Percentage - GRE Quantitative Reasoning
Card 0 of 880
A factory has fixed costs of \$25,000 per month. It manufactures widgets at a total manufacturing cost of \$45 per widget. They are sold at \$60. How many widgets must be sold in any given month in order to break even?
A factory has fixed costs of \$25,000 per month. It manufactures widgets at a total manufacturing cost of \$45 per widget. They are sold at \$60. How many widgets must be sold in any given month in order to break even?
Let's first represent the total costs per month:
C = 25000 + 45n, where n is the number of widgets manufactured.
The profit can be represented as 60n – C or 60n – 25000 – 45n = 15n – 25000. Now, we merely have to solve this for 0 in order to find the "break even" line.
15n – 25000 = 0 → 15n = 25000 → n = 1666.67. We must sell a whole number of widgets, so it must be 1667.
Let's first represent the total costs per month:
C = 25000 + 45n, where n is the number of widgets manufactured.
The profit can be represented as 60n – C or 60n – 25000 – 45n = 15n – 25000. Now, we merely have to solve this for 0 in order to find the "break even" line.
15n – 25000 = 0 → 15n = 25000 → n = 1666.67. We must sell a whole number of widgets, so it must be 1667.
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According to the graph above, what was the percent change in the sales of camcorders from 2002-2006?
According to the graph above, what was the percent change in the sales of camcorders from 2002-2006?
For this problem, pay attention only to the values between 2002 and 2006 - each of which is 17 (thousand) and 22 (thousand). Note that the decrease within this range does not need to be accounted for, as the question asks only for values relative to 2002 and 2006.
To calculate percent change, take it as a fraction: 22/17 = 1.294; this represents approximately 129% of the actual value or a 29% increase in sales across these 4 years.
For this problem, pay attention only to the values between 2002 and 2006 - each of which is 17 (thousand) and 22 (thousand). Note that the decrease within this range does not need to be accounted for, as the question asks only for values relative to 2002 and 2006.
To calculate percent change, take it as a fraction: 22/17 = 1.294; this represents approximately 129% of the actual value or a 29% increase in sales across these 4 years.
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What number is 150% greater than 6?
What number is 150% greater than 6?
In the problem, 150% of 6 represents the change in the value, not the new value. Percent "greater than" is a key phrase that refers to percent change. Therefore, 9, or 150% of 6, is how much 6 increases. The answer is 6 + 9 = 15.
Formula: Original * (1 + percent increase/100) = New
6(1 + 1.50) = 15
In the problem, 150% of 6 represents the change in the value, not the new value. Percent "greater than" is a key phrase that refers to percent change. Therefore, 9, or 150% of 6, is how much 6 increases. The answer is 6 + 9 = 15.
Formula: Original * (1 + percent increase/100) = New
6(1 + 1.50) = 15
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A department store sells a set of hand weights for $X. If the store offers a 20% discount on the original price of the weights, and then an additional 10% employee discount, what will be the price of the weights if an employee purchases them?
A department store sells a set of hand weights for $X. If the store offers a 20% discount on the original price of the weights, and then an additional 10% employee discount, what will be the price of the weights if an employee purchases them?
This is a straightforward percentage problem. After the first discount, the price of the weights is \$0.8X. This price is then further reduced by 10% for the employee discount. 90% of 0.8X = 0.9(0.8X) = 0.72X.
This is a straightforward percentage problem. After the first discount, the price of the weights is \$0.8X. This price is then further reduced by 10% for the employee discount. 90% of 0.8X = 0.9(0.8X) = 0.72X.
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A shirt is originally \$20 and marked down 30%. After this it is marked up by 40% then marked down again by 10%. What is its final price?
A shirt is originally \$20 and marked down 30%. After this it is marked up by 40% then marked down again by 10%. What is its final price?
The easiest way to solve this is to note that a 30% markdown reduces the cost to 70% of the original cost. Likewise, a 40% markup is the same as making the price 140% of its current value. Using this, we can solve our problem in one string of multiplications:
New cost = Original * 0.7 * 1.4 * 0.9
New cost = 20 * 0.7 * 1.4 * 0.9 = 17.64
The easiest way to solve this is to note that a 30% markdown reduces the cost to 70% of the original cost. Likewise, a 40% markup is the same as making the price 140% of its current value. Using this, we can solve our problem in one string of multiplications:
New cost = Original * 0.7 * 1.4 * 0.9
New cost = 20 * 0.7 * 1.4 * 0.9 = 17.64
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A dress originally costs \$50 but is on sale for 25% off. In addition, you have a 10% off coupon. How much will the dress cost after these discounts?
