Generally, we've been taught that you should never divide by a variable unless you are certain that the value of the variable is not 0.
I was reviewing a data sufficiency question in the Manhattan GMAT Algebra Strategy guide (pg 116 in 5th ed) and I noticed that the explanation allowed for division by a variable.
The question reads:
If a = 3bc, what is the value of c?
The book suggests you manipulate a = 3bc to c = a/3b or 1/3(a/b) where if you can find a/b, it's sufficient.
Statement 1) a = 10-b
a/b = (10-b)/b Insufficient
Statement 2) 3a = 4b
a/b = 4/3 Sufficient
How do we distinguish between situations where dividing by a variable is ok? How do we know for sure that neither a,b, or c = 0?
For example, when ab = a, we cannot assume that b = 1. What's different? Does it have to do with simplifying vs. eliminating a variable entirely?
I was reviewing a data sufficiency question in the Manhattan GMAT Algebra Strategy guide (pg 116 in 5th ed) and I noticed that the explanation allowed for division by a variable.
The question reads:
If a = 3bc, what is the value of c?
The book suggests you manipulate a = 3bc to c = a/3b or 1/3(a/b) where if you can find a/b, it's sufficient.
Statement 1) a = 10-b
a/b = (10-b)/b Insufficient
Statement 2) 3a = 4b
a/b = 4/3 Sufficient
How do we distinguish between situations where dividing by a variable is ok? How do we know for sure that neither a,b, or c = 0?
For example, when ab = a, we cannot assume that b = 1. What's different? Does it have to do with simplifying vs. eliminating a variable entirely?
