"$x$ times as many as" versus "$x$ times more than"?

Question

I keep coming across such questions during my GRE preparation:

• A is how many times of B versus A is how many times greater than B
• A is what percentage of B versus A is what percentage greater than B

Some websites treat both phrasings in each pair as meaning the same, however I believe that "$A$ is __times greater than $B$" is asking for $$\frac AB-1.$$ As such, I think that these four options are all correct:

Let A=9 and B=3.

1: A is 3 times of B.
2: A is 2 times greater than B.
3: A is 300% times of B.
4: A is 200% times greater than B.

Yet the author of the following question would pick only options 1 and 3 above:

What is the right convention to interpret these phrasings?

Answer 1

The phrase "A is what % of B" should be written as $A=x\cdot B$. And now solve for x, and then multiply by 100.

Example 1a: If A is 100, and B is 50, then $100=x\cdot 50$, means that $x = 2$, and A is 200% of B.

The phrase "A is what % greater than B," should be written as $A=x\cdot B$, just as before. But now, when you solve for x, and multiply by 100, you want to take the additional step of subtracting 100. Notice that this will only work if A is actually greater than B.

Example 1b: In the above example, A would be 100% greater than B.

Example 2: if A is 150, and B is 100, then solving for x in $A=x\cdot B$, would give us $x = 1.5$, and so A is 150% of B. But A is 50% greater than B.

Answer 2

The question that you link to uses the phrase "...how many times larger was...".

You use the phrase greater than in your question, and this is what causes the problem. There is an ambiguity about whether it is the comparative sizes of their differences that you discuss.

The fact is that 2 is two times larger than 1. The fact is that 1.5 is three times larger than 0.5. The fact is that $b$ is $(b \div a)$ times larger than $a$. The page you link to is correct.