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
Remainders
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- singhmaharaj
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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]
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]
R A H U L
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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: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
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