BTGModeratorVI wrote: ↑Mon Jun 08, 2020 11:56 am
What is the remainder when a positive integer N is divided by 24?
(1) When n is divided by 6 the remainder is 3
(2) When n is divided by 4 the remainder is 1.
Answer:
E
Source: Jamboree
Target question: What is the remainder when a positive integer N is divided by 24?
Statement 1: When n is divided by 6 the remainder is 3
Aside: 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.
So, from statement 1, we can say that the possible values of N are: 3, 9, 15, 21, 27, 33, etc
Here are two possible cases:
Case a: N = 3. In this case, the answer to the target question is
When N is divided by 24, the remainder is 3
Case b: N = 9. In this case, the answer to the target question is
When N is divided by 24, the remainder is 9
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: When N is divided by 4 the remainder is 1.
Some possible values of N are: 1, 5, 9, 13, 17, 21, 25, 29, etc
Here are two possible cases:
Case a: N = 5. In this case, the answer to the target question is
When N is divided by 24, the remainder is 5
Case b: N = 9. In this case, the answer to the target question is
When N is divided by 24, the remainder is 9
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 1 tells us that the possible values of N are: 3,
9, 15,
21, 27, 33, etc
Statement 2 tells us that the possible values of N are: 1, 5,
9, 13, 17,
21, 25, 29, etc
Here are two possible cases:
Case a: N =
9. In this case, the answer to the target question is
When N is divided by 24, the remainder is 9
Case b: N =
21. In this case, the answer to the target question is
When N is divided by 24, the remainder is 21
Since we cannot answer the
target question with certainty, the combined statements are NOT SUFFICIENT
Answer: E
Cheers,
Brent
