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What number is 150 percent greater than 3? [#permalink]

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26 Jun 2013, 16:55

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I know that this is an easy question but I need to solidify the mechanical processes correctly for answering these types of percent questions.

For every other question similar to this one, I simply multiplied by the number by the percent multiple. Example: What number is 25% greater than 40? I multiplied 40 by 1.25 and got 50. What number is 6% greater than 200? I multipled 200 by 1.06 and got 212. What number is 90% less than 180? I multiplied 180 by .1 and got 18.

As I was working on this question, I knew that multiplying 1.5 times 3 would yied 4.5 and that this did not make sense since 100% of 3 is 6. However, I cannot pinpoint why multiplying the 3 by the multiple 1.5 does not work in this case? Or is it simple coincidence that the multiple method worked in all other problems?

Re: What number is 150 percent greater than 3? [#permalink]

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26 Jun 2013, 17:49

You kind of answered your own question I think...100% greater than 3 is 6, so 150% greater than 3 is 7.5. 150% of 3 is in fact 4.5 When you're doing these ratio/proportion type problems with percents that are asking for a "x percent greater" and x is over 100% then you have to add 100% to that number in order to take account for the number itself being 100% greater. You can also take 3*1.5 and just add it to your original number. When you take 3*1.5 you're in fact only finding a number 50% greater than 3. Hope that makes sense.

Make sure you're distinguishing between the terms "percent of" and "percent greater than." Notice that in your post you said that "100% of 3 is 6." That should be "100% greater than 3 is 6."

"Percent of" indicates straight multiplication:

50% of 3 = .5*3 = 1.5 100% of 3 = 1*3 = 3

"Percent greater than" means to add the given percent to the original number. For "150% greater than 3," we can find 150% of 3 and add that to the original number:

150% of 3 = 1.5*3 = 4.5

4.5 + 3 = 7.5

Alternatively, as others have indicated, you can also just add 1 to your multiplier to represent the original number:

Re: What number is 150 percent greater than 3? [#permalink]

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27 Jun 2013, 02:24

DmitryFarber wrote:

Make sure you're distinguishing between the terms "percent of" and "percent greater than." Notice that in your post you said that "100% of 3 is 6." That should be "100% greater than 3 is 6."

"Percent of" indicates straight multiplication:

50% of 3 = .5*3 = 1.5 100% of 3 = 1*3 = 3

"Percent greater than" means to add the given percent to the original number. For "150% greater than 3," we can find 150% of 3 and add that to the original number:

150% of 3 = 1.5*3 = 4.5

4.5 + 3 = 7.5

Alternatively, as others have indicated, you can also just add 1 to your multiplier to represent the original number:

Thanks Dmitry. ur explanation is crystal clear. I have a small doubt in the text "what number is 150% greater than 3" does it mean to add the orginal number "3"? i.e. 3+4.5?

Yes. "percent greater than/less than" is always about how much more/less than the original number. "Percent of" is about how much of the original number.

30% of 10 = .3(10) = 3 80% of 5 = .8(5) = 4

30% greater than 10 = 10 + .3(10) = 10 + 3 = 13 80% less than 5 = 5 - .8(5) = 5 - 1 = 4

Now, for these latter problems (% greater/less than), we don't have to use addition/subtraction as above. We can add 1 or subtract from 1:

30% greater than 10 = (1+.3) * 10 = 1.3(10) = 13 80% less than 5 = (1-.8) * 5 = .2(5) = 1

This gets the same result, but it can be a little quicker. We can even use it if we have a variable:

x% less than 50 is 35. What is x?

Here, we can represent "x%" as "x/100."

50 - (x/100)(50) = 35 (50)(1 - x/100) = 35 (With practice, you might see this second step directly and not write the first version.) (1 - x/100) = 35/50 = 7/10 1 - 7/10 = x/100 3/10 = x/100 300 = 10x 30 = x
_________________

Dmitry Farber | Manhattan GMAT Instructor | New York

Re: What number is 150 percent greater than 3? [#permalink]

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07 Oct 2014, 05:23

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Re: What number is 150 percent greater than 3? [#permalink]

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24 Feb 2016, 02:25

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Re: What number is 150 percent greater than 3? [#permalink]

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10 Aug 2017, 08:06

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