A dress originally costs \$50 but is on sale for 25% off. In addition, you have a 10% off coupon. How much will the dress cost after these discounts?
To find 25% of \$50 you multiply 50 and 0.25. This gives you 12.50. This means the dress is \$12.50 cheaper, so it now costs 50 – 12.50 = \$37.50. You have an additional 10% off, so you multiply 37.50 by 0.10 to get 3.75. 37.50 – 3.75 = \$33.75. This is the cost of the dress. NOTE: You CANNOT add 25% and 10% and take 35% off of the \$50 dress. You will get the wrong answer.
To find 25% of \$50 you multiply 50 and 0.25. This gives you 12.50. This means the dress is \$12.50 cheaper, so it now costs 50 – 12.50 = \$37.50. You have an additional 10% off, so you multiply 37.50 by 0.10 to get 3.75. 37.50 – 3.75 = \$33.75. This is the cost of the dress. NOTE: You CANNOT add 25% and 10% and take 35% off of the \$50 dress. You will get the wrong answer.
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Column A: 
Column B: 
Column A:
Column B:
2/5% = 0.40% = 0.004. Therefore, Column B is greater.
2/5% = 0.40% = 0.004. Therefore, Column B is greater.
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For every 1000 cookies baked, 34 are oatmeal raisin.
Quantity A: Percent of cookies baked that are oatmeal raisin
Quantity B: 3.4%
For every 1000 cookies baked, 34 are oatmeal raisin.
Quantity A: Percent of cookies baked that are oatmeal raisin
Quantity B: 3.4%
Simplify Quantity A by dividing the number of oatmeal raisin cookies by the total number of cookies to find the percentage of oatmeal raisin cookies. Since a percentage is defined as being out of 100, either multiply the resulting decimal by 100 or reduce the fraction until the denominator is 100. You will find that the two quantities are equal.
Simplify Quantity A by dividing the number of oatmeal raisin cookies by the total number of cookies to find the percentage of oatmeal raisin cookies. Since a percentage is defined as being out of 100, either multiply the resulting decimal by 100 or reduce the fraction until the denominator is 100. You will find that the two quantities are equal.
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50 students took an exam. There were 4 A's, 9 B's, 15 C's, 8 D's, and the rest of the students failed. What percent of the students failed?
50 students took an exam. There were 4 A's, 9 B's, 15 C's, 8 D's, and the rest of the students failed. What percent of the students failed?
students failed.
which equals 28%.
which equals 28%.
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36 is x% of 133. What is x
36 is x% of 133. What is x
36 is x% of 133
that means that 36 = (x%)(133)
x% = 36/133 X 100 = 27%
36 is x% of 133
that means that 36 = (x%)(133)
x% = 36/133 X 100 = 27%
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is 
percent of 
is 
percent of 
Quantity A: 
Quantity B: 
Quantity A:
Quantity B:
To do this problem, translate each expression into mathematical terms:
is 
percent of 
:
is 
percent of 
:
Quantity B is greater.
To do this problem, translate each expression into mathematical terms:
Quantity B is greater.
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Quantity A: 20% of 
Quantity B: 30% of 
Quantity A: 20% of
Quantity B: 30% of
To solve this problem, consider writing the quantities in terms of only fractions:
Quantity A: 20% of 
Quantity B: 30% of 
Quantity B has the smaller denominator for an equal numerator. There is no need for calculation beyond this, and time on the GRE would be best spent elsewhere.
Quantity B is greater.
To solve this problem, consider writing the quantities in terms of only fractions:
Quantity A: 20% of
Quantity B: 30% of
Quantity B has the smaller denominator for an equal numerator. There is no need for calculation beyond this, and time on the GRE would be best spent elsewhere.
Quantity B is greater.
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What percentage of a solution is blood if it contains 
ml blood and 
ml water? Round to the nearest thousandth?
What percentage of a solution is blood if it contains
First, you must find the total amount of solution. This is 
, or 
.
Now, the percentage of the solution that is blood can be represented:
, or 
This is the same as 
% Rounded, it is 
%
First, you must find the total amount of solution. This is
Now, the percentage of the solution that is blood can be represented:
This is the same as
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What is the percentage increase of an account that began with a balance of 
and increased to 
?
What is the percentage increase of an account that began with a balance of
Recall that the formula for percentage increase is:
, where 
is your ending value and 
is your starting value.
