Word Problems - GMAT Quantitative
Card 1 of 920
Susan went to a clearance sale and bought various items on sale. She saves 20% on a purse, retailing for $100. She saves 30% on a skirt that was marked down from a retail price of $40. She also bought a jacket that was on sale, and she spent a total of $150 . How much did the jacket retail for?
1. Her overall savings were 25% off the combined retail price of all three items.
2. Her discount on the jacket was $6 more than her savings on the skirt.
Susan went to a clearance sale and bought various items on sale. She saves 20% on a purse, retailing for $100. She saves 30% on a skirt that was marked down from a retail price of $40. She also bought a jacket that was on sale, and she spent a total of $150 . How much did the jacket retail for?
1. Her overall savings were 25% off the combined retail price of all three items.
2. Her discount on the jacket was $6 more than her savings on the skirt.
Tap to reveal answer
Using statement 1, it is easy to see how much the total retail amount should have been. The total retail amount discounted by 25% is the amount that Susan spent. So, we name a variable. Let x be the total retail amount. Then x - .25x = $122. We can rewrite this as x(1-.25) or x(.75)=150 thus, x = 200. So we subtract the known retail prices of the skirt and the purse to get the retail price of the jacket. So 200 - 100 - 40 = $60 is the retail price of the jacket.
Now, we should check statement 2. Using statement 2, we can calculate the savings we had on the jacket. We can first calculate how much we saved on the skirt. So 30% of the $40 retail price is $12. After we find this, we use the information from statement 2 to find the savings we had on the jacket. So $12 + $6 = $18 saved on the jacket.
Now, we need to figure out how much we spent on the jacket. We do this by taking the total amount we spent and subtracting the discounted price of the purse and the discounted price of the skirt. So, a $100 purse, at 20% off, is $80. We calculated our savings on the skirt earlier, so we know we spent $28 on the skirt. So $150 - $80 - $28 = $42.
Now combining these two pieces of information, we see we spent $42 and saved $18 so 42+18 = $60 retail price for the jacket.
We can see that either statement alone is sufficient to solve the problem.
Using statement 1, it is easy to see how much the total retail amount should have been. The total retail amount discounted by 25% is the amount that Susan spent. So, we name a variable. Let x be the total retail amount. Then x - .25x = $122. We can rewrite this as x(1-.25) or x(.75)=150 thus, x = 200. So we subtract the known retail prices of the skirt and the purse to get the retail price of the jacket. So 200 - 100 - 40 = $60 is the retail price of the jacket.
Now, we should check statement 2. Using statement 2, we can calculate the savings we had on the jacket. We can first calculate how much we saved on the skirt. So 30% of the $40 retail price is $12. After we find this, we use the information from statement 2 to find the savings we had on the jacket. So $12 + $6 = $18 saved on the jacket.
Now, we need to figure out how much we spent on the jacket. We do this by taking the total amount we spent and subtracting the discounted price of the purse and the discounted price of the skirt. So, a $100 purse, at 20% off, is $80. We calculated our savings on the skirt earlier, so we know we spent $28 on the skirt. So $150 - $80 - $28 = $42.
Now combining these two pieces of information, we see we spent $42 and saved $18 so 42+18 = $60 retail price for the jacket.
We can see that either statement alone is sufficient to solve the problem.
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Data sufficiency question
During a semi-annual sale, the price of a shirt is discounted. Calculate the percent discount.
1. The sale price is $23.
2. The sale price is $6 less than the original price.
Data sufficiency question
During a semi-annual sale, the price of a shirt is discounted. Calculate the percent discount.
1. The sale price is $23.
2. The sale price is $6 less than the original price.
Tap to reveal answer
In order to calculate the percent discount, both the original price and the sale price must be known. From statement 1, we know the sale price and with the additional information from statement 2, we can calculate the original price and then overall percent discount.
In order to calculate the percent discount, both the original price and the sale price must be known. From statement 1, we know the sale price and with the additional information from statement 2, we can calculate the original price and then overall percent discount.
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What quantity of solution is obtained by diluting 
liters of pure acid with water?
(1) The final solution contains 20% of acid.
(2) 
ml.
What quantity of solution is obtained by diluting
(1) The final solution contains 20% of acid.
