singhmaharaj wrote: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
