Exponents and English Words Question

Question

Hi,
So finally I started studying for my GMAT which I will take in summer.

I began with Manhattan GMAT 2007 (Number properties) as it was suggested on the forum. My first question is about exponents.
On page 51, the MGMAT says the following:

5^1 = 5
5^2 = 25 Increased by 20
5^3 = 125 Increased by 100
5^4 = 625  Increased by 500

Now, my primary language is not English but why is 5^4 (aka 625) increased by 500?
  Why can't we say that it increased by 620? I mean that why can't we start counting from the 5^1?

Also, in Russian there are two ways how to say the number has increased:
a. Arithmetically
b. Geometrically

In the example of 5^4 compared to 5^1, we can say that
a. 5^1 has increased by 620 arithmetically (that is 620 has been added)
b. 5^1 has increased by 125 geometrically (that is 5 has been multiplied by 125)

However, English language does not specify when somebody says that "Number A has increased by B". Naturally, I start thinking that a geometrical progression is being used. Nevertheless, I found out that by default the expression "Number A has increased by B" means the addition of the B.

So, what are the common ways for GMAT to ask questions when multiplication (and not addition) is involved?

Thanks.

testprep2010 · Answer

5^1 = 5
5^2 = 25 Increased by 20
5^3 = 125 Increased by 100
5^4 = 625  Increased by 500

Now, my primary language is not English but why is 5^4 (aka 625) increased by 500? 
because 
with respect to 5, 25 increased by 20, and 
with respect to 25, 125 increased by 100, and 
with respect to 125, 625 increased by 500

However, English language does not specify when somebody says that "Number A has increased by B". Naturally, I start thinking that a geometrical progression is being used. Nevertheless, I found out that by default the expression "Number A has increased by B" means the addition of the B.

Number A has increased by B -- as long as B is a number, it refers to addition
if B is rate, like A increased by 2 times, then it is multiplication --

IanStewart · Answer

If that's what the book says, then it is not being very clear. As we can work out from the numbers provided, when they say 'increased by 500', they mean to describe the increase from 5^3 to 5^4, but if I simply read "5^4 --- increased by 500", my first question will be "increased from what?" It is perfectly natural to think they might be describing the increase from 5^1 here, and we can only figure out what they mean by subtracting; they don't make clear what they are comparing. You don't see such casual language on the real GMAT, fortunately.

There are, as you suggest, many ways to describe the increase from one number to another. If we simply talk about "increasing x by 45", then what we mean is "adding 45 to x". If instead we mean to describe a multiplication, we would need to say "increasing x by a factor of 45", or "increasing x by 4400%", or something similar - a word will need to be added to the sentence to make clear that the increase is based on multiplication, not addition.

Exponents and English Words Question

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