(2)
Tap to reveal answer
(1) The final solution contains 20% of acid.
Using Statement (1), we know the concentration of acid in the final solution. However, we cannot find the quantity of the final solution as we do not know what quantity of acid was diluted.
So Statement (1) Alone is not sufficient.
(2) x=20 ml
Using statement (2) we know the quantity of the original acid solution, but we do not know what quantity of water was added or the concentration of the final solution.
So Statement (2) Alone is not sufficient.
Combining both Statements,
We have 20 ml of a 100% acid solution. Note that there is 0% acid in water. After diluting the solution, we obtain y ml of a solution containing 20% of acid. The amount (in ml) of acid in the final solution equals the amount of acid of the initial solution:
Therefore 100 ml of solution is obtained by diluting the original acid solution with water.
Both Statements Together are sufficient.
(1) The final solution contains 20% of acid.
Using Statement (1), we know the concentration of acid in the final solution. However, we cannot find the quantity of the final solution as we do not know what quantity of acid was diluted.
So Statement (1) Alone is not sufficient.
(2) x=20 ml
Using statement (2) we know the quantity of the original acid solution, but we do not know what quantity of water was added or the concentration of the final solution.
So Statement (2) Alone is not sufficient.
Combining both Statements,
We have 20 ml of a 100% acid solution. Note that there is 0% acid in water. After diluting the solution, we obtain y ml of a solution containing 20% of acid. The amount (in ml) of acid in the final solution equals the amount of acid of the initial solution:
Therefore 100 ml of solution is obtained by diluting the original acid solution with water.
Both Statements Together are sufficient.
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An amusement park sells Children and Adult tickets. What was the total revenue for the day?
Statement 1: The amusement park sold 259 Children tickets and 345 Adult tickets.
Statement 2: Children tickets cost $32 and Adult tickets cost $45.
An amusement park sells Children and Adult tickets. What was the total revenue for the day?
Statement 1: The amusement park sold 259 Children tickets and 345 Adult tickets.
Statement 2: Children tickets cost $32 and Adult tickets cost $45.
Tap to reveal answer
Statement 1 gives us the number of tickets sold but not the price. Insufficient.
Statement 2 gives us the price of the tickets but not the number sold. Insufficient.
Together, the two statements give us both the number of tickets sold AND the price of each ticket. From this we can calculate the total revenue.
Note: We are only trying to determine if we have enough information to answer the question. We don't have to actually do the computations!
Statement 1 gives us the number of tickets sold but not the price. Insufficient.
Statement 2 gives us the price of the tickets but not the number sold. Insufficient.
Together, the two statements give us both the number of tickets sold AND the price of each ticket. From this we can calculate the total revenue.
Note: We are only trying to determine if we have enough information to answer the question. We don't have to actually do the computations!
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How much money did Mary make this week?
Statement 1: Mary worked 40 hours of regular time and an additional 6 hours of overtime.
Statement 2: Mary made $30 an hour during normal working hours and $37 an hour during overtime.
How much money did Mary make this week?
Statement 1: Mary worked 40 hours of regular time and an additional 6 hours of overtime.
Statement 2: Mary made $30 an hour during normal working hours and $37 an hour during overtime.
Tap to reveal answer
We need both statements to find out how much money Mary made.
Statement 1 gives the type and number of hours, and statement 2 gives the amount she made per hour. Both together are sufficient, but neither is sufficient alone.
We need both statements to find out how much money Mary made.
Statement 1 gives the type and number of hours, and statement 2 gives the amount she made per hour. Both together are sufficient, but neither is sufficient alone.
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Jorge runs a business making picture frames.
I) Jorge made 
in gross profit last year, 
more than the previous year.
II) Jorge had a profit margin of 
.
What was Jorge's net profit?
Jorge runs a business making picture frames.
I) Jorge made
II) Jorge had a profit margin of
What was Jorge's net profit?
Tap to reveal answer
Ignore the comment about 15% more than the previous year. We want to find net profit and in statement one we are given the gross profit. Statement II gives us the profit margin or percent profit.
We can use percent profit and gross profit to find net profit, but we cannot do it with only I or only II. Thus, they are both needed.
Ignore the comment about 15% more than the previous year. We want to find net profit and in statement one we are given the gross profit. Statement II gives us the profit margin or percent profit.
