Remainders

[singhmaharaj]

If r is the remainder when the positive integer n is divided by 7, what is the value of r?

1) When n is divided by 21, the remainder is an odd number.

2) When n is divided by 28, the remainder is 3

[theCodeToGMAT]

n/7 ==> Remainder is "r"

Possible values 1,2,3,4,5,6

TO find: "r"

Statement 1:
n/21 leave "R" ODD Number
ODD Possible = 1,3,5
INSUFFICIENT

Statement 2:
n/28 leaves remainder = 3
Possible numbers = 31, 59, 87
Then, r = 3, 3, 3 ..
SUFFICIENT

[spoiler]{B}[/spoiler]

[Brent@GMATPrepNow]

If r is the remainder when the positive integer n is divided by 7, what is the value of r?

1) When n is divided by 21, the remainder is an odd number.
2) When n is divided by 28, the remainder is 3

We can use a variety of divisibility rules to solve this, or we can list possible values of n based on the statements. The rule for listing possible values of n is as follows:
If, when N is divided by D, the remainder is R, then the possible values of N include: R, R+D, R+2D, R+3D,. . .

Target question: What is the value of r?

Statement 1: When n is divided by 21, the remainder is an odd number.
There are several possible values of n that satisfy this condition. Here are two:
Case a: n = 1 (since 1 divided by 21 leaves remainder 1, which is odd). Here, r = 1
Case b: n = 3 (since 3 divided by 21 leaves remainder 3, which is odd). Here, r = 3
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: When n is divided by 28, the remainder is 3
Possible values of n: 3, 31, 59, 87, . . .
We can see that for all possible values of n, the remainder is always 3 when n is divided by 7
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = B

Cheers,
Brent