Calculating percents - GMAT Quantitative Reasoning
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A GMAT score increases from 450 to 540. By what percent did the score increase?
A GMAT score increases from 450 to 540. By what percent did the score increase?
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330 is what percent of 11?
330 is what percent of 11?
This problem can be solved by the equation: 
, where 
is the answer in terms of a percentage. To solve for 
both sides are divided by 
: 
. This can be simplified to: 
. Now 
is converted to a percentage to find the answer.
as a percentage is 
This problem can be solved by the equation:
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Three years ago, Anum invested $25,000 in a new mutual fund account. The value of the account increased by 15% during the first year, increased by 7% during the second year, and decreased by 15% during the third year. What is the approximate value of the account today?
Three years ago, Anum invested $25,000 in a new mutual fund account. The value of the account increased by 15% during the first year, increased by 7% during the second year, and decreased by 15% during the third year. What is the approximate value of the account today?
The first year increase of 15% can be represented as 1.15; the second year increase of 7% can be represented as 1.07; and the third year decrease of 15% can be represented as 0.85.
Multiply the original investment by each annual change.
25,000(1.15)(1.07)(0.85) = 26,148
approx. $26,000
The first year increase of 15% can be represented as 1.15; the second year increase of 7% can be represented as 1.07; and the third year decrease of 15% can be represented as 0.85.
Multiply the original investment by each annual change.
25,000(1.15)(1.07)(0.85) = 26,148
approx. $26,000
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Max the cat has 70 toy mice. If 30% of the mice are new, how many mice are not new?
Max the cat has 70 toy mice. If 30% of the mice are new, how many mice are not new?
If 30% of the mice are new, then 70% are not new.
If 30% of the mice are new, then 70% are not new.
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37% of the greatest common factor of 50 and 350 is
37% of the greatest common factor of 50 and 350 is
The greatest common factor of 50 and 350 is simply 50. Now we must take 37% of 50.
.
The greatest common factor of 50 and 350 is simply 50. Now we must take 37% of 50.
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A shirt costs $60. The price was then increased by 30%. What is the new price as expressed in terms of the original price?
A shirt costs $60. The price was then increased by 30%. What is the new price as expressed in terms of the original price?
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An elementary school was polled to find out what the children's favorite foods were. When asked what their favorite foods were, 42 students said pizza. 33 students said cheeseburgers, 12 students said hot dogs, 10 students said chicken nuggets, and the remaining 18 students filled in other various answers. What percentage of the students had pizza as their favorite food?
An elementary school was polled to find out what the children's favorite foods were. When asked what their favorite foods were, 42 students said pizza. 33 students said cheeseburgers, 12 students said hot dogs, 10 students said chicken nuggets, and the remaining 18 students filled in other various answers. What percentage of the students had pizza as their favorite food?
To calculate the percentage of students who chose pizza as their favorite food, you take the number of students who chose pizza and divide by the total number of students. So first, we must calculate the total number of students. Which is simply 
total sudents.
So,
Multiply our result by 100 to get into percentage form we get 36.5%
To calculate the percentage of students who chose pizza as their favorite food, you take the number of students who chose pizza and divide by the total number of students. So first, we must calculate the total number of students. Which is simply
So,
Multiply our result by 100 to get into percentage form we get 36.5%
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Given a number 
, which of these is the greatest quantity of the three?
(a) 30% of 40% of 50% of 
(b) 40% of 50% of 30% of 
(c) 50% of 30% of 40% of 
Given a number
(a) 30% of 40% of 50% of
(b) 40% of 50% of 30% of
(c) 50% of 30% of 40% of
All three are equal.
30% of 40% of 50% of 
is 
of 
of 
of 
: that is, 
40% of 50% of 30% of 
is 
of 
of 
of 
: that is, 
50% of 30% of 40% of 
is 
of 
of 
of 
: that is 
All three are equal.
30% of 40% of 50% of
40% of 50% of 30% of
50% of 30% of 40% of
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Out of 60 students, 15 prefer to study at night. What percent of students prefer nighttime studying?
Out of 60 students, 15 prefer to study at night. What percent of students prefer nighttime studying?
Cross multiply
Divide both sides by 60
Cross multiply
Divide both sides by 60
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Geri earns a commission of 22.5% on everything she sells for KM Cosmetics. As of the fifteenth of the month, she has sold $2,100 worth of cosmetics. How much more in cosmetics must she sell in order to earn at least $900 commission for the month?
Geri earns a commission of 22.5% on everything she sells for KM Cosmetics. As of the fifteenth of the month, she has sold $2,100 worth of cosmetics. How much more in cosmetics must she sell in order to earn at least $900 commission for the month?
Commission can be calculated by muliplying the commission rate - 22.5%, or 0.225 - by the amount of sales, so the amount of sales needed can be found by dividing the desired commission by 0.225.
Since Geri has already sold $2,100 worth of cosmetics, she needs to sell 
more.
Commission can be calculated by muliplying the commission rate - 22.5%, or 0.225 - by the amount of sales, so the amount of sales needed can be found by dividing the desired commission by 0.225.
Since Geri has already sold $2,100 worth of cosmetics, she needs to sell
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Gary weighs 20 percent more than Harry who's weight is 80 percent of James' weight. If James weighs 172 pounds, how much would Gary weigh if he lost 12 pounds? (Rounded to the nearest pound).
