If j 1, is integer j a prime number? (1) When j is divided by 3, th

Question

If j > 1, is integer j a prime number?

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

(2) When j is divided by 2, the remainder is 1.

Lettherebelight · Answer

Took me a little over a min.

Statement 1. All this tells us is that j is not divisible by 3. Not all numbers not divisible by 3 are prime. e.g. 10, not divisible by 3 and is composite (not prime).
Statement 2. Similarly, all this tells us is that j is not divisible by 2, not all numbers not divisible by 2 are prime. e.g. 15, 25.

Statement 1 + 2 if j>1, and not divisible by 3 or 2, is j prime? Ans... Not necessarily, though it might be tempting to think that j is indeed prime. lets think of examples where a number is not divisible by 2 or 3. e.g 17(prime), 19 (prime), 23(prime, 25 (NOT PRIME).

Ans - E.

Hope it is clear.

BrentGMATPrepNow · Answer

When it comes to remainders, we have a nice rule that says:

If N divided by D, leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc.

For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.

Okay, now onto the question.

Target question :  Is integer j a prime number?

Statement 1 : When j is divided by 3, the remainder is 1.
Possible values of j: 4, 7, 10, 13, 16, 19, 22, 25...
As you can see, some values of j are prime and some are not.
Since we cannot answer the  target question  with certainty, statement 1 is NOT SUFFICIENT

Statement 2 : When j is divided by 2, the remainder is 1.
Possible values of j: 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, ...
As you can see, some values of j are prime and some are not.
Since we cannot answer the  target question  with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined : 
From statement 1: j could equal 4, 7, 10, 13, 16, 19, 22, 25...
From statement 2: j could equal 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, ...

Some numbers that satisfy  both  statements are 7, 13, 19, 25, . . .
Once again, some values of j are prime and some are not.
Since we cannot answer the  target question  with certainty, the combined statements are NOT SUFFICIENT

Answer = E

Cheers,
Brent

MathRevolution · Answer

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If j > 1, is integer j a prime number?

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

(2) When j is divided by 2, the remainder is 1.
 
In the original condition, there is 1 variable(x), which should match with the number of equation. So you need 1 equation. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer. 
For 1), j=7 -> yes, j=25 -> no, which is not sufficient.
For 2), =7-> yes, j=25 -> no, which is not sufficient. 
When 1) & 2), j=7 -> yes, j=25 -> no, which is not sufficient. Therefore, the answer is E.

 For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.

fabricioka · Answer

Statement 1 - J could be 4, 7, 10, 13, 16, 19, 22, 25, 28 (keep adding 3) . NOT SUFF.
Statement 2 - J could be 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27 (keep adding 2). NOT SUFF.
Statement 1 and 2 - J could be 7, 13, 19 and 25 (which is not a prime number) . NOT SUFF.

Hope it helps.

stonecold · Answer

The general expression for J will be 6P+1 and it may be a prime or non prime hence E

dcummins · Answer

Statement 1
j could be : ,4, 7 ,10,13,16,19,22, 25 
non-prime and prime

Statement 2:
J could be: , 3, 5,  7 , 9,11,13,15,17,19,21,23, 25 
non-prime and prime

Combined, j could be 7 or 25 from what we know - prime or non prime

Insufficient

Logo · Answer

What is confusing about this problem is that all primes, besides 2 & 3, will be a product of 6n+1 or 6n-1. However, given that E is the correct answer, we should notice that all numbers that are products of 6n+1 or 6n-1 will not always be prime.

GMATBusters · Answer

Possible trap associated with this ques :
 
After combining we can say that j is of form 6k+1. However, it is not a sufficient condition to prove that j is a prime number.

If j > 1, is integer j a prime number? (1) When j is divided by 3, th

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