J and K

[gmatblood]

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

[HSPA]

A is okay.. B is not
remainder is 5

[rijul007]

k = jm+5

value of j ............remainder of k/j

1 ------------------------ 0
2 ------------------------ 1
3 ------------------------ 2
4 ------------------------ 3
5 ------------------------ 0
6 ------------------------ 5
7 ------------------------ 5
8 ------------------------ 5
9 ------------------------ 5
10------------------------ 5

Pattern continues

Hence you need both statements for the remainder.

Option C


I did a similar ques in Thursdays with Ron y'day.

[user123321]

should be C.

The second statement actually says the divisor should be always greater than remainder.

user123321

[mankey]

Can some expert please help on this one?

Thanks.

[Anurag@Gurome]

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

If x is divided by y (x and y are both positive integers), then x = qy + r, where q is the quotient and r is the remainder (0 <= r < y which means remainder is always less than divisor).
In this question, k is divided by j implies k = qj + r, so we have to find r.

(1) k = jm + 5, where m is a positive integer. Here we do not know if 5 < j or not, as the remainder must be less than divisor; NOT sufficient.

(2) j > 5 is again NOT sufficient.

Combining (1) and (2), k = jm + 5 and j > 5, which implies r = 5; SUFFICIENT.

The correct answer is C.

[mankey]

Thanks Anurag. That was brilliant!

Was missing out on the most crucial point of this question that we always need to remember that "0<=r<divisor".

Thanks for the help.

[PGMAT]

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

If x is divided by y (x and y are both positive integers), then x = qy + r, where q is the quotient and r is the remainder (0 <= r < y which means remainder is always less than divisor).
In this question, k is divided by j implies k = qj + r, so we have to find r.

(1) k = jm + 5, where m is a positive integer. Here we do not know if 5 < j or not, as the remainder must be less than divisor; NOT sufficient.

(2) j > 5 is again NOT sufficient.

Combining (1) and (2), k = jm + 5 and j > 5, which implies r = 5; SUFFICIENT.

The correct answer is C.

Please help me understand statement 1. I am missing some thing here.
How can j be less than 5 here? For example, j=2, then remainder is either 0 or 1. But stmt 1 clearly says remainder is 5. So, shouldn't this statement be sufficient by itself?
Thanks.

[Anurag@Gurome]

How can j be less than 5 here? For example, j=2, then remainder is either 0 or 1. But stmt 1 clearly says remainder is 5. So, shouldn't this statement be sufficient by itself?

Does it?
Statement 1 just says k = jm + 5

Consider the following situations,

• # k = 6, j = 1, m = 1 ---> Remainder of k/j = 0
  # k = 8, j = 3, m = 1 ---> Remainder of k/j = 2
  # k = 13, j = 4, m = 2 ---> Remainder of k/j = 1

Hope that helps.