We can use percent profit and gross profit to find net profit, but we cannot do it with only I or only II. Thus, they are both needed.
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Data sufficiency question- do not actually solve the question
How many hours did it take to drive from city A to city B without stopping?
1. The drive started at 10 am.
2. The average speed during the trip is 65 miles/hour.
Data sufficiency question- do not actually solve the question
How many hours did it take to drive from city A to city B without stopping?
1. The drive started at 10 am.
2. The average speed during the trip is 65 miles/hour.
Tap to reveal answer
The total time is calculated by the equation 
. Statement 2 provides the rate, but we have no information regarding distance, therefore, the quesiton is impossible to solve without more information.
The total time is calculated by the equation
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Cassie and Derek must decorate 60 cupcakes. It takes them 150 minutes to complete the task together. How long would it take Derek to decorate the cupcakes by himself?
Statement 1: It would take Cassie 240 minutes to decorate the cupcakes by herself.
Statement 2: Derek can decorate 9 cupcakes in 1 hour.
Cassie and Derek must decorate 60 cupcakes. It takes them 150 minutes to complete the task together. How long would it take Derek to decorate the cupcakes by himself?
Statement 1: It would take Cassie 240 minutes to decorate the cupcakes by herself.
Statement 2: Derek can decorate 9 cupcakes in 1 hour.
Tap to reveal answer
From the first statement, we can calculate the number of cupcakes Cassie can decorate in 150 minutes. From there, we can calculate the rate at which Derek decorates. Therefore, Statement 1 alone is sufficient to answer the question.
The second statement gives the rate at which Derek decorates cupcakes. Therefore, Statement 2 alone is also sufficient to answer the question.
From the first statement, we can calculate the number of cupcakes Cassie can decorate in 150 minutes. From there, we can calculate the rate at which Derek decorates. Therefore, Statement 1 alone is sufficient to answer the question.
The second statement gives the rate at which Derek decorates cupcakes. Therefore, Statement 2 alone is also sufficient to answer the question.
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The route from Tom's house to his mother's house involves traveling for 55 miles along Interstate 10, then 20 miles along State Route 34. How long does it take for Tom to travel between the two houses, if he drives at precisely the speed limit on each highway?
Statement 1: The speed limit on Interstate 10 is 70 miles per hour for the entire stretch.
Statement 2: The speed limit on State Route 34 is 50 miles per hour for the first half of the distance Tom drives on it, and 40 miles per hour for the second half.
The route from Tom's house to his mother's house involves traveling for 55 miles along Interstate 10, then 20 miles along State Route 34. How long does it take for Tom to travel between the two houses, if he drives at precisely the speed limit on each highway?
Statement 1: The speed limit on Interstate 10 is 70 miles per hour for the entire stretch.
Statement 2: The speed limit on State Route 34 is 50 miles per hour for the first half of the distance Tom drives on it, and 40 miles per hour for the second half.
Tap to reveal answer
The rate formula 
- or, actually, the equivalent equation 
- will help.
Let 
be the speed limits along the interstate, the first half of the state route, and the second half of the state route, respectively.
Then Tom can drive I-10 in 
hours; the first half of SR 34, 
; the second half of SR 34, 
.
The time 
it takes, in hours, for Tom to make the entire trip is the sum of these fractions:
.
To calculate 
, we need 
. Statement 1 only tells us 
; Statement 2 only tells us 
and 
. Therefore, both together, but neither alone, are enough to allow us to calculate 
.
The rate formula
Let
Then Tom can drive I-10 in
The time
To calculate
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Two trains (Train A and Train B) leave their stations at exactly 6 pm, travelling towards each other from stations exactly 60 miles apart. There are no other stops between these two stations. What time does Train B arrive at its destination?
1. Train A travels twice as fast as Train B.
2. At 6:40 pm, the two trains pass each other.
Two trains (Train A and Train B) leave their stations at exactly 6 pm, travelling towards each other from stations exactly 60 miles apart. There are no other stops between these two stations. What time does Train B arrive at its destination?
