Here are five quick tips to make you much more effective at interpreting and solving GMAT problems involving percents, one of the most common GMAT questions.

## Percents and Decimals

Fundamentally, a percent is a fraction out of 100 – it is *per centum* (Latin for “per 100”). It’s easy to change a percent to a decimal. For example, 37% means 37 parts out of one hundred, or 37/100. As a decimal, that’s just 0.37. Changing a percent to a decimal simply involves sliding the decimal to the left two places.

## Percent Changes as Multipliers

This is one of the **BIG** math ideas for GMAT. A multiplier is a factor by which you multiply a number to get a desired result. There are three percent-related multipliers you will need to understand

**a) X% of a number**

Suppose I have $400 in an account, and need to know what 30% of this account is. The multiplier = the percent as a decimal. 30% as a decimal is 0.30, and $400(0.30) = $120, so $120 is 30% of $400.

**b) an X% increase**

Suppose I have $400 in an account, over time period, I am going to get an additional 5% of interest; in other word, my account is going to increase by 5%. Here, the **multiplier = 1 + (the percent as a decimal)**. Thus, $400(1.05) = $420, so that’s the amount I would have after a 5% increase

**c) an X% decrease**

Suppose I have $400 in an account, and because of some kind of penalty, I am going to be nailed with a 15% deduction; in other words, my account will decrease by 15%. Here, the **multiplier = 1 – (the percent as a decimal)**. In this case, the multiplier = 1 – 0.15 = 0.85, and the result after the deduction is ($400)(0.85) = $340.

## Calculating a percent change

Basically, a percent is a simple ratio times 100. The GMAT will ask you to calculate percent changes, and here you have to be very careful with order, i.e., what’s the starting number and what’s the ending number. IMPORTANT:* in a percent change, the starting number is always 100%*. Thus, we can say:

Here are a couple examples

a) *Price increases from $400 to $500; find the percentage increase. *

Of course, that’s a change of $100, so $100 divided by starting value of $400 is 0.25, times 100 is 25%. A move from $400 to $500 is a 25% increase.

b) *Price decreases from $500 to $400; find the percentage decrease.*

Change is still $100, but now the starting value is $500, and $100/$500 = 0.20, times 100 is 20%. A move from $500 to $400 is a 20% decrease.

**BIG IDEA**: Order matters. When you change from one value to another and want the percentage change, it matters which value was the starting value.

## A Series of Percentage Changes

Example: “Profits increased by 40% in January, then decreased by 30% in February, then increased by 20% in March. Express the change over the entire first quarter as a single percentage.” This may seem like a nightmare problem, but it’s quite approachable with multipliers. First Caution: *NEVER** add a series of percent*. That’s what many people will do, and on multiple choice, it’s always an answer choice – here, that would be 40 – 30 + 20 = 30. That is **not** the way to go about answering the question.

The way to attack this question is with a series of multipliers:

In January, a 40% increase –> multiplier = 1.40

In February, a 30% decrease –> multiplier = 0.70

In March, a 20% increase –> multiplier = 1.20

Aggregate change = (1.40)(0.70)(1.20) = 1.176 –> that’s a 17.6% increase for the quarter.

**BIG IDEA**: For a series of percentage changes, simply multiply the respective multipliers.

## The Increase – Decrease Trap

This is a predictable GMAT Math trap: the result of a percentage increase, followed by a percentage decrease of the same numerical value. For example, “The price of the appliance increase 20%, and then decreased 20%. The final price is what percent of the original price.” Every single time that question is asked on multiple choice, the incorrect answer of 100% will be an answer choice, and every single time, a large portion of folks who take the GMAT will select it. You have a leg up if you simply recognize and remember that this is a trap.

In fact, solving this problem is just an extension of the previous item:

a 20% increase –> multiplier = 1.20

a 20% decrease –> multiplier = 0.80

total change = (1.20)(0.80) = 0.96

Thus, after the increase and decrease, the final price is 96% of the original price, which means it is a 4% *decrease*.

