BTGModeratorVI wrote: ↑Sat Apr 18, 2020 9:21 am
If a, b, and c are positive integers, and a/6 + b/5 = c/30, is c divisible by 5?
(1) b is divisible by 5.
(2) a is even.
Answer:
A
Source: Veritas Prep
Target question: Is c divisible by 5?
Given: a/6 + b/5 = c/30
First let's eliminate the fractions by multiplying both sides of the equation be the least common multiple of 6, 5 and 30.
So, we'll multiply both sides by 30 to get:
5a + 6b = c
Statement 1: b is divisible by 5
We can apply a useful divisibility rule that says:
"If j is divisible by x and k is divisible by x, then (j+k) is divisible by x"
We can ready see that
5a is divisible by 5.
And, if b is divisible by 5, then we know that
6b is divisible by 5.
So, by the above
rule, we know that
5a + 6b is divisible by 5.
Since
5a + 6b = c, we can conclude that
c IS divisible by 5
Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: a is even
There are several cases that satisfy statement 2. Here are two:
Case a: a = 2 and b = 5. we know that c = 5a + 6b. So, c = 5(2) + 6(5) = 40, which is divisible by 5. In this case,
c IS divisible by 5
Case b: a = 2 and b = 1. we know that c = 5a + 6b. So, c = 5(2) + 6(1) = 16, which is NOT divisible by 5. In this case,
c is NOT divisible by 5
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Answer: A
Cheers,
Brent
