This video explains GMAT Percentage Problems and how to deal with them on the GMAT Test.

GMAT Percentage Problems [Video Transcript]

In this lesson, we will take an introductory look at percents. Now to begin, the word percent literally means per 100 in Latin. So percentages are essentially fractions and decimals in disguise. For example, 19 percent literally means nineteen one hundredths, and since we already know how to convert fractions to decimals, we can say that nineteen one hundredths is equal to 0.19. Similarly, 0.43 percent is the same as 0.43 over 100 and this is equal to 0.0043. 6% is equal to 6 one hundredths and this is equal to 0.06. 300% is equal to 300 over 100 which equals 3.

Now as you might imagine, it’s important to be able to make conversions from percent to fraction to decimal. So let’s spend some time doing this. As you can see, conversions between percent and decimal are pretty straight forward, so lets tackle this first. Now when it comes to converting a decimal to a percent, the rule is to move the decimal point two spaces to the right. So to convert the decimal 0.0007 to a percent, we move the decimal two spaces to the right to get 0.07 percent. Applying the same rule, the decimal 0.465 converts to 46.5 percent. Now when it comes to converting a percent to a decimal, the rule is to move the decimal point two spaces to the left. So to convert 9.63 percent to a decimal, we move the decimal point two spaces to the left to get 0.0963. Applying the same rule 125% converts to the decimal 1.25.

Okay, now lets learn how to convert a fraction to a percent. For example, to convert three eighths to a percent, we could recognize that since we already know how to convert fractions to decimals, we can first convert three eighths to a decimal, and then convert that decimal to a percent. So first we’ll convert three eighths to a decimal by dividing 8 into 3 to get 0.375. From here, we can convert the decimal 0.375 to a percent by moving the decimal two spaces to the right to get 37.5 percent. So three eighths is equal to 37.5 percent. Now on the GMAT, we don’t want to spend valuable time performing long division to make conversions from fractions to percents. So one way to speed up these conversions is to memorize the following table. As you can see, this table is identical to the fraction decimal conversion table we examined in a previous lesson, except we have now added a new column for percent.

Now if you can memorize these base conversions than you will be able to make similar conversions with these. For example, to convert three eighths into a percent, we can use the fact that one eighth is equal to 12.5%. This means that three eighths should be 3 times as large as 12.5 percent. In other words, three eighths must equal 37.5%. Similarly, to convert two ninths into a percent, we first recognize that if one ninth is approximately equal to 11.1%, than two ninths is approximately equal to 22.2%. What about the fraction 87 over 100? Well, we don’t have one one hundredth on our table here, but we should recognize that any fraction with 100 in the denominator is quickly converted to a percent since the numerator will be equal to the percent conversion. So, 87 over 100 is equal to 87%.

Finally, how do we convert 11 over 49 into a percent? To make this conversion, lets go over here. Let’s say we are solving some question and we find that the answer is equal to 11 over 49, and we must now convert this into a percent. Let’s also say that also say that our answer choices are as follows. Now since these answer choices are so close to one another, we might feel that we cannot use estimation and then resort to long division to convert this fraction to a percent. Well, this is a valid option, it is too time consuming for the GMAT. Instead, we should be able to convert this fraction to a percent within seconds and in our heads.

Here’s how we do this. First, remember that we already know that converting fractions to percents is very simple if we have 100 in the denominator. So let’s see if we can take our fraction here, 11 over 49, and find an equivalent fraction with 100 in the denominator. To find equivalent fractions, we must multiply numerator and the denominator by the same number. So what number must we multiply 49 by to get 100? Well, if we multiply 49 by 2 we get 98 which is very close to 100. So to get exactly 100, we must multiply 49 by a number a little bit bigger than 2, which we will denote as follows. Now if we multiply the denominator by a number a little bit bigger than 2, we must also multiply the numerator by a number a little bit bigger than 2. When we do this, we get a number a little bit bigger than 22. And when we convert this fraction to a percent, we get a number a little bit bigger than 22%. When we check our answer choices, we see that only one answer is a little bit bigger than 22%. So the answer must be E.

Okay, let’s try another one. Here we want to convert 9 over 34 into a percent, and these are our answer choices. Can you make this conversion in under five seconds? Well, let’s see if we can find an equivalent fraction with 100 in the denominator. So what must we multiply 34 by to get 100? Well, if you multiply 34 by 3, we get 102 which is just a little bit to big. So to get exactly 100, we must multiply 34 by a number a little bit smaller than 3 which we will denote as follows. Now, do not confuse this notation with negative numbers. This notation does not represent negative 3, it represents a number a little bit smaller than 3. Now if we multiply the denominator by a number a little bit smaller than 3, we must also multiply the numerator by a number a little bit smaller than 3. When we do this, we get a number a little bit smaller than 27, and when we convert this fraction to a percent, we get a number a little bit smaller than 27%. When we check our answer choices, we see that only one answer is a little bit smaller that 27%. So the answer here must be C.

Okay, let’s summarize. In this lesson, we learned about percents and we learned how to make conversions involving fractions and decimals.