Percent Query - very simple!

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AndyXL: Junior | Next Rank: 30 Posts; Posts: 10; Joined: Sun Oct 09, 2011 6:23 am

by AndyXL » Sun Dec 11, 2011 12:17 pm

I'm confused by something which is quite simple. It's to do with rephrasing a percentage relationship.

Take this example "if a quantity is increased by x%, the new quantity is (100 + x% of the original".

I'm told by my study guide that you can write this relationship as:

Original x [1 + percent increase over 100] = NEW

Now, I don't quite understand how we get from the bit in italics to the bit in bold...(where for example does the "1" come from)?

To take a similar example: "z minus y percent of z" can be rewritten as:

z[1 - y over 100]

When it comes to percents, I get a complete mental block and I would be appreciative if somebody could describe how / why we get from the phrase in italics to the equation in bold.

Thanks

Source: Beat The GMAT — Problem Solving | Sun Dec 11, 2011 12:17 pm

pemdas: Legendary Member; Posts: 1084; Joined: Fri Apr 15, 2011 2:33 pmFollowed by: 21 members; Thanked: 158 times

by pemdas » Sun Dec 11, 2011 2:45 pm

first of all 'percent' is nothing more than 'per cent' two words in one whole joint
'percent' mathematically can be described as related to 100 (per cent). Hence 1% (percent) is one related to 100 or 1/100. You can rephrase every time you see symbol of % put 1/100 instead of % symbol. E.g. 20%=20*1/100=20/100, 35%=35*1/100=35/100. Now you can see that every expression in percents can be rewritten as a real number - ratio 20/100=20% or decimal 20/100=20%=0.2

your '1' in parenthesis means 100% and the percents should be expressed in real numbers as you don't have the % symbol in parenthesis anymore. You may compare or operate with expressions containing % symbols or numbers. You cannot operate with one number containing % symbol and another (or other) number(s) expressed as real number(s) without % symbol. Again % means 1/100 and 1 means 100%.

Original x [1 + percent increase over 100] = NEW

z[1 - y over 100]

100% percent is implied, 1 is 100% and over 100% is greater than 1

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AndyXL: Junior | Next Rank: 30 Posts; Posts: 10; Joined: Sun Oct 09, 2011 6:23 am

by AndyXL » Mon Dec 12, 2011 2:29 pm

Thanks very much for your reply - that has helped clear things up

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