Percentage - GRE Quantitative Reasoning
Card 1 of 880
Choose the answer below which best expresses the following as a decimal:
Choose the answer below which best expresses the following as a decimal:
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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:
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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:
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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:
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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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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:
Tap to reveal answer
To express a decimal as a percent, multiply the decimal by one hundred:
Then add your percent sign:
To express a decimal as a percent, multiply the decimal by one hundred:
Then add your percent sign:
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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:
Tap to reveal answer
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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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:
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To find the equivalent percentage we need to multiply the decimal by 100.
Then, add your percent sign:
To find the equivalent percentage we need to multiply the decimal by 100.
Then, add your percent sign:
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Quantitative Comparison
Quantity A: 10% of $45
Quantity B: 45% of $10
Quantitative Comparison
Quantity A: 10% of $45
Quantity B: 45% of $10
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Quantity A: .1 * 45 = $4.50
Quantity B: .45 * 10 = $4.50
Therefore the two quantities are equal. This is always true: a% of $b = b% of $a.
Quantity A: .1 * 45 = $4.50
Quantity B: .45 * 10 = $4.50
Therefore the two quantities are equal. This is always true: a% of $b = b% of $a.
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A shirt costs $12 to manufacture. If the marketing and sales costs are a 75% addition to this manufacturing cost. What is the minimum price necessary for making a 50% profit?
A shirt costs $12 to manufacture. If the marketing and sales costs are a 75% addition to this manufacturing cost. What is the minimum price necessary for making a 50% profit?
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Based on the prompt, we know that the additional marketing and sales costs are 12 * 0.75 = 9; therefore, the total cost for purchase and sale is 12 + 9 = $21. To make a 50% profit, we must make 21 * 0.5, or $10.5, on the sale; thus the shirt must be sold for 21 + 10.5, or $31.5.
Based on the prompt, we know that the additional marketing and sales costs are 12 * 0.75 = 9; therefore, the total cost for purchase and sale is 12 + 9 = $21. To make a 50% profit, we must make 21 * 0.5, or $10.5, on the sale; thus the shirt must be sold for 21 + 10.5, or $31.5.
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What percent of 5 is 
?
What percent of 5 is
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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?
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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:
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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%
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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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Sally buys a dress that is a 20% discount from the original price. If she sells it at a 10% markup from her purchase price and profits $10 from the sale, what was the original price of the dress?
Sally buys a dress that is a 20% discount from the original price. If she sells it at a 10% markup from her purchase price and profits $10 from the sale, what was the original price of the dress?
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Set Original = O
and Discount = D
then
D = (1 – 20%) x O = 0.80 x O
and Profit = $10 so:
10 = ((1 + 10%) x D) – D = 1.1 * D – D = 0.1D
D = 100
and O = D / 0.8 = 125
Set Original = O
and Discount = D
then
D = (1 – 20%) x O = 0.80 x O
and Profit = $10 so:
10 = ((1 + 10%) x D) – D = 1.1 * D – D = 0.1D
D = 100
and O = D / 0.8 = 125
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is 
percent of 
is 
percent of 
Quantity A: 
Quantity B: 
Quantity A:
Quantity B:
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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
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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
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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
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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?
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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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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?
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students failed.
which equals 28%.
which equals 28%.
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