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

Question

(1) 4j + 3k = 18
(2) |64k2 + 32kj + 4j2| = (-22)2

paras7424 · Answer

In statement 2 shudnt it b 32kj?

Posted from my mobile device

BrentGMATPrepNow · Answer

You're absolutely right. I've edited the question. 
KUDOS for you!

Cheers and thanks, 
Brent

Mo2men · Answer

(1) 4j + 3k = 18

The only positive integers pair (j,k) =(3,2)

Sufficient

(2) |64k² + 32kj + 4j²| = (-22)²

(2) |(8k + 2j)²| = (-22)²

Then only viable is 8k + 2j =22 (because I can't be 8k + 2j =-22 as j & are positive

8k + 2j =22.......Divide by 2

4k + j =11

It is either pair of (j,k) =(3,2) or (7,1)

insufficient

Answer: A

BrentGMATPrepNow

May I ask why you tag this question as Target test prep? should not it you own question and hence tagged with GMATPrep Now??

BrentGMATPrepNow · Answer

Good question. 
I originally posted the question in the PS forum by mistake. When the question was moved to the DS forum, it looks like it was accidentally tagged with the wrong source.

Bunuel · Answer

Edited the source. My mistake. Sorry.

Kinshook · Answer

Asked: If j and k are positive integers, what is the value of j?

(1) 4j + 3k = 18
If j=1; k = 14/3; Not feasible since k is an integer
If j=2; k = 10/3; Not feasible since k is an integer
If j=3; k = 2; Feasible
If j=4; k = 2/3; Not feasible since k is an integer
If j=5; k = -2/3; Not feasible since k is a positive integer
For all other values of j; k is negative
j=3; k = 2 is the only solution
SUFFICIENT

(2) |64k² + 32kj + 4j²| = (-22)²
4|16k^2 + 8kj + j^2| = 4* 11^2
|(4k + j)^2| = (4k+j)^2 = 11^2
4k + j = 11
4k + j = - 11; Not feasible since k & j are positive integers
4k + j = 11
If k=1; j=7
But if k=2;j=3
NOT SUFFICIENT

IMO A

ashwink · Answer

(1) 4j + 3k = 18

Even + ? = Even, hence k should also be Even
Only matching pair is j=3 & k=2

Hence,  (1) is sufficient . ==> B,C & E is out.

(2) |64k² + 32kj + 4j²| = (-22)²

|(8k + 2j)²| = (-22)²

| (Even + Even)² | would be an even value, hence we take only 22.
Thus, 8k + 2j = 22 , 4k + j = 11

We can have multiple values for this solution: k=1 & j=7, k=2 & j=3

Hence,  (2) is not sufficient .

Thus, A should be the answer.

BrentGMATPrepNow · Answer

I created this question to highlight a common mistake students make.

Target question :    What is the value of j?

Given : j and k are   positive integers

Statement 1 : 4j + 3k = 18   
Many students will see this equation with 2 variables and automatically conclude that there are infinitely many solutions, in which case, statement 1 is not sufficient. 
Under most conditions, this conclusion would be correct. However, the given information tells us that j and k are  positive integers , which severely limits the possible solutions. 
In fact, there is only ONE pair of positive integers that satisfy the equation: j = 3 and k = 2. 
So, we can be certain that  j = 3 
Since we can answer the  target question  with certainty, statement 1 is SUFFICIENT

Statement 2 : |64k² + 32kj + 4j²| = (-22)²  
First factor the part inside the absolute value to get: |(8k + 2j)²| = (-22)²
This means that EITHER (8k + 2j)² = (-22)² OR (8k + 2j)² = -(-22)²
We can quickly dismiss the second case, (8k + 2j)² = -(-22)², since (8k + 2j)² must be greater than or equal to zero. So, it could never equal -(-22)²

So, what about (8k + 2j)² = (-22)² ? 
This means that either 8k + 2j = 22 or 8k + 2j = -22
If j and k are both  positive , we know that 8k + 2j will be positive, which means there are no solutions to the equation 8k + 2j = -22 
What about the equation 8k + 2j = 22? 
If we take this equation and divide both sides by 2, we get a simpler (yet equivalent) equation: 4k + j = 11
Under the restriction that j and k are POSITIVE INTEGERS, there are two possible solutions. 
 Case a : k = 1 and j = 7. In this case, the answer to the target question is  j = 7 
 Case b : k = 2 and j = 3. In this case, the answer to the target question is  j = 3 
Since we can’t answer the  target question  with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers, 
Brent

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

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

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