1. Train A travels twice as fast as Train B.
2. At 6:40 pm, the two trains pass each other.
Tap to reveal answer
Statement 1 alone does not tell us enough about the speed of train B to answer the question. Statement 2 alone does not tell us about the rates of either individual train, so it is also not sufficient by itself to answer the question.
But can we figure out the answer using both pieces of information? Yes, we can! If we know that the trains meet at 6:40, then their combined rate of travel is 60 total miles in 40 minutes. Statement 1 says that Train A travels twice as fast as Train B, so we can determine the distances covered by the two trains in those 40 minutes. From there, we can find rates for both trains and then answer the question. Thus, both statements together are sufficient to answer the question, but neither statement alone is sufficient.
Note: We didn't actually answer the question of Train B's arrival time. For data sufficiency questions, don't waste time trying to find the specific answer. All that is necessary is determining whether or not it is POSSIBLE to answer the question with the information given.
Statement 1 alone does not tell us enough about the speed of train B to answer the question. Statement 2 alone does not tell us about the rates of either individual train, so it is also not sufficient by itself to answer the question.
But can we figure out the answer using both pieces of information? Yes, we can! If we know that the trains meet at 6:40, then their combined rate of travel is 60 total miles in 40 minutes. Statement 1 says that Train A travels twice as fast as Train B, so we can determine the distances covered by the two trains in those 40 minutes. From there, we can find rates for both trains and then answer the question. Thus, both statements together are sufficient to answer the question, but neither statement alone is sufficient.
Note: We didn't actually answer the question of Train B's arrival time. For data sufficiency questions, don't waste time trying to find the specific answer. All that is necessary is determining whether or not it is POSSIBLE to answer the question with the information given.
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Jake and Colin are painting a house together. How long would it take Colin to paint the house alone?
(1) Jake and Colin can paint the house together in 6 hours, working at the same rate.
(2) Jake can paint the house alone in 12 hours
Jake and Colin are painting a house together. How long would it take Colin to paint the house alone?
(1) Jake and Colin can paint the house together in 6 hours, working at the same rate.
(2) Jake can paint the house alone in 12 hours
Tap to reveal answer
Here we can see that there are two people painting the house, so we should set the following equation : 
, where 
is the rate for Jake and where 
is the rate for Colin, 
stands for their rate together. Statement one gives us a value for 
and even though it doesn't tell us what is 
or 
it tells us that 
which allow us to answer the question.
For Statement 2, we are left with two other unknowns in our equation and we can clearly see that (2) is not sufficient.
Here we can see that there are two people painting the house, so we should set the following equation :
For Statement 2, we are left with two other unknowns in our equation and we can clearly see that (2) is not sufficient.
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Celine and Jack are painting a house together at their respective rates. After working 1 hour together, Jack starts to feel tired and stops. How long does it take Celine to finish the work?
(1) Celine could have painted the house alone in 3 hours.
(2) It would have taken Jack 5 hours to paint the house alone.
Celine and Jack are painting a house together at their respective rates. After working 1 hour together, Jack starts to feel tired and stops. How long does it take Celine to finish the work?
(1) Celine could have painted the house alone in 3 hours.
(2) It would have taken Jack 5 hours to paint the house alone.
Tap to reveal answer
We should start by setting equations 
and 
, these are the two equation we should be able to solve. Where 
is the amount of the work they did togetherm 
is the amount of work left, 
is Celine's rate and 
is the rate of Celine and Jack together. So with 
we can see that we would need both Jack and Celine's rate. Since they work at a different rate, we shoud only be able to answer this problem taking both statements together.
We should start by setting equations
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Machine X and machine Y both produce screwdrives at their respective rates. What is the rate of the machines working together?
(1) Machine X can produce 200 screwdrivers in an hour and machine Y can produce as many in 2 more hours.
(2) Machine Y can produce 200 screwdrivers in 3 hours. Machine X is three times as fast as machine Y.
Machine X and machine Y both produce screwdrives at their respective rates. What is the rate of the machines working together?
(1) Machine X can produce 200 screwdrivers in an hour and machine Y can produce as many in 2 more hours.
(2) Machine Y can produce 200 screwdrivers in 3 hours. Machine X is three times as fast as machine Y.
