moonlite wrote:If K is a positive integer less than 10 and N=4321 + K what is the value of K?

1) N is divisible by 3
2) N is divisible by 7

B

Please explain. Thanks.

Before looking at the statements, we know k is between 1 and 9. Thus, N is between 4322 and 4330. That is, N must be one of these nine consecutive integers. If we can find N, we can definitely find K.

From 1), N is divisible by 3. We know N is one number in a list of nine consecutive integers. But, in any list of nine consecutive integers, exactly three of these numbers will be divisible by 3. So we still have three possible values for N --> not sufficient.

From 2), N is divisible by 7. We know N is one number in a list of nine consecutive integers. In a list of nine consecutive integers, we might have only one multiple of 7, but we might have two multiples of 7. We need to check: you will find that 4326 is divisible by 7, but there is no other multiple of 7 in the required range (the nearest multiples of seven are 4326 + 7 = 4333 and 4326 -7 = 4319). Thus, we get only one value for N, and therefore only one value for K --> sufficient.

B