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

Let's take each statement one by one.

(1) When n is divided by 6 the remainder is 3.

Case 1: Say n = 6 + 3 = 9. So, the remainder when n = 9 is divided by 24 is 9.
Case 2: Say n = 6*2 + 3 = 15. So, the remainder when n = 15 is divided by 24 is 15.

No unique answer. Insufficient.

(2) When n is divided by 4 the remainder is 1.

Case 1: Say n = 4*2 + 1 = 9. So, the remainder when n = 9 is divided by 24 is 9.
Case 2: Say n = 4 + 1 = 5. So, the remainder when n = 5 is divided by 24 is 5.

No unique answer. Insufficient.

(1) and (2) together

We see that Case 1 of each statement is the same (Remainder = 9). Let's take another case.

Case 3: Say n = 21. We see than 21 divided by 4 gives 1 as a remainder and divided by 6 gives 3 as a remainder; so this is an eligible case.

But 21 divided by 24 gives 21 as a remainder. No unique answer. Insufficient.

Correct answer: E

Hope this helps!

-Jay
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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