How many times vs how many times greater?
Sophia Terry 
I keep on coming into these problems while my gre prepration
How many times vs how many times greater or
a is what % of b or a is what % greater than b
What is the right convention to solve these problems? Some websites treat both of these scenarios similar? However I believe that in case of larger you have to do
if how many times b greater than a
do b-a/a.
Let's say a=9, b=3;
So I get these answers. Are these answers correct?
1: a is 3 times b.
2: a is 2 times greater than b.
3: a is 300% times b.
4: a is 200% times greater than b.
My confusion is that in this question, author does the opposite of what he should do.
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$\begingroup$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.
$\endgroup$ 1 $\begingroup$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.
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