BTGModeratorVI wrote: ↑

Mon Sep 07, 2020 6:59 am

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.

Answer: E
Source: Veritas

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