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# Percentage increase/decrease- WHAT should be the denominator??

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Math Expert
Joined: 02 Aug 2009
Posts: 8625
Percentage increase/decrease- WHAT should be the denominator??  [#permalink]

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29 Jan 2019, 04:54
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OK, so at many times we get confused between what should be the base or denominator when we are looking for a % increase or a % decrease. I had few students asking this through PMs and seen few on the forum with the same query.

You choose the wrong one and you will still find your answer in the choices as the test makers are looking for you to commit these mistakes

So, choosing the correct denominator is very important. It may be a very easy thing for a person who is thorough with % problems and on other hand it may be a very taxing job for someone else.

When we are looking at such question, a simple rule would be to see what comes after THAN and almost everytime you should be correct.

(I) R is what % less than T.
So, we have T after THAN, thus T becomes the denominator or the BEFORE value and R becomes the AFTER value..
% decrease = $$\frac{before-after}{before}*100=\frac{T-R}{T}*100$$ .

(II) Say, now the question read - T is what % more than R
So, we have R after THAN, thus R becomes the denominator or the BEFORE value and T becomes the AFTER value..
% increase = $$\frac{after-before}{before}*100=\frac{T-R}{R}*100$$ .

A question on the same concept

The number of television sets sold by Store R last month was approximately what percent less than the number of television sets sold by Store T last month? ( The number of television sets sold by Store R was 20 and number of television sets sold by Store T was 45 as per the attached figure)

A) 40%

B) 56%

C) 86%

D) 95%

E) 125%

so simplify it -
R is what % less than T
so T is after THAN and becomes BEFORE and R becomes AFTER.

Now we are looking for % less = $$\frac{Before-After}{Before}*100=\frac{45-20}{45}*100=\frac{2500}{45}=55.55$$% or ~56%

But say you took the other way $$=\frac{45-20}{20}*100=\frac{2500}{20}=125$$% .. AND the wrong answer is there in the choice.
so be careful

I would add more examples with a slight different wordings slightly later
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Re: Percentage increase/decrease- WHAT should be the denominator??  [#permalink]

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31 Jan 2020, 17:20
Here's another article about the same "than" technique! It's a useful trick!

https://www.manhattanprep.com/gre/blog/ ... -decrease/
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Chelsey Cooley | Manhattan Prep | Online tutoring and curriculum

My latest GMAT blog posts | My latest GRE blog posts | Suggestions for blog articles are always welcome!
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Re: Percentage increase/decrease- WHAT should be the denominator??  [#permalink]

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10 Mar 2020, 04:41
1
I apply a simpler thought process.
% increase or %decrease is always between 2 numbers. We know the numerator will always be the difference between the numbers * 100. What should be the base?

If it's % increase (which is a number going up), then the base on the other side will be a number going down, which is the smaller of the 2 numbers. i.e % Increase = (Difference) * 100 / smaller of the 2 numbers.

Similarly, if it's % decrease (which is a number going down), the base on the other side will be a number going up, which is the larger of the 2 numbers.
Therefore [b]% Decrease = (Difference) * 100 / larger of the 2 numbers.

For eg sales in 2019 is $20 which becomes$35. What is the % change?
Here the value has increased,
therefore % increase = Difference * 100 / smaller number = (35 - 20) * 100 / 20 = 75% increase

Similarly if sales had decreased from $35 in 2019 to$20 in the next year,
then % decrease = (difference) * 100 / larger number = 15 * 100 / 35 = 42.86% decrease
Re: Percentage increase/decrease- WHAT should be the denominator??   [#permalink] 10 Mar 2020, 04:41