If K is a positive integer less than 10 and N = 4,321 + K, what is the value of K?
(1) N is divisible by 3.
(2) N is divisible by 7.
10 and N = 4,321 + K
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N = 4321 + K (where K is a positive integer less than 10)
So the possible values of N are 4322 to 4330 inclusive.
1. N is divisible by 3.
The sum of the digits must be a multiple of 3.
4+3+2 = 9. So the 4th digit must be 3,6 or 9. 4330 is not a multiple of 3.
So possible values for N are : 4323, 4326, and 4329. So K = 2, 5 or 8.
INSUFFICIENT.
2. N is divisible by 7.
First find out the remainder for the lowest value of N i.e. 4322 . This is = 617 remainder 3
So the next value of N which is divisible by 7 is 4322 + 4 = 4326 which is 618*7
After this the next multiple is 619*7 = 4333 which is outside the range for N
Thus the value of N must be 4326. So K = 5
SUFFICIENT
Pick B.
So the possible values of N are 4322 to 4330 inclusive.
1. N is divisible by 3.
The sum of the digits must be a multiple of 3.
4+3+2 = 9. So the 4th digit must be 3,6 or 9. 4330 is not a multiple of 3.
So possible values for N are : 4323, 4326, and 4329. So K = 2, 5 or 8.
INSUFFICIENT.
2. N is divisible by 7.
First find out the remainder for the lowest value of N i.e. 4322 . This is = 617 remainder 3
So the next value of N which is divisible by 7 is 4322 + 4 = 4326 which is 618*7
After this the next multiple is 619*7 = 4333 which is outside the range for N
Thus the value of N must be 4326. So K = 5
SUFFICIENT
Pick B.
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