Whole and Part - GRE Quantitative Reasoning
Card 0 of 20
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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What percent of 5 is 
?
What percent of 5 is
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Quantity A:
, where 
is 
of 
Quantity B:
, where 
is 
of 
Which of the following is true?
Quantity A:
Quantity B:
Which of the following is true?
This type of problem is very easy. You merely need to translate the text into the form of an equation. For this, remember that "of" is translated as multiplication and "is" as equality. This gives us the following.
Quantity A:
is 
of 
Becomes...
Quantity B:
is 
of 
Becomes...
Therefore, quantity B is larger.
This type of problem is very easy. You merely need to translate the text into the form of an equation. For this, remember that "of" is translated as multiplication and "is" as equality. This gives us the following.
Quantity A:
Becomes...
Quantity B:
Becomes...
Therefore, quantity B is larger.
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Quantity A:
, where 
is 
of 
Quantity B:
, where 
is 
of 
Which of the following is true?
Quantity A:
Quantity B:
Which of the following is true?
This type of problem is very easy. You merely need to translate the text into the form of an equation. For this, remember that "of" is translated as multiplication and "is" as equality. This gives us the following.
Quantity A:
is 
of 
Becomes...
Quantity B:
is 
of 
Becomes...
Therefore, quantity B is larger.
This type of problem is very easy. You merely need to translate the text into the form of an equation. For this, remember that "of" is translated as multiplication and "is" as equality. This gives us the following.
Quantity A:
Becomes...
Quantity B:
Becomes...
Therefore, quantity B is larger.
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Quantity A:
, where 
is 
of 
Quantity B:
, where 
is 
of 
Which of the following is true?
Quantity A:
Quantity B:
Which of the following is true?
This type of problem is very easy. You merely need to translate the text into the form of an equation. For this, remember that "of" is translated as multiplication and "is" as equality. This gives us the following.
Quantity A:
is 
of 
Becomes...
Quantity B:
is 
of 
Becomes...
Therefore, the two quantities are equal.
This type of problem is very easy. You merely need to translate the text into the form of an equation. For this, remember that "of" is translated as multiplication and "is" as equality. This gives us the following.
Quantity A:
Becomes...
Quantity B:
Becomes...
Therefore, the two quantities are equal.
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A bag contains 
. 
are quarters, 
are dimes and the rest are nickels. How much money is in the bag in nickels?
A bag contains
To solve this problem we must first find what percent of the money in the bag is in nickels. We know that combined, quarters and dimes make up 40% of the coins and that the rest are nickels. Therefore 60% of the money in the bag are nickels. We then multiply the total amount of coins in the bag with that percentage in order to find out how many nickels are in the bag. 
. There are 300 nickels in the bag and nickels are worth 5 cents each. Therefore 
worth of nickels in the bag.
To solve this problem we must first find what percent of the money in the bag is in nickels. We know that combined, quarters and dimes make up 40% of the coins and that the rest are nickels. Therefore 60% of the money in the bag are nickels. We then multiply the total amount of coins in the bag with that percentage in order to find out how many nickels are in the bag.
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What is 
of 
?
What is
To find the part from the whole, just take the percentage and turn it into an algebra problem.
In decimal form, 20% is .2. To turn it into an equation, recognize that "is" means equal to and "of" means multiply.
Therefore, "17% of 325" becomes (.17)(325) = X.
A way of solving this without a calculator:
10% of 325 is easy to find: 32.5.
20% will be twice as much as 10%, so 65.
1% is easy to find: 3.25.
3% is three times 1%: 9.75.
20% – 3% = 17%
65 – 9.75 = 55.25
To find the part from the whole, just take the percentage and turn it into an algebra problem.
In decimal form, 20% is .2. To turn it into an equation, recognize that "is" means equal to and "of" means multiply.
Therefore, "17% of 325" becomes (.17)(325) = X.
A way of solving this without a calculator:
10% of 325 is easy to find: 32.5.
20% will be twice as much as 10%, so 65.
1% is easy to find: 3.25.
3% is three times 1%: 9.75.
20% – 3% = 17%
65 – 9.75 = 55.25
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Bob and Nancy, while working together at the same rate, can clean their entire house in 3 hours. What fraction of the house can Bob clean in 45 minutes?
Bob and Nancy, while working together at the same rate, can clean their entire house in 3 hours. What fraction of the house can Bob clean in 45 minutes?
