Calculating percents rapidly

Question

I've searched all over the internet and here but found no real useful ideas, wondering if any of you have one for dividing a number by 1+n in a very speed-efficient way.

For any percentage question that would make me do x+ n%, I usually divide x by 10% or 5% or 1% and then just add. For example: 12% out of 80 would be:
1% = 0.8 + 
1% = 0.8 +
10% = 8

Which would be 9.6.

However, if I want the previous number that when added 12% gives me 9.6, I do not know any quick method. Yes, you can easily do 9.6/1.12, but you would require a calculator or more time that what is usually good to spend on the gmat in these types of things.

Any quick methods you guys use?

chetan2u · Answer

hi,
finding % out of any number or finding certain % of a number is atraight forawrd multiplication by that % and divide by 100..
example 12 % out of 80 is nothing but 80*12/100= 960/100=9.6..
hope this is what u wanted to know..

EMPOWERgmatRichC · Answer

Hi eflores89,

The GMAT Quant section rewards Test Takers for being "flexible" with how they organize their work. Sometimes a question becomes easier to solve if you convert the data from one 'format' to another:

For example....

2/5 = 0.4 = 40% = 40/100 etc.

There are patterns in the math itself that you can sometimes take advantage of....

Consider these calculations....

(4)(5) = 20
(.4)(5) = 2.0
(.4)(.5) = .20
(40)(.5) = 20.0
(.04)(.05) = .0020

Notice how the produce is "20" with a certain number of decimal points. Sometimes, to save time, you should ignore the 0s and decimal points until the end (then put them back in).

In your example: 12% of 80

Try this....what is (12)(8)?

Now, put the 0 back in (because we're really multiplying by 80 and not 8), THEN put in the two decimal points....

(12)(8) = 96

put in the 0.....960

put in the two decimal points......9.60

By building up more than just the skills that you're comfortable with, you'll find that you'll have plenty of ways to make solving GMAT problems easier and faster.

GMAT assassins aren't born, they're made,
Rich

eflores89 · Answer

I guess no one understood the question. I was not asking about the 12% of 80 but rather going the other way around: "x" number when added a certain percent gives you "y" number.

Anyway, I found a clever trick, maybe some of you will find it easier, I will illustrate with an example:

The final price of a sold item is 5000 and the markup by the retailer is 25% of the cost, what is the original cost?

This of course is 5000/1.25 <- which was not my question but rather how do you calculate that number faster.

My way of thinking would be to divide 1 by its parts composed of the % (in this case 0.25).

We can easily see that .25 fits neatly 4 times in 1, so we have 5 parts in total in the denominator (4 in the "1" + 1 in the "0.25"). We can thus divide the 5000 in 5 equal parts, each being 1000.

Finally, we "lose" the part we don't want (which is 1 part or "0.25"), by simply subtracting that part from the 5000, which gives us 4000. Thus, 5000/1.25= 4000.

When dividing by a fraction (i.e. 0.5), we can apply a similar logic:

5000/0.5 <- we have 1 "parts" consisting of 0.5 and need another "part" to get to one. So, we want "2" parts in total... if one part is 5000, two parts is? 5000*2. Thus, 5000/0.5= 10,000.

Anyway, this might seem complicated to some but I find it helpful, specially for problems where an approximation is sufficient and the numbers are very ugly.

EMPOWERgmatRichC · Answer

Hi eflores89,

As I mentioned in my prior post, you mind find it helpful to "convert" information to a different format. That "flexibility" to look at information in more than one way can help you to find (and take advantage of) the 'shortcuts' that the GMAT writers build into Test Day questions.

In your example, you chose to keep the information in decimal format. What if you converted it to fraction though.....?

(1.25)(X) = 5,000

Instead of having to deal with.....
X = 5,000/1.25

Try this....
1.25 = 5/4

(5/4)(X) = 5,000

X = 5,000/(5/4)
X = 5,000(4/5)
X = 20,000/5
X = 4,000

GMAT assassins aren't born, they're made,
Rich

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Calculating percents rapidly

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