Arithmetic - GRE Quantitative Reasoning
Card 0 of 4976
x = the total number of positive, odd 2 digit numbers less than 100
Column A
x
Column B
45
x = the total number of positive, odd 2 digit numbers less than 100
Column A
x
Column B
45
There are 50 positive, odd numbers less than 100, and 45 of them are 2 digit numbers.
There are 50 positive, odd numbers less than 100, and 45 of them are 2 digit numbers.
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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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Quantitative Comparison
Quantity A: 10% of \$45
Quantity B: 45% of \$10
Quantitative Comparison
Quantity A: 10% of \$45
Quantity B: 45% of \$10
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 baker is able to sell doughnut holes made from his doughnuts in groups of 6 for \$0.50. If he wastes one hole per dozen doughnuts, how much money does he fail to make when selling the holes that can be packaged from 22 dozen doughnuts?
A baker is able to sell doughnut holes made from his doughnuts in groups of 6 for \$0.50. If he wastes one hole per dozen doughnuts, how much money does he fail to make when selling the holes that can be packaged from 22 dozen doughnuts?
Given his waste rate, the baker would waste 22 holes. That is the equivalent 3 2/3 bags; however, since that would leave him with a 1/3 of a bag, the waste really is 4 bags of holes. He therefore fails to make 4 * 0.5 or \$2 on this batch of 22 dozen doughnuts and holes.
Given his waste rate, the baker would waste 22 holes. That is the equivalent 3 2/3 bags; however, since that would leave him with a 1/3 of a bag, the waste really is 4 bags of holes. He therefore fails to make 4 * 0.5 or \$2 on this batch of 22 dozen doughnuts and holes.
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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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Joe has a set of 10 books that he hasn't yet read. If he takes 3 of them on vacation, how many possible sets of books can he take?
Joe has a set of 10 books that he hasn't yet read. If he takes 3 of them on vacation, how many possible sets of books can he take?
He can choose from 10, then 9, then 8 books, but because order does not matter we need to divide by 3 factorial
(10 * 9 * 8) ÷ (3 * 2 * 1) = 720/6 = 120
He can choose from 10, then 9, then 8 books, but because order does not matter we need to divide by 3 factorial
(10 * 9 * 8) ÷ (3 * 2 * 1) = 720/6 = 120
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What is the number of possible 4-letter words that can be made from the 26 letters in the alphabet, where all 4 letters must be different?
Assume non-sensical words count, i.e. "dnts" would count as a 4-letter word for our purposes.
What is the number of possible 4-letter words that can be made from the 26 letters in the alphabet, where all 4 letters must be different?
Assume non-sensical words count, i.e. "dnts" would count as a 4-letter word for our purposes.
This is a permutation of 26 letters taken 4 at a time. To compute this we multiply 26 * 25 * 24 * 23 = 358,800.
This is a permutation of 26 letters taken 4 at a time. To compute this we multiply 26 * 25 * 24 * 23 = 358,800.
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Quantity A: The total number of combinations when a combination of two choices is made out of ten options and a combination of one choice is made from two options.
Quantity B: The total number of permutations formed when two choices are made from ten options.
Quantity A: The total number of combinations when a combination of two choices is made out of ten options and a combination of one choice is made from two options.
Quantity B: The total number of permutations formed when two choices are made from ten options.
With 
selections made from 
potential options, the total number of possible combinations (order doesn't matter) is:
With 
selections made from 
potential options, the total number of possible permutations(order matters) is:
Quantity A:
This quantity involves two combinations being made to create one grand combination, the number of potential results of which is equal to the product of the subresults.
The total number of combinations is 
Quantity B:
The total number of permuations is 
The two quantities are equal.
With
With
Quantity A:
This quantity involves two combinations being made to create one grand combination, the number of potential results of which is equal to the product of the subresults.
The total number of combinations is
Quantity B:
The total number of permuations is
The two quantities are equal.