Since Bob and Nancy work at the same rate, each person can finish 
of the job in 3 hours. Because 45 minutes is 
of 3 hours, Bob working alone would get 
of the job done, 
.
Since Bob and Nancy work at the same rate, each person can finish
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A given colony of ants was made up of 
insects. 
% of these were workers and 
% were drones. If the remainder were warrirors, how many warriors were there?
A given colony of ants was made up of
To begin with, you know that there are 
, or 
% that are warriors. This means that 
% of 
are warriors. Remember, translate of as multiplication and "are" / "is" as equals. This gives you:
warriors.
To begin with, you know that there are
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If 
% of students in a school have brown eyes and the rest have green, how many green-eyed students are there in a school of 
students?
If
Based on our data, we know that 
, or 
percent of the students have green eyes. Explicitly written, this is: 
percent of 
students are green-eyed.
Remember that we translate "of" as multiplication and "is" / "are" as equals. Therefore, this is:
Based on our data, we know that
Remember that we translate "of" as multiplication and "is" / "are" as equals. Therefore, this is:
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36 is what percent of 145
36 is what percent of 145
divide: 36/145 = 0.248; multiply by 100 to get percent
24.8%
divide: 36/145 = 0.248; multiply by 100 to get percent
24.8%
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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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If 
, 
is what percent of 
?
If
Let's first pick numbers. If y = 25, x = 100. It's tempting to pick 25% as the answer, but x is greater than y, so the percentage must be greater than 100%. x is four times y, or 400% of y.
Let's first pick numbers. If y = 25, x = 100. It's tempting to pick 25% as the answer, but x is greater than y, so the percentage must be greater than 100%. x is four times y, or 400% of y.
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Max walks 1 mile in 15 minutes. Belinda takes only 12 minutes to walk 1 mile. If Max and Belinda leave their homes at the same time, how far has Belinda walked when Max has walked 1 mile?
Max walks 1 mile in 15 minutes. Belinda takes only 12 minutes to walk 1 mile. If Max and Belinda leave their homes at the same time, how far has Belinda walked when Max has walked 1 mile?
Belinda walks faster than Max, so she should walk over a mile in the same time that Max walks 1 mile. We can eliminate the answer choices that aren't over a mile. It takes Max 3 minutes longer to walk a mile, so Belinda will walk for 3 more minutes after she finishes her first mile. If she walks 1 mile in 12 minutes, she walks 1/12 miles in 1 minute, or 3/12 = 1/4 mile in 3 minutes. So she walks 1 1/4 miles, or 5/4 miles.
Belinda walks faster than Max, so she should walk over a mile in the same time that Max walks 1 mile. We can eliminate the answer choices that aren't over a mile. It takes Max 3 minutes longer to walk a mile, so Belinda will walk for 3 more minutes after she finishes her first mile. If she walks 1 mile in 12 minutes, she walks 1/12 miles in 1 minute, or 3/12 = 1/4 mile in 3 minutes. So she walks 1 1/4 miles, or 5/4 miles.
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If 4/13 of z is 2/7 then what is 8/11 of z?
If 4/13 of z is 2/7 then what is 8/11 of z?
First solve for z by multiplying 2/7 by the reciprocal of 4/13.
Then multiply this number by 8/11 to find the solution.
In setting up the problem, notice how “of” means to multiply z by 4/13 and “is” means to set (4/13)z equal to 2/7.
First solve for z by multiplying 2/7 by the reciprocal of 4/13.
Then multiply this number by 8/11 to find the solution.
In setting up the problem, notice how “of” means to multiply z by 4/13 and “is” means to set (4/13)z equal to 2/7.
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The ratio of men to women in the room is 5 to 3. 3 men in the room are seniors, which represents 30% of the men. How many people are in the room?
The ratio of men to women in the room is 5 to 3. 3 men in the room are seniors, which represents 30% of the men. How many people are in the room?
If 3 senior men = 30% * All Men →
All Men = 3/30% = 10 Men.
The Ratio Men : Women = 5 : 3 = 10 : 6.
Thus there are 6 Women. 6 + 10 = 16.
If 3 senior men = 30% * All Men →
All Men = 3/30% = 10 Men.
The Ratio Men : Women = 5 : 3 = 10 : 6.
Thus there are 6 Women. 6 + 10 = 16.
