If j and k are positive integers and j + k is odd

Question

If j and k are positive integers and j + k is odd, what is the value of k?

(1) When j is divided by k, the remainder is 3

(2) j > 7 > 6 > k

Bunuel · Answer

If j and k are positive integers and j + k is odd, what is the value of k?

j + k is odd, means that one of the unknowns is even and another odd.

(1) When j is divided by k, the remainder is 3. Since the remainder (3 in our case) is always less than the divisor (k in our case), then this statement implies that k is greater than 3. Not sufficient.

(2) j > 7 > 6 > k. Clearly insufficient.

(1)+(2) From above: 3 < k < 6 < 7 < j, thus k can be 4 (in this case j can be for example, 11) or 5 (in this case j can be for example, 8) Not sufficient.

Answer: E.

Hope it's clear.

bhatiamanu05 · Answer

Statement 1::

J = nK +3

J+K = odd their must be one number from J,K so that sum will be odd.
If K is odd depending on n value J can be even or odd. So In sufficient.
It also signifies k >3

Statement 2:

j > 7 So J can be 10,9,8

K can be 5,4,3,2,1

So In Sufficient.

Combining both of them.
K cn be 4,5 K can have two values.

So In sufficient.
Ans is E.

BillyZ · Answer

Official solution from Veritas Prep.

E. Statement 1 is not sufficient, as there are infinite combinations of values. For example, if j is 3, then k could be any even number > 4. Statement 2 is also not sufficient, as k could be any integer 1 through 5. Taken together, the statements are still not sufficient, as j and k could be 11 and 4 (leaving 2 remainder 3) or 8 and 5 (1 remainder 3). The "trap" here is that 8 and 5 are the only values that work for the quotient to be 1 with the remainder 3. But because j could be any large number, the possibilities are endless.

Archit3110 · Answer

given condition that j and k are positive integers and j + k is odd
j+k odd means either of them is even and odd
so k can be even or odd
#1
When j is divided by k, the remainder is 3
j,k possible pairs ; ( 3,6) ; (3,10) ; ( 9,6) insufficient
#2
 j > 7 > 6 > k
many possible pairs of j,k where odd+even are values 
insufficient
from 1 &2
we can have j,k pairs ; ( 8,5) ; ( 7,4)
insufficient 
OPTION E

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If j and k are positive integers and j + k is odd

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If j and k are positive integers and j + k is odd

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