**BIG IDEA #1**: when you go up by a percent, then down by the same percent, you do *not* wind up where you started: that’s the trap.

**BIG IDEA #2**: in this situation, as in any situation in which you have a series of percentage changes, simply multiply the respective multipliers.

If you simply remain clear on these five tips, you will be a master of percent & percentage change, one of the most frequently asked topics on GMAT Math.

#### Special Note:

To find out where percents sit in the “big picture” of GMAT Quant, and what other Quant concepts you should study, check out our post entitled:

What Kind of Math is on the GMAT? Breakdown of Quant Concepts by Frequency

Hi Mike,

This may be a silly question but on what type of questions do we apply the (new -old)/old formula?

Hi sal,

No such thing as a silly question 😀 This formula is another way to describe the percent change formula! If you think about it using the formula we provide under the “Calculating a Percent Change” heading, “new-old” is the same as the “amount of change” or difference between the two values, and “old” is the same as “starting amount.” I hope that clears your doubt 🙂

Hi Mike,

Regarding the successive percent increase and decrease questions:

The price of the appliance increase 20%, and then decreased 20%. The final price is what percent of the original price.”

In fact, solving this problem is just an extension of the previous item:

a 20% increase –> multiplier = 1.20

a 20% decrease –> multiplier = 0.80

total change = (1.20)(0.80) = 0.96

Thus, after the increase and decrease, the final price is 96% of the original price, which means it is a 4% decrease.

Query:

After the 20% increase the price would be 100+20 = 120;

So shouldn’t this be 20% decrease on the “increase” rather than on the original; which would be 24 percent decrease..so the final price would be 100-24 = 76

Hi Shraddha,

Happy to help! 🙂 The decrease is applied to the intermediate value not to the 100. So we need to take away 20% of the 120 not the 100 AND this needs to come out of the intermediate value, not the starting value. So 100 increases 20% –> now we have 120. Then that intermediate value of 120 decreases 20% –> now we have 120 – 24 = 96.

I hope that makes sense! 🙂

Hi Mike,

Thanks for the wonderful lesson on % increase and decrease. I need help with another question type (rather I guess it is just worded differently) involving percentage– How much % is “A” greater than “B” (instead of – what is the % increase from B to A)

So, in this case the original value would be B (and not A) and the ans would be = (A-B) *100/B ?

Hi Mike!

Great content, as always! 🙂

I have always been calculating percentages in fractions. if its 25%, I use 25/100 almost always, and dont even reduce it to 1/4 at times. Should I stick to the way I solve things or would you suggest that I should change my application to reduced fractions or decimals. When I see decimals, my eyes keep searching for where to place the dot, and then I wear out. Would practice using decimals bring up any drastic performance change in the exam?

Can this information be used when calculating the difference between a company’s percent increase versus the national average percent increase?

For example:

Shoreline increased 6% while the national average was an increase of 38%. The national average is the whole and Shoreline is the part correct? Thank you. spoole

Very useful thank you .

Dear Anahita,

You are quite welcome, my friend! 🙂 I am very glad you found this helpful! 🙂 Best of luck to you in your future!

Mike 🙂

Good one. Bookmarked !

Dear Kris,

I’m glad you found this helpful! Best of luck to you!

Mike 🙂

Hi ,

37% means 37 parts out of one hundred, or 37/100. As a decimal, that’s just 0.37. Changing a percent to a decimal simply involves sliding the decimal to the right two places.

I think there is a typo mistake , Changing a Percent to a Decimal simply involves sliding the Decimal to the left two places as if just Divide by 100 ex: 0.25% = 0.0025

Sorry Instead of Left it is written is Right.

If i am not wrong please correct me.

Dear Anusha,

Great eye! Yes, you are perfectly correct! Hundreds of people have read this blog, but you were the first to point out this typo. I just fixed it. That’s a very good eye for detail, and that will serve you well on the GMAT. Thanks for pointing this out, and best of luck to you!

