Condition 1
k%j=(jm+5)%j=5%j=0 to 5 depending on value of j.Insufficient
Condition 2
j > 5 Insuff
Combining 1 and 2,
5%j=5 Sufficient
Option C
n.b. a%b means the remainder when a is divided by b.

abhi332 wrote:If j and k are positive integers where k > j, what is the value of the remainder when k is divided by j?

(1) There exists a positive integer m such that k = jm + 5.

(2) j > 5

Right off the bat you can see that (2) itself is not sufficient. Lets say j = 6, which satisfies (2). Well then k could be 6, and the answer would be 0, or k could be 7 and the answer is 1. (2) is not sufficient.

(1) is more interesting. The question asks for the remainder when k is divided by j

k/j = X r R

Where X is the integer value of k/j and R is the remainder. But whats another way to say this? You might say that, since k>j, that k is equal to some integer times j plus the remainder. For example say k = 10 and j = 7

10/7 = 1 R 3

OR

10 = 7*1 + 3

Which is exactly what (1) is giving you. Its giving you that k = j*m + 5 where m is an integer and 5 is the remainder. But you don't know that the multiple is greater than 5, which would be necessary for this to work. (2) gives you that condition.

Hence choose (c)

B is clearly insufficient.

When I look at A I think of plugging numbers. Taking a clue from B my numbers have to be above 5 and less than equal to 5

I realise that just A is not sufficient, but A and B combined are sufficient.

So C

So the takeaway from this Q is if X = Y + z then for all the values of x and Y where Y >Z, X/Y will have a remainder of Z.

Guys do you concur.

I don't know I may be missing something basic here. But how would the remainder be 5 when j > 5?

Actaully I think the remainder will be 0 when the denominator (here j) is greater than the numerator (here 5).

Thanks ...Got confused between the Quotient and Remainder