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Quantity A: The number of possible permutations when seven choices are made from ten options.
Quantity B: The number of possible permutations when five choices are made from eleven options.
Quantity A: The number of possible permutations when seven choices are made from ten options.
Quantity B: The number of possible permutations when five choices are made from eleven options.
With 
selections made from 
potential options, the total number of possible permutations(order matters) is:
Quantity A:
Quantity B:
Quantity A is greater.
With
Quantity A:
Quantity B:
Quantity A is greater.
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Write 
in scientific notation.
Write
We want to move the decimal point to the place just after the first non-zero number, in this case 6, and then drop all of the non-significant zeros. We need to move the decimal point five spaces to the right, so our exponent should be negative. If the decimal had moved left, we would have had a positive exponent.
In this case we get 6.009 * 10–5.
We want to move the decimal point to the place just after the first non-zero number, in this case 6, and then drop all of the non-significant zeros. We need to move the decimal point five spaces to the right, so our exponent should be negative. If the decimal had moved left, we would have had a positive exponent.
In this case we get 6.009 * 10–5.
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find 0.72
find 0.72
0.7 * 0.7 = 0.49
Trick: do the numbers without the decimals (7*7)
49; move the decimal of the answer the total number of spaces per each number (one for each 0.7)
0.49
0.7 * 0.7 = 0.49
Trick: do the numbers without the decimals (7*7)
49; move the decimal of the answer the total number of spaces per each number (one for each 0.7)
0.49
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Quantitative Comparison: Compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given.
10 < n < 15
Quantity A Quantity B
7/13 4/n
Quantitative Comparison: Compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given.
10 < n < 15
Quantity A Quantity B
7/13 4/n
To determine which quantity is greater, we must first determine the range of potential values for Quantity B. Let's call this quantity m. This is most efficiently done by dividing 4 by the highest and lowest possible values for n.
4/10 = 0.4
4/15 = 0.267
So the possible values for m are 0.267 < m < 0.4
Now let's find the value for 7/13, to make comparison easier.
7/13 = 0.538
Given this, no matter what the value of n is, 7/13 will still be a higher proportion, so Quantity B is greater.
To determine which quantity is greater, we must first determine the range of potential values for Quantity B. Let's call this quantity m. This is most efficiently done by dividing 4 by the highest and lowest possible values for n.
4/10 = 0.4
4/15 = 0.267
So the possible values for m are 0.267 < m < 0.4
Now let's find the value for 7/13, to make comparison easier.
7/13 = 0.538
Given this, no matter what the value of n is, 7/13 will still be a higher proportion, so Quantity B is greater.
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Choose the answer below which best expresses the following decimal as a fraction (choose the answer which has been reduced/simplified the most):
Choose the answer below which best expresses the following decimal as a fraction (choose the answer which has been reduced/simplified the most):
To convert from a decimal to a fraction, simply put the digits over one followed by a number of zeroes equal to the number of digits:
The zero in front of the 
can be removed, leaving: 
, which can be reducted to:
To convert from a decimal to a fraction, simply put the digits over one followed by a number of zeroes equal to the number of digits:
The zero in front of the
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Which of the following is true?
Quantity A: 
Quantity B: 
Which of the following is true?
Quantity A:
Quantity B:
First, consider each quantity separately.
Quantity A
These two fractions do not have a common factor. Their common denominator is 
. Thus, we multiply the fractions as follows to give them a common denominator:
This is the same as:
Quantity B
The common denominator of these two values is 
. Therefore, you multiply the fractions as follows to give them a common denominator:
This is the same as:
Since Quantity A is larger than 
and Quantity B is a positive fraction less than 
, we know that Quantity A is larger without even using a calculator.
First, consider each quantity separately.
Quantity A
These two fractions do not have a common factor. Their common denominator is
This is the same as:
Quantity B
The common denominator of these two values is
This is the same as:
Since Quantity A is larger than
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When television remotes are shipped from a certain factory, 1 out of every 200 is defective. What is the ratio of defective to nondefective remotes?