Mike 🙂

Dear Mike,

Like your post, but need little bit more info.

how about this: that is X% of X% of y? or when z=X% less than y?

would most appreciate your help

Regards

My friend,

I’m sorry, but I don’t understand you question at all. Here’s what I suggest. Post an expanded version of this question in the Magoosh forum of GMAT Club, here:

http://gmatclub.com/forum/magoosh-324/

Then send me a private message through the GC system, and I will help you there.

Mike 🙂

Hi Mike, I’m sorry if this sounds like a silly question but going back to the 117.6% or 17.6% I understand that its an increase in profits and that’s the change but then why in the next question didn’t we change anything for the 96% answer?

Is the step to multiply all the multipliers and the convert to a percent by sliding the decimal to places to the right or is there something I’m missing? I’m preparing for the GRE so I presume he questions will be similar?

Tanks in advance

Dione,

You’re correct — there are always two closely related questions: (a) the end result is what percent of the start? (first answer = 117.6%, second answer = 96%), or (b) the end result is what percent increase/decrease from the first? (first answer 17.6% increase, second answer = 4% decrease). I hadn’t originally included that last one, but just added now for symmetry and clarity. The GMAT & GRE more frequently ask the second question, but technically, they could ask either. Does all this make sense?

Mike 🙂

Hi Mike, isnt Aggregate change = (1.40)(0.70)(1.20) = 1.176 = 117.6%?

Why is it 17.6?

Dear Sadia,

My friend, you are confusing two closely related concepts. Suppose something starts at 100 and goes up to 117.6 — then the ending value is 117.6%

ofthe starting value, but the ending value is a 17.6%increaseabove the starting value. It’s very important to be clear on (percentofsomething) vs. (percentincrease). Does this make sense?Mike 🙂

Hi Mike,

I am also confused about this concepts of what Sadia and Dione were asking. I understand when something is 100 and goes up to 117.6, that is a 17.6% increase (117.7-100)/100 thats 17.6%. Then, what is the product of (1.40)(0.70)(1.20) gives us?

I’m also confused about the 96% answer. The product of (0.2)(1.20) is 0.96, which is 96%, but why is this a 4% decrease?

Dear Xian,

I’m happy to help. 🙂 Yes, when something goes from 100 to 117.6, or in other words, when

any quantityis multiplied by 1.176, that’s a 17.6% increase. The product (1.40)(0.70)(1.20) = 1.176, so multiplying by each of these three factors will also produce a 17.6% increase.As for 0.96 — this is a number less than one. How much less? Well, 0.96 = 1 – 0.04, and 0.04 is the multiplier for 4% of something. If we subtract 4% of something, that’s a 4% decrease.

These ideas of thinking about percents in terms of multiplies is very deep. You would do well to spent time with these ideas, because they have the potential to revolutionize your understanding of percents on the GMAT.

Does all this make sense?

Mike 🙂

Hi Mike,

After watching the video about Sequential Percent Changes, I think I understand the concepts here.

Here’s what I understand:

1.176 is the multiplier of 17.6%, in another word, it is 1+0.176, that’s a percent increase.

0.94 is the multiplier of 4%, which is 1-0.94=0.4. That is a percent decrease.

I might sound confusing here, but I think I understand the two concepts now. Thanks Mike!!

Xian,

I believe you have a typo — 0.96 is a 4% decrease, and 0.94 is a 6% decrease. Other than that, I think you understand the basics of this idea now. Don’t underestimate this perspective: it is very powerful.

Mike 🙂

Mike,

Yes, that was a typo. This concept is very powerful. Before I watch your video and this blog, I usually solve this type of questions by using a random number and calculate it by each percent given in the problem, and that takes a lot of time to do! Now I learned a shortcut and it saves a lot of time!

Dear Xian,

I am very glad you have found the power and efficiency of this method. I wish you the very best of good fortune in your preparation for the GMAT.

Mike 🙂

Hi, Mike we can apply a direct formula like

a+b + ab/100

the sign before a and b depends on weather the number increased or decreased

Hi Trisha!

It looks like that formula is a shortcut for calculating compound interest. 🙂 So, the answer depends on what you’re trying to calculate.

