3*3*7 = 63
So, (2) is SUFFICIENT.
The correct answer is [spoiler](D)[/spoiler].
Rahul Lakhani
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