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If k is a positive integer and 175 divided by k leaves a remainder of 7, what is the value of k?
This means 175-7 is divisible by k. This implies k is a factor of 168.
Now, 168 = 2^3 x 3 x 7
k can be any combination of these
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(1) The product of any two factors of k is odd
This means k doesn't have any even factors. Which means k is itself an odd number.
So, k can be 3, 7 or 21(i.e. 3x7)
Hence statement 1 alone isn't sufficient to give us the value of k
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(2) The sum of any two factors of k is even.
this means the factors of k are either all odd or all even.
k can still be what we got from statement 1 (i.e 3, 7 or 21), in addition to also being 2, 4, or 8.
Again, statement 2 alone is not sufficient to find k
From statement 1 and 2 together, we get:
K has to be ODD. But, that still leaves us with 3 choices (3,7, 21).
Hence, the 2 statements together are also insufficient to determine the value of k.
Answer: EPosted from my mobile device