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problem with language describing percentage.

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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problem with language describing percentage.

by kwan » Wed Nov 14, 2012 12:07 am
i'm having tremendous problems with language describing percentage. for example:
x is m percent of Y
I understood as: x/y=m which in the OG answer it should be x=y m/100

another one
a photography dealer ordered 60 model x cameras to be sold for 250 each, which represents a 20 percent markup over the dealer's initial cost for each camera.
I understood as: ah since 20% is the profit then the cost must be 250*80% which of course you know the frustration i had when i found out the final answer.
may it is because i'm not native English speaker or something else, is there a chance to identify precisely what the problem is talking about? many thanks in advance.
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by Brent@GMATPrepNow » Wed Nov 14, 2012 7:50 am
kwan wrote:i'm having tremendous problems with language describing percentage. for example:
x is m percent of Y
I understood as: x/y=m which in the OG answer it should be x=y m/100
The word "percent" means "out of 100" in Latin.
In fact, you can almost see a /100 hiding in the notation for percent" %
So, m percent is the same as m/100

So, m percent of y is the same as m/100 of y, which is the same as (m/100)(y)

Cheers,
Brent
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by Brent@GMATPrepNow » Wed Nov 14, 2012 8:03 am
kwan wrote: a photography dealer ordered 60 model x cameras to be sold for 250 each, which represents a 20 percent markup over the dealer's initial cost for each camera.
I understood as: ah since 20% is the profit then the cost must be 250*80% which of course you know the frustration i had when i found out the final answer.
may it is because i'm not native English speaker or something else, is there a chance to identify precisely what the problem is talking about? many thanks in advance.
This is a very common error.
Here's an example: A retail price of $100 represents a 10 percent markup.
Incorrect conclusion: This means the original price must be 10 percent less than $100. In other words, the original price was $90
To show that this conclusion is incorrect, let's work backwards.
Take $90 and add 10 percent to it. Well, 10% of $90 is $9. So, a 10 percent markup would result in a retail price of $99 (not $100)

Now let's examine your question:
A $250 retail price represents a 20 percent markup. What was the dealer's initial cost?

Let x represent the initial cost.
So, (20/100)x = 20 percent of the initial cost.
This means that x + (20/100)x = the new (marked up) price
Since we're told that the new price is $250, we can write the following equation:
x + (20/100)x = 250

When we solve this equation for x, we get x = 208 1/3

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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