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Jessica bought a few pairs of socks for $50. If there had been a 20% discount, she could have bought 5 more pairs of socks for the same total price. How many pairs of socks did she buy?
Jessica bought a few pairs of socks for $50. If there had been a 20% discount, she could have bought 5 more pairs of socks for the same total price. How many pairs of socks did she buy?
Say cost of each pair of socks = y and pairs of socks = x.
Since \[quantity x cost per item = total cost\]:
First, xy = 50.
Secondly, (x + 5) \[y (1 - 20%)\] = 50
Simplify the second equation:
80%y(x + 5) = 50 or
0.8xy + 4y = 50
Insert xy =50 here.
.8(50) + 4y = 50
40 + 4y = 50 or 4y = 10
Thus y = 10/4 = 5/2
Need to find x = pairs of socks.
xy = 50 = x(5/2)
So 5x = 100 or x = 20
Say cost of each pair of socks = y and pairs of socks = x.
Since \[quantity x cost per item = total cost\]:
First, xy = 50.
Secondly, (x + 5) \[y (1 - 20%)\] = 50
Simplify the second equation:
80%y(x + 5) = 50 or
0.8xy + 4y = 50
Insert xy =50 here.
.8(50) + 4y = 50
40 + 4y = 50 or 4y = 10
Thus y = 10/4 = 5/2
Need to find x = pairs of socks.
xy = 50 = x(5/2)
So 5x = 100 or x = 20
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An elevated train traveling its night route drops off exactly 2/3 of all passengers currently on board at each stop. Assuming no more passengers board the train tonight, if two passengers get off at the fifth stop, how many passengers were originally on the train when it started its route?
An elevated train traveling its night route drops off exactly 2/3 of all passengers currently on board at each stop. Assuming no more passengers board the train tonight, if two passengers get off at the fifth stop, how many passengers were originally on the train when it started its route?
This problem requires you to work backwards from stop 5 to the passengers present at stop 1. If 2 person gets out at stop 5, that means there were 3 people on board at stop 5. This means there were 9 people present at stop 4 (9 total, 2/3 (6) got off, leaving the 3 for stop 5), 27 people present at stop 3 (27 total, 2/3 (18) got off, leaving 9 for stop 4), 81 people present at stop 2 and 243 passengers present at stop 1. That is, the number of passengers on board the train at any stop follows a logarithmic reduction along powers of three, from 35 at stop 1 to 31 at stop 5.
This problem requires you to work backwards from stop 5 to the passengers present at stop 1. If 2 person gets out at stop 5, that means there were 3 people on board at stop 5. This means there were 9 people present at stop 4 (9 total, 2/3 (6) got off, leaving the 3 for stop 5), 27 people present at stop 3 (27 total, 2/3 (18) got off, leaving 9 for stop 4), 81 people present at stop 2 and 243 passengers present at stop 1. That is, the number of passengers on board the train at any stop follows a logarithmic reduction along powers of three, from 35 at stop 1 to 31 at stop 5.
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For every two pounds of fudge are bought at the regular price of $4.25 per pound, the store gives a free pound of fudge to the customer. Lauren’s fudge bill was $21.25. How many pounds of fudge did she leave the store with?
For every two pounds of fudge are bought at the regular price of $4.25 per pound, the store gives a free pound of fudge to the customer. Lauren’s fudge bill was $21.25. How many pounds of fudge did she leave the store with?
21.21/ 4.25 = 5 pounds paid for. Since a pound is given for every 2 pounds sold, that is 5/2 = 2.5 so an extra 2 pounds is given to Lauren, totaling 7 pounds.
21.21/ 4.25 = 5 pounds paid for. Since a pound is given for every 2 pounds sold, that is 5/2 = 2.5 so an extra 2 pounds is given to Lauren, totaling 7 pounds.
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If you travel 
meters per minute for 
hours, how far do you travel in meters?
If you travel
We need to convert 5 hours into minutes. There are 60 minutes in an hour, so 5 hours = 5 * 60 minutes = 300 minutes. Therefore, you go 20 meters/minute for 300 minutes, or 20 * 300 = 6000 meters.
We need to convert 5 hours into minutes. There are 60 minutes in an hour, so 5 hours = 5 * 60 minutes = 300 minutes. Therefore, you go 20 meters/minute for 300 minutes, or 20 * 300 = 6000 meters.
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