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10 and N = 4,321 + K

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by sanju09 » Fri Jul 02, 2010 1:22 am
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.
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by albatross86 » Fri Jul 02, 2010 1:37 am
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

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