For our numbers, this would be:
Recall that to find a percentage from a decimal, you multiply by 
:
Recall that the formula for percentage increase is:
For our numbers, this would be:
Recall that to find a percentage from a decimal, you multiply by
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If one of the employees across both industries were to be selected at random, what is the probability that the employee will be a construction industry worker who stayed in the same role for 5 years or more?
If one of the employees across both industries were to be selected at random, what is the probability that the employee will be a construction industry worker who stayed in the same role for 5 years or more?
The first step is to figure out the percentage of construction employees that have stayed in the same role for 5 years or more—this would include both the "5 to 9 year" and "10+ years" ranges. This would be 0.25 + 0.4 = 65% of all construction employees. To convert to the number of employees, we take the percentage of their total, 0.65 * 8,000,000 = 5,200,000 workers. However, since the probability we are attempting to find is of workers between both industries, we must add the 8 million to the 12 million = 20 million workers total. 5,200,000/20,000,000 = 0.26, or a 26% chance.
The first step is to figure out the percentage of construction employees that have stayed in the same role for 5 years or more—this would include both the "5 to 9 year" and "10+ years" ranges. This would be 0.25 + 0.4 = 65% of all construction employees. To convert to the number of employees, we take the percentage of their total, 0.65 * 8,000,000 = 5,200,000 workers. However, since the probability we are attempting to find is of workers between both industries, we must add the 8 million to the 12 million = 20 million workers total. 5,200,000/20,000,000 = 0.26, or a 26% chance.
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Robert has 
of his cereal left. Choose the answer which best expresses as a decimal, how much of his cereal he has eaten.
Robert has
The easiest way to convert between percent and decimal is to first convert the percentage into a fraction:
Then, from the fraction, you can convert quite easily to a decimal:
HOWEVER--in this problem, they are asking you for the portion that makes up the rest of the cereal--so you need to subtract your decimal above from 
, which yields the correct answer:
The easiest way to convert between percent and decimal is to first convert the percentage into a fraction:
Then, from the fraction, you can convert quite easily to a decimal:
HOWEVER--in this problem, they are asking you for the portion that makes up the rest of the cereal--so you need to subtract your decimal above from
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Choose the answer below which best expresses the following as a decimal:
Choose the answer below which best expresses the following as a decimal:
When converting percents into decimals, know that the tens and ones digit of the percent will occupy the tenths and hundredths places of the decimal. Any decimal following the whole percent will follow in sequence (i.e. the first decimal place in a percent corresponds to the thousandth place, and so on). Therefore, ninety-seven point five percent is equal to:
When converting percents into decimals, know that the tens and ones digit of the percent will occupy the tenths and hundredths places of the decimal. Any decimal following the whole percent will follow in sequence (i.e. the first decimal place in a percent corresponds to the thousandth place, and so on). Therefore, ninety-seven point five percent is equal to:
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Choose the answer which best expresses the following percentage as a decimal:
%
Choose the answer which best expresses the following percentage as a decimal:
To convert a percentage into a decimal, simply place the decimal point in front of the tens digit of the percentage. So, 
% becomes 
.
To convert a percentage into a decimal, simply place the decimal point in front of the tens digit of the percentage. So,
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Choose the answer below which best expresses the following decimal as a percent:
Choose the answer below which best expresses the following decimal as a percent:
To convert a percent into a decimal, simply know that the tenths place of the decimal will correspond to the tens digit of the percent, and the thousandths place of the decimal will correspond to the ones digit of the percent. Any ensuing digits will be behind a decimal in the final percent.
Also converting a decimal to a percent can be accomplished by multiplying the percent by 100.
Therefore, the best answer here is:
To convert a percent into a decimal, simply know that the tenths place of the decimal will correspond to the tens digit of the percent, and the thousandths place of the decimal will correspond to the ones digit of the percent. Any ensuing digits will be behind a decimal in the final percent.
Also converting a decimal to a percent can be accomplished by multiplying the percent by 100.
Therefore, the best answer here is:
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Choose the answer which best expresses the following decimal as a percentage, rounded to the nearest tenth of a percent if necessary:
Choose the answer which best expresses the following decimal as a percentage, rounded to the nearest tenth of a percent if necessary:
To express a decimal as a percent, multiply the decimal by one hundred:
Then add your percent sign after:
To express a decimal as a percent, multiply the decimal by one hundred:
Then add your percent sign after:
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