What number is 150 percent greater than 3?

Question

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?

Please help!

Thanks!

DmitryFarberMPrep · Accepted Answer

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:

150% greater than 3 = (1.5 + 1) * 3 = 2.5 * 3 = 7.5

You can do the same with "% less than":

60% less than 10 = 10 - .6(10) = 10 -6 = 4

OR

60% less than 10 = 10 (1-.6) = 10 * .4 = 4

sathiyanarayanan · Answer

if you add 50 % , it is because you are adding (x + 50/100(x) ) = 1.5x 
now for 150 % you should add (x + 150/100(x)) = 2.5x

as you said 100% of 3 is 3
so 50% of 3 is 1.5
now 150% of 3 is (3+1.5) ie 4.5
so adding 3+4.5 we get 7.5.

Nwsmith11 · Answer

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.

rrsnathan · Answer

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?

Thanks,
nathan

DmitryFarberMPrep · Answer

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

GAL064 · Answer

if you add 50 % , it is because you are adding (x + 50/100(x) ) = 1.5x 
now for 150 % you should add (x + 150/100(x)) = 2.5x

as you said 100% of 3 is 3
so 50% of 3 is 1.5
now 150% of 3 is (3+1.5) ie 4.5
so adding 3+4.5 we get 7.5.

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What number is 150 percent greater than 3?

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