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

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards