Remainders

[shivanigs]

Hi,

Request help with the following question.Thanks..


For integer n, f(n) denotes the remainder when n is divided by integer k. Is k greater than 10?
1). f(k+32)=8
2). f(k+42)=6

[Bill@VeritasPrep]

1) If k+32 gives a remainder of 8 when divided by k, then k+24 must be a multiple of k. We also know that k must be greater than 8; the remainder cannot be greater than the divisor. Neither 9 nor 10 is a factor of 24, so k must be greater than 10. (it can be 12 or 24, but we don't need to find the exact values). Sufficient.

2) If k + 42 gives a remainder of 6 when divided by k, then k+36 must be a multiple of k. K must be greater than 6, but it could be less than 10 (6 or 9, for instance) or greater than 10 (12 or 18, for instance). Insufficient.