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
