BTGmoderatorLU wrote:Source: Manhattan Prep
What is the remainder when positive integer x is divided by 5?
1. x divided by 10 has a remainder of 7.
2. x divided by 2 has a remainder of 1.
The OA is A
Target question: What is the remainder when positive integer x is divided by 5?
Statement 1: x divided by 10 has a remainder of 7.
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
We can rewrite statement 1 as "x divided by 10 equal some integer k with 7
So, x = 10k + 7
We can rewrite this as: x = 5(2x) + 5 + 2
Which is the same as x =
5(2x + 1) + 2
Since
5(2x + 1) is a multiply of
5, we can see that
5(2x + 1) + 2 is
2 greater that a multiple of 5
So, if we divide
5(2x + 1) + 2 by 5,
the remainder must be 2
Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: x divided by 2 has a remainder of 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 2, we can see that some possible values of x are: 1, 3, 5, 7, 9, 11, etc
Let's examine 2 possible cases:
Case a: x = 1. In this case, the answer to the target question is
when x is divided by 5, the remainder is 1
Case b: x = 3. In this case, the answer to the target question is
when x is divided by 5, the remainder is 3
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Answer: A
Cheers,
Brent
