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 right 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.

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

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:

http://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

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 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