Prep question

[goods81]

Can anybody help with a question on GMAT prep? See attached image.

File is in word format.

[Feep]

This is a bit of a caveat that most people don't quite realize.

When someone says something increased by 300%, that is on TOP of the original value. It does NOT mean the new value is now 3x the original value. If that were the case, than 200% would be 2x the value, and 100% would be the original value...which would imply that saying "the value increased by 100%" does nothing to the value at all, which is just silly.

So, an increase of 400% is FIVE times the original, and an increase of 300% is FOUR times the original. Thus, the total multiplier is 4*5 = 20.

[kanha81]

This is a bit of a caveat that most people don't quite realize.

When someone says something increased by 300%, that is on TOP of the original value. It does NOT mean the new value is now 3x the original value. If that were the case, than 200% would be 2x the value, and 100% would be the original value...which would imply that saying "the value increased by 100%" does nothing to the value at all, which is just silly.

So, an increase of 400% is FIVE times the original, and an increase of 300% is FOUR times the original. Thus, the total multiplier is 4*5 = 20.

I don't understand your solution. Can you please break it down? I know that 300% increase does not mean 3x, but I did not understand the part highlighted above.

Best regards,
Kanha81

[goods81]

[quote="kanha81"][quote="Feep"]This is a bit of a caveat that most people don't quite realize.

When someone says something increased by 300%, that is on TOP of the original value. It does NOT mean the new value is now 3x the original value. If that were the case, than 200% would be 2x the value, and 100% would be the original value...which would imply that saying "the value increased by 100%" does nothing to the value at all, which is just silly.

[color=blue]So, an increase of 400% is FIVE times the original, and an increase of 300% is FOUR times the original. Thus, the total multiplier is 4*5 = 20[/color].[/quote]


I don't understand your solution. Can you please break it down? I know that 300% increase does not mean 3x, but I did not understand the part highlighted above.

Best regards,
Kanha81[/quote]

You take the original number and times it by %+ 1 because new % needs to include original number...so (n+1) * n where n is original number

Look at it this way...
let's say N=2
what is 100% of 2? 4 (2*2)
what is 200% of 2? 6 (2*3)
what is 800* of 2? 18 (2*9)

[goods81]

[quote="goods81"][quote="kanha81"][quote="Feep"]This is a bit of a caveat that most people don't quite realize.

When someone says something increased by 300%, that is on TOP of the original value. It does NOT mean the new value is now 3x the original value. If that were the case, than 200% would be 2x the value, and 100% would be the original value...which would imply that saying "the value increased by 100%" does nothing to the value at all, which is just silly.

[color=blue]So, an increase of 400% is FIVE times the original, and an increase of 300% is FOUR times the original. Thus, the total multiplier is 4*5 = 20[/color].[/quote]


I don't understand your solution. Can you please break it down? I know that 300% increase does not mean 3x, but I did not understand the part highlighted above.

Best regards,
Kanha81[/quote]

You take the original number and times it by %+ 1 because new % needs to include original number...so (n+1) * n where n is original number

Look at it this way...
let's say N=2
what is 100% of 2? 4 (2*2)
what is 200% of 2? 6 (2*3)
what is 800* of 2? 18 (2*9)[/quote]

And to answer your question...we need to multiple both values to get the total increase...

[Ian Stewart]

Look at it this way...
let's say N=2
what is 100% of 2? 4 (2*2)
what is 200% of 2? 6 (2*3)
what is 800* of 2? 18 (2*9)

There's a difference between the question "What is 800% of 2", and "What is the result if 2 is increased by 800%?"

If we need to find 800% of 2, we multiply 2 by 800% = 800/100 = 8. That is, 800% of 2 is equal to 8*2 = 16.

On the other hand, if we need to increase 2 by 800%, we need to add 800% of 2 to 2. It may be easier to remember:

original value + increase = final value

So to increase 2 by 800%, we have:

2 + (800/100)*2 = 2 + 16 = 18

Of course, if we increase something by 800%, we're really multiplying it by 9, not by 8.

We can see why increasing something by 800% is the same as multiplying something by 9 by using factoring. Let's do that for any percent increase at all. Say we increase 2 by x%. Then the result would be equal to:

2 + (x/100)*2 = 2(1 + x/100)

So when we increase something by x%, we're really multiplying it by (1+x/100), and not just by x/100.