Gary weighs 20 percent more than Harry who's weight is 80 percent of James' weight. If James weighs 172 pounds, how much would Gary weigh if he lost 12 pounds? (Rounded to the nearest pound).
If James weighs 172 pounds, and Harry weighs 80% of that, then
pounds. If Gary weighs 20% more than Harry, then
he is 120% Harry's weight 
. If he loses 12 pounds,
he would weigh 153.12 or 153 pounds.
If James weighs 172 pounds, and Harry weighs 80% of that, then
he is 120% Harry's weight
he would weigh 153.12 or 153 pounds.
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A number is divided by two; then its decimal point is moved to the left two spaces. This is the same as taking what percent of the number?
A number is divided by two; then its decimal point is moved to the left two spaces. This is the same as taking what percent of the number?
Let's do these two things to 100. Dividing 100 by 2 yields 50; moving the decimal point two places left changes 50, or 50.0, to 0.50.
This means that the new number is 0.50% , or 
%, of the original number.
Let's do these two things to 100. Dividing 100 by 2 yields 50; moving the decimal point two places left changes 50, or 50.0, to 0.50.
This means that the new number is 0.50% , or
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A number is multiplied by six; then its decimal point is moved to the left three spaces. This is the same as taking what percent of the number?
A number is multiplied by six; then its decimal point is moved to the left three spaces. This is the same as taking what percent of the number?
Let's do these two things to 100. Multiplying 100 by 6 yields 600; moving the decimal point three places left changes 600, or 600.0, to 0.60.
This means that the new number is 0.60% , or 
%, of the original number.
Let's do these two things to 100. Multiplying 100 by 6 yields 600; moving the decimal point three places left changes 600, or 600.0, to 0.60.
This means that the new number is 0.60% , or
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If 10 percent of 
is 25 percent of half of 
, what is 
?
If 10 percent of
This is simply a matter of breaking down the problem. 10 percent of 
is 
.
25 percent of (half of y) is 25 percent of 
which is
.
Now we have these two being equal, so
or
giving
.
Finally,
This is simply a matter of breaking down the problem. 10 percent of
25 percent of (half of y) is 25 percent of
Now we have these two being equal, so
or
giving
Finally,
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A number is divided by 6; its decimal point is then moved to the left one place. This is the same as taking what percent of the number?
A number is divided by 6; its decimal point is then moved to the left one place. This is the same as taking what percent of the number?
Dividing the number by 6 is the same as multiplying it by 
. Moving the decimal point left one digit is dividing it by ten, or multiplying it by 
. The two actions together amount to multiplying the number by 
.
To find its percent equivalent, multiply by 100:
The correct choice is 
% .
Dividing the number by 6 is the same as multiplying it by
To find its percent equivalent, multiply by 100:
The correct choice is
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Ten students in a class of 
students have a learning disability. What is the percentage of students who do not have a learning disability in the class?
Ten students in a class of
The number of students who don't have a learning disability is:
Using part over whole we get the percentage of students who don't have a learning disability as:
The number of students who don't have a learning disability is:
Using part over whole we get the percentage of students who don't have a learning disability as:
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Let 
be a positive real number. In terms of 
, what percent of 20 is 
?
Let
Set up a proportion statement.
Solve for 
:
Set up a proportion statement.
Solve for
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The Republic of Fredonia uses an unusual currency system. 14 fluts are equal to 1 glut, and 16 gluts are equal to 1 blut.
A hat that cost 14 gluts 10 fluts yesterday now costs an even 1 blut. To the nearest tenth of a percent, what percent markup does this represent?
The Republic of Fredonia uses an unusual currency system. 14 fluts are equal to 1 glut, and 16 gluts are equal to 1 blut.
A hat that cost 14 gluts 10 fluts yesterday now costs an even 1 blut. To the nearest tenth of a percent, what percent markup does this represent?
This can be most easily done by looking at the current and former price in fluts.
The current price is 1 blut, or 
fluts.
Yesterday's price was 14 gluts 10 fluts, or 
fluts.
This represents a markup of 
percent.
This can be most easily done by looking at the current and former price in fluts.
The current price is 1 blut, or
Yesterday's price was 14 gluts 10 fluts, or
This represents a markup of
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What is 15 percent of 80?
What is 15 percent of 80?
This word problem can be written as
Simplifying this, we get
This word problem can be written as
Simplifying this, we get
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The price of an item is decreased by 10%, then by 20%, then by 30%. This is equivalent to doing what?
The price of an item is decreased by 10%, then by 20%, then by 30%. This is equivalent to doing what?
Decreasing a price by 10%, then by 20%, then by 30% is equivalent to taking 90% of a price, then taking 80% of that, then taking 70% of that. That, in turn, is equivalent to multiplying the price by 0.90, then by 0.80, then by 0.70.
For simplicity's sake, assume the initial price was $100. Then we can calculate the final price as follows:
The final price is $50.40, so we essentially discounted the price by $49.60, which is 49.6%.
Decreasing a price by 10%, then by 20%, then by 30% is equivalent to taking 90% of a price, then taking 80% of that, then taking 70% of that. That, in turn, is equivalent to multiplying the price by 0.90, then by 0.80, then by 0.70.
For simplicity's sake, assume the initial price was $100. Then we can calculate the final price as follows:
The final price is $50.40, so we essentially discounted the price by $49.60, which is 49.6%.
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