Tap to reveal answer
To be able to solve this problem, we need to figure out 
where 
is the rate of machine X and 
is the rate of machine Y. Statement 1 tells us the rate for machine X, but tells us as well that it takes 2 more hours for machine Y to produce the same amount of screwdrivers. Therefore, we are told that 
and 
, which is sufficient to answer the question. Statement 2 tells us that the rate of machine Y is 
and also that that rate of machine X is 3 times as fast as machine Y: 
so 
.
Each statement alone is therefore sufficient.
To be able to solve this problem, we need to figure out
Each statement alone is therefore sufficient.
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Machine O working together with machine P produces telephones at a rate of 1056 per hour. How many telephones can machine O produce in an hour?
(1) It takes machine P four hours longer than machine O to produce 880 telephones.
(2) Machine P produces telephones at a rate of 176 telephones per hour.
Machine O working together with machine P produces telephones at a rate of 1056 per hour. How many telephones can machine O produce in an hour?
(1) It takes machine P four hours longer than machine O to produce 880 telephones.
(2) Machine P produces telephones at a rate of 176 telephones per hour.
Tap to reveal answer
To solve this problem we first have to set up an equation for our variables: 
where 
is the rate of machine O and 
is the rate of machine P.
The first statement tells us that 
and 
, where 
is the time it takes machine O to produce 880 telephones.
At first it might look insufficient but, by pluging in the values for 
and 
in our first equation we get :
, this gives us a quadratic equation, in which we can solve and find t, and therefore find the number of telephones O can produce in 1 hour.
The second statement tell us that 
, therefore, we can plug in this value in our first equation to find the rate for machine O and this will allow us to answer the question.
To solve this problem we first have to set up an equation for our variables:
The first statement tells us that
At first it might look insufficient but, by pluging in the values for
The second statement tell us that
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Machines A,B and C working together take 12 minutes to complete a watch.
What is the rate of both machines B and C working together?
(1) Machines A and B together can complete a watch in 20 minutes.
(2) Machines A and C together can complete a watch in 15 minutes.
Machines A,B and C working together take 12 minutes to complete a watch.
What is the rate of both machines B and C working together?
(1) Machines A and B together can complete a watch in 20 minutes.
(2) Machines A and C together can complete a watch in 15 minutes.
Tap to reveal answer
Firstly we should set up an equation for this problem: 
where 
are the respective rates of machines A, B and C. We need to find 
.
Statement 1 tells us that 
.
This alone is not suffient since we will have no precise information on machine B. Similarly, with statement 2 We can find the value of the rate for machine B but we cannot know what is the rate of machine C, from what we are told. However, taking both statements together, with statement 1 we can find the value for 
and with statement 2 we can find the value for 
and thereby we can find the value of 
.
Firstly we should set up an equation for this problem:
Statement 1 tells us that
This alone is not suffient since we will have no precise information on machine B. Similarly, with statement 2 We can find the value of the rate for machine B but we cannot know what is the rate of machine C, from what we are told. However, taking both statements together, with statement 1 we can find the value for
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An online store sells costum computers. Find the profit the store made on a 
sale.
I) The computer cost the store 
to build.
II) The store generally makes a 
profit.
An online store sells costum computers. Find the profit the store made on a
I) The computer cost the store
II) The store generally makes a
Tap to reveal answer
To find the profit, we either need to know the cost or the percent profit.
I) Gives us the cost.
II) Gives us the percent profit.
Either of these can be used to find profit.
To find the profit, we either need to know the cost or the percent profit.
I) Gives us the cost.
II) Gives us the percent profit.
Either of these can be used to find profit.
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16 very precise machines, working at the same constant rate, can produce a luxury necklace working together. How many machines should we add in order for the necklace to be produced in an hour.
(1) It takes 5 hours for these machines to produce the necklace
(2) A single machine produces a necklace in 80 hours.
16 very precise machines, working at the same constant rate, can produce a luxury necklace working together. How many machines should we add in order for the necklace to be produced in an hour.
(1) It takes 5 hours for these machines to produce the necklace
(2) A single machine produces a necklace in 80 hours.
Tap to reveal answer
We know that there are 16 machines and we are looking for how many we should add. Let us set an equation representing the number of machines in use 
, where 
is the total number of machines we need and 
is the rate of an individual machine. We should therefore find a rate for a single machine to be able to solve this problem, since we can then calculate 
.