With that said, I’d recommend using the percent change equation for “Percent Increase or Decrease” questions.

[(New Value − Old Value) / Old Value] × 100%

Thanks Mike for putting together quick tips. This is very helpful.

Two questions

1) In example given under “A Series of Percentage Changes” section , aggregate change value is given as 1.176.

However, while converting this value to percentage, it’s given as 17.6%.Shouldn’t it be 117.6% ?

2) I came across following example on http://www.platinumgmat.com/gmat_study_guide/percents

Example:- “From 2004 through 2007, the Dow Jones Industrials Average rose about 30%. However, during 2008, the Dow fell about 35%. About what percent did the Dow Jones change from 2004 through 2008?”

My analysis:-

For 30% increase –> multiplier = 1.30

For 35% decrease –> multiplier = 0.65

Aggregate change =(1.30)*(0.65)=0.845 .Hence percentage change is 84.5%

However, answer given in platinumgmat website(http://www.platinumgmat.com/gmat_study_guide/percents) is -15.5%

So whichone is correct answer? 84.5% or -15.5

Appreciate your reply.

Dear Mike,

Your questions are less about math and more about semantics. You see, suppose the price goes from $100 to $130 — that’s a 30% increase, a 30% change, but the new price is 130% of the old price. Which number is correct depends on the semantics.

In my problem, the decimal 1.176 means the number increased 17.6%, the number changed by 17.6%, and the final number is 117.6 of the starting number. I was talking about the percent change, so that’s why 17.6% is correct there.

On this blog, we generally don’t answer questions about outside material, and this question gives a good example why. The right answer would depend very much on the exact wording of the question. Good GMAT question sources are impeccable in their wording, but I’m sorry to say, some not-so-good sources have atrociously vague and misleading wording. I’ll recommend sticking to the best GMAT resources:

https://magoosh.com/gmat/2013/best-gmat-books-and-resources-2013/

Mike 🙂

Thanks a lot Mike. Really appreciate your detailed explanation.Now it’s clear to me.

Mike

You’re quite welcome. Best of luck to you.

Mike 🙂

Hi Mike!!

I’m still confused with the answer being 117.6 and not 17.6. The aggregate change is 1.176—> 117.6%

Isn’t it?

Dear Ankita,

This is a very tricky language issue. The aggregate multiplier for three months is 1.176. This means that the profits at the end of the three months are 117.6% OF the profits at the beginning, BUT the change, the increase, in profits, is 17.6% — that’s how much they’re up from the starting point. I have never seen the GMAT ask for the former, the end is what percent of the beginning — I have always seen them ask about the change, the increase/decrease. Does this make sense?

Mike 🙂

Hey Mike!

Thanks! That helped!! 🙂

And bdw I’m giving Gre, but the explanations given here are so good, I just couldn’t stop myself from going through the entire summary and problems!! And the multiplier trick is so awesome..saved much of my time!!!! Thanks a ton!! 🙂

Ankita,

I’m glad you are finding this helpful. Thank you for your kind words, and I wish you the best of luck!

Mike 🙂

Thanx a lot Mike.These shortcuts never occurred to me!

Thanks a lot Mike. These shortcuts never occurred to me!

Dear Nahida,

You are more than welcome. Best of luck to you!

Mike 🙂

Thanks Mike! I never thought of the shorter method of multiplying respective multipliers.

great help!!!!

You are quite welcome. I’m glad you found it helpful. Best of luck to you!

Mike 🙂

thanx..% is something which worries me most of the time..i hope now i will be solving % questions with better accuracy and in less time

Dear Anish,

Thank you for your kind words. Best of luck to you!

Mike 🙂

This answers so many questions in a concise manner and clears any doubts I had on approaching percent problems. Thank you!

!This will save me so much time on these type problems. Thanks!

Maurice,

I am very glad you found this helpful. Best of luck to you.

Mike 🙂

Thanks Mike! I never thought of the shorter method of multiplying respective multipliers. Big help.

Sam:

I’m glad you found it helpful. Best of luck to you!

Mike 🙂