BTGModeratorVI wrote: ↑Sat Jun 13, 2020 5:33 am
If a, b and c are integers, is ab a multiple of 18?
(1) 2a = 3b
(2) 2b = 3c
Answer:
C
Source: Economist GMAT
Target question: Is ab a multiple of 18?
Given: a, b and c are INTEGERS
Statement 1: 2a = 3b
This statement doesn't FEEL sufficient, so I'm going to test some values.
There are several values of a and b that satisfy this condition. Here are two:
Case a: a = 3 and b = 2, in which case
ab = 6, and 6 is NOT a multiple of 18
Case b: a = 9 and b = 6, in which case
ab = 54, and 54 IS a multiple of 18
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: 2b = 3c
There's no information about the variable a, so a can have ANY value. So, this statement SEEMS/FEELS insufficient. Let's test some values.
There are several values of a, b and c that satisfy this condition (keeping in mind that variable a can have ANY value). Here are two possible cases:
Case a: a = 1, b = 3 and c = 2, in which case
ab = 3, and 3 is NOT a multiple of 18
Case b: a = 6, b = 3 and c = 2, in which case
ab = 18, and 18 IS a multiple of 18
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 1 tells us that 2a = 3b
Divide both sides by 2 to get: a = 3b/2
Since a is an INTEGER, we know that 3b/2 is an INTEGER
If 3b/2 is an INTEGER, then
b must be divisible by 2
Statement 2 tells us that 2b = 3c
Divide both sides by 3 to get: c = 2b/3
Rewrite as
c = (2/3)b
Let's also take the statement 1 equation (2a = 3b) and divide both sides by 3 to get: b =
2a/3
Now take
c = (2/3)b and replace b with
2a/3
We get: c = (2/3)(
2a/3)
Simplify to get: c = 4a/9
Since c is an INTEGER, we know that 4a/9 is an INTEGER
If 4a/9 is an INTEGER then
a must be divisible by 9
We now know that
b must be divisible by 2 and
a must be divisible by 9.
So, we can conclude that ab is divisible by (2)(9)
In other words,
ab is a multiple of 18
Since we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer: C
Cheers,
Brent