When television remotes are shipped from a certain factory, 1 out of every 200 is defective. What is the ratio of defective to nondefective remotes?
One remote is defective for every 199 non-defective remotes.
One remote is defective for every 199 non-defective remotes.
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You are making a cake that requires, by volume, three times as much flour as sugar, twice as much sugar as milk, eight times more milk than baking powder and twice as much baking powder as salt. If you start with a teaspoon of salt, how many cups of flour do you need (there are 48 teaspoons in one cup)?
You are making a cake that requires, by volume, three times as much flour as sugar, twice as much sugar as milk, eight times more milk than baking powder and twice as much baking powder as salt. If you start with a teaspoon of salt, how many cups of flour do you need (there are 48 teaspoons in one cup)?
One teaspoon of salt requires 2 teaspoons of baking powder, which requires 16 teaspoons of milk and 32 teaspoons of sugar. 32 teaspoons of sugar requires 96 teaspoons of flour, which equals two cups of flour.
One teaspoon of salt requires 2 teaspoons of baking powder, which requires 16 teaspoons of milk and 32 teaspoons of sugar. 32 teaspoons of sugar requires 96 teaspoons of flour, which equals two cups of flour.
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You have a rope of some length, but 2/3rds of it is cut off and thrown away. 1/4th of the remaining rope is cut off and thrown away. What proportion of the original rope remains?
You have a rope of some length, but 2/3rds of it is cut off and thrown away. 1/4th of the remaining rope is cut off and thrown away. What proportion of the original rope remains?
If 2/3 is cut off and thrown away, that means 1/3 of the original length remains. Of this, 1/4 gets cut off and thrown away, meaning 3/4 of 1/3 still remains. Multiplying 3/4 * 1/3, we get 1/4.
If 2/3 is cut off and thrown away, that means 1/3 of the original length remains. Of this, 1/4 gets cut off and thrown away, meaning 3/4 of 1/3 still remains. Multiplying 3/4 * 1/3, we get 1/4.
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Quantitative Comparison
Alice has a puppy and a kitten. The puppy weighs 4 pounds and grows at a rate of 1 pound per month. The kitten weighs 2 pounds and grows at a rate of 2 pounds per month.
Quantity A: Weight of the puppy after 8 months
Quantity B: Weight of the kitten after 7 months
Quantitative Comparison
Alice has a puppy and a kitten. The puppy weighs 4 pounds and grows at a rate of 1 pound per month. The kitten weighs 2 pounds and grows at a rate of 2 pounds per month.
Quantity A: Weight of the puppy after 8 months
Quantity B: Weight of the kitten after 7 months
The puppy starts at 4 pounds and gains 1 pound per month for 8 months, so he weighs 4 + 8 = 12 pounds at the end of 8 months. The kitten starts at 2 pounds and gains 2 pounds per month for 7 months, so he weighs 2 + 14 = 16 pounds at the end of 7 months. Therefore Quantity B is greater.
The puppy starts at 4 pounds and gains 1 pound per month for 8 months, so he weighs 4 + 8 = 12 pounds at the end of 8 months. The kitten starts at 2 pounds and gains 2 pounds per month for 7 months, so he weighs 2 + 14 = 16 pounds at the end of 7 months. Therefore Quantity B is greater.
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In a solution, 
of the fluid is water, 
is wine, and 
is lemon juice. What is the ratio of lemon juice to water?
In a solution,
This problem is really an easy fraction division. You should first divide the lemon juice amount by the water amount:
Remember, to divide fractions, you multiply by the reciprocal:
This is the same as saying:
This problem is really an easy fraction division. You should first divide the lemon juice amount by the water amount:
Remember, to divide fractions, you multiply by the reciprocal:
This is the same as saying:
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Which fraction is the SMALLEST?
Which fraction is the SMALLEST?
estimate or calculate decimals after simplifying
estimate or calculate decimals after simplifying
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