How to find the whole from the part - GRE Quantitative Reasoning
Card 0 of 80
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 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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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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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.
Compare your answer with the correct one above
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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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%
Compare your answer with the correct one above
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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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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