Statement 1 tells us that for 16 machines, it takes 5 hours to produce a necklace. From this we can find the rate of a single machine.
Statement 2 tells us direclty the rate of a single machine, therefore both these statements allow us to answer the problem.
We know that there are 16 machines and we are looking for how many we should add. Let us set an equation representing the number of machines in use
Statement 1 tells us that for 16 machines, it takes 5 hours to produce a necklace. From this we can find the rate of a single machine.
Statement 2 tells us direclty the rate of a single machine, therefore both these statements allow us to answer the problem.
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Train A and Train B are moving toward one another. How long does it takes for train A to pass by train B?
(1) The distance between train A and train B is 180 miles.
(2) Train A's rate is 45 mph and train B's rate is 60 mph.
Train A and Train B are moving toward one another. How long does it takes for train A to pass by train B?
(1) The distance between train A and train B is 180 miles.
(2) Train A's rate is 45 mph and train B's rate is 60 mph.
Tap to reveal answer
Since the problem doesn't tell us anything about the rates and the distance between the two train, there is not much we can say. Statement one tells us that there is 180 miles between the two trains. This is not sufficient, since we don't know how fast the trains are.
Statement 2 alone tells us the rates of the trains, but we don't know how far away they are, this statement alone doesn't help us answer the question.
If we take both statements together however, we can see that the distance that each train would have made when both trains meet, is a total of 180 miles, since both trains were 180 miles away.
We can create the following equation 
, where 
is the time it takes for both train to meet at a given point and 
and 
are the trains A and B respective rates. The information we have allows us to solve the equation for 
and therefore we can answer the problem.
Since the problem doesn't tell us anything about the rates and the distance between the two train, there is not much we can say. Statement one tells us that there is 180 miles between the two trains. This is not sufficient, since we don't know how fast the trains are.
Statement 2 alone tells us the rates of the trains, but we don't know how far away they are, this statement alone doesn't help us answer the question.
If we take both statements together however, we can see that the distance that each train would have made when both trains meet, is a total of 180 miles, since both trains were 180 miles away.
We can create the following equation
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A train makes roundtrips between two cities at an average speed of 75 mph. What is the distance between the two cities, taking into consideration that the train does not travel at the same speed for both trips?
(1) The train takes 50 minutes to do one way.
(2) The train takes 60 minutes to do the other way, which is uphill.
A train makes roundtrips between two cities at an average speed of 75 mph. What is the distance between the two cities, taking into consideration that the train does not travel at the same speed for both trips?
(1) The train takes 50 minutes to do one way.
(2) The train takes 60 minutes to do the other way, which is uphill.
Tap to reveal answer
Firstly, we should remember that the average rate is given by the following formula 
, where 
is the total distance and 
is the total time. So to answer this question we should find a value for 
. 
can only be found by adding the two times for both trips. By pluging in the values we can find a value for 
, therefore we need both statements.
Firstly, we should remember that the average rate is given by the following formula
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How long does it take train A to reach a town which is 500 miles away, knowing that the entire portion of the rails are damaged?
(1) The train usually goes 500 miles in 675 minutes.
(2) Since the rails are damaged it typically takes train A twice the usual time.
How long does it take train A to reach a town which is 500 miles away, knowing that the entire portion of the rails are damaged?
(1) The train usually goes 500 miles in 675 minutes.
(2) Since the rails are damaged it typically takes train A twice the usual time.
Tap to reveal answer
To solve this problem, we need to find the rate of the train considering the fact that the rails are damaged. The first statement tells us only the usual rate of the train and is therefore not sufficient because we don't know how fast the train will be going on the damaged portions of the railroad.
Statement two only tells us that the train must progress at a rate half as slow as its usual rate.
Using statements 1 and 2 we can easily find the rate which is given by 
. Note that this rate is given in miles per minutes but we don't have to calculate it, we just need to know that we can calculate it.
To solve this problem, we need to find the rate of the train considering the fact that the rails are damaged. The first statement tells us only the usual rate of the train and is therefore not sufficient because we don't know how fast the train will be going on the damaged portions of the railroad.
Statement two only tells us that the train must progress at a rate half as slow as its usual rate.
Using statements 1 and 2 we can easily find the rate which is given by
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