BTGModeratorVI wrote: ↑Sat Jun 13, 2020 5:29 am
What is the remainder when the positive integer n is divided by 5 ?
(1) When n is divided by 3, the quotient is 4 and the remainder is 1.
(2) When n is divided by 4, the remainder is 1.
Answer:
A
Source: Official guide
Target question: What is the remainder when the positive integer n is divided by 5 ?
Statement 1: When n is divided by 3, the quotient is 4 and the remainder is 1.
There's a nice rule that says, "
If N divided by D equals Q with remainder R, then N = DQ + R"
For example, since 17 divided by 5 equals 3 with remainder 2, then we can write 17 = (5)(3) + 2
Likewise, since 53 divided by 10 equals 5 with remainder 3, then we can write 53 = (10)(5) + 3
So, from statement 1, we can write: n = (3)(4) + 1 = 13
If n = 13, then
we get a remainder of 3 when we divide 13 by 5
Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: When n is divided by 4, the remainder is 1.
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.
Some possible values of n are: 1, 5, 9, 13, 17, . . . etc.
Case a: If n = 1, then
we get a remainder of 1 when we divide 1 by 5.
Case b: If n = 5, then
we get a remainder of 0 when we divide 5 by 5.
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Answer: A
