Word Problems - GMAT Quantitative
Card 0 of 1904
Shawn is competing in an archery tournament. He gets to shoots three arrows at a target, and his best two shots count.
He hits the bullseye with 40% of his shots. What is the probability that he will hit the bullseye at least twice out of the three times?
Shawn is competing in an archery tournament. He gets to shoots three arrows at a target, and his best two shots count.
He hits the bullseye with 40% of his shots. What is the probability that he will hit the bullseye at least twice out of the three times?
There are three scenarios favorable to this event.
1: He hits a bullseye with his first two shots; the third shot doesn't matter.
The probability of this happening is 
2: He hits a bullseye with his first shot, misses with his second shot, and hits with his third shot.
The probability of this happening is 
3: He misses with his first shot and hits a bullseye with his other two shots.
The probability of this happening is 
Add these probabilities:
There are three scenarios favorable to this event.
1: He hits a bullseye with his first two shots; the third shot doesn't matter.
The probability of this happening is
2: He hits a bullseye with his first shot, misses with his second shot, and hits with his third shot.
The probability of this happening is
3: He misses with his first shot and hits a bullseye with his other two shots.
The probability of this happening is
Add these probabilities:
Compare your answer with the correct one above
Sheryl is competing in an archery tournament. She gets to shoot three arrows at a target, and her best one counts.
Sheryl hits the bullseye 42% of the time. What is the probability (two decimal places) that she will hit the bullseye at least once in her three tries?
Sheryl is competing in an archery tournament. She gets to shoot three arrows at a target, and her best one counts.
Sheryl hits the bullseye 42% of the time. What is the probability (two decimal places) that she will hit the bullseye at least once in her three tries?
This is most easily solved by finding the probability that she will not hit the bullseye at all in her three tries. If she hits 42% of the time, she misses 58% of the time, and the probability she misses three times will be
.
The probability of hitting the bullseye at least once in three tries is the complement of this, or 
.
This is most easily solved by finding the probability that she will not hit the bullseye at all in her three tries. If she hits 42% of the time, she misses 58% of the time, and the probability she misses three times will be
The probability of hitting the bullseye at least once in three tries is the complement of this, or
Compare your answer with the correct one above
It costs $10 to buy a ticket to a charity raffle in which three prizes are given - the grand prize is $3,000, the second prize is $1,000, and the third prize is $500. Assuming that all of 1,000 tickets are sold, what is the expected value of one ticket to someone who purchases it?
It costs $10 to buy a ticket to a charity raffle in which three prizes are given - the grand prize is $3,000, the second prize is $1,000, and the third prize is $500. Assuming that all of 1,000 tickets are sold, what is the expected value of one ticket to someone who purchases it?
If 1,000 tickets are sold at $10 apiece, then $10,000 will be raised. The prizes are $3,000, $1,000, and $500, so $4,500 will be given back, meaning that the 1,000 ticket purchasers will collectively lose $5,500. This means that on the average, one ticket will be worth
This is the expected value of one ticket.
If 1,000 tickets are sold at $10 apiece, then $10,000 will be raised. The prizes are $3,000, $1,000, and $500, so $4,500 will be given back, meaning that the 1,000 ticket purchasers will collectively lose $5,500. This means that on the average, one ticket will be worth
This is the expected value of one ticket.
Compare your answer with the correct one above
If you have a bag with 15 grey marbles, 15 yellow marbles and 20 green marbles, what is the probability of choosing a green marble followed by a yellow marble? Assume no replacement.
If you have a bag with 15 grey marbles, 15 yellow marbles and 20 green marbles, what is the probability of choosing a green marble followed by a yellow marble? Assume no replacement.
To calculate probability of multiple events, find the probability of each event and multiply them together. We begin with 50 total marbles in the bag.
For the first case, we are asked to pick a green marble. Because there are 20 green marbles and 50 total, our probability of this event is as follows:
For the second case, we need to pick a yellow marble. However, this time there are only 49 marbles left in the bag, because we didn't replace the green marble. Because we have 15 yellow marbles, the probability of this event is as follows:
To find our final answer, we need to multiply these two together.
To calculate probability of multiple events, find the probability of each event and multiply them together. We begin with 50 total marbles in the bag.
For the first case, we are asked to pick a green marble. Because there are 20 green marbles and 50 total, our probability of this event is as follows:
For the second case, we need to pick a yellow marble. However, this time there are only 49 marbles left in the bag, because we didn't replace the green marble. Because we have 15 yellow marbles, the probability of this event is as follows:
To find our final answer, we need to multiply these two together.
Compare your answer with the correct one above
If you flip a quarter three times, what is the probability of it landing on heads all three times?
If you flip a quarter three times, what is the probability of it landing on heads all three times?
Every time you flip a coin, there is a 1 in 2 chance of it landing on heads. So, if we want to know the probability of a coin landing on heads a certain number of times times in a row, we multiply the probability of that occurrence for however many times the coin is flipped. For three flips, this gives us:
So there is a 1 in 8 chance that a coin will land on heads three times in a row.
Every time you flip a coin, there is a 1 in 2 chance of it landing on heads. So, if we want to know the probability of a coin landing on heads a certain number of times times in a row, we multiply the probability of that occurrence for however many times the coin is flipped. For three flips, this gives us:
So there is a 1 in 8 chance that a coin will land on heads three times in a row.
Compare your answer with the correct one above
A drawer has 4 green socks, 6 blue socks, 12 white socks, 8 black socks, and 2 pink socks. If you reach in and pull out a sock at random, what is the probability the sock will be blue?
A drawer has 4 green socks, 6 blue socks, 12 white socks, 8 black socks, and 2 pink socks. If you reach in and pull out a sock at random, what is the probability the sock will be blue?
If you reach in and pull out a sock at random, the probability of it being blue is equal to the number of blue socks divided by the total number of socks in the drawer. First we'll calculate the total number of socks in the drawer:
Now we divide the number of blue socks by the total number of socks to find the probability of picking a blue sock:
If you reach in and pull out a sock at random, the probability of it being blue is equal to the number of blue socks divided by the total number of socks in the drawer. First we'll calculate the total number of socks in the drawer:
Now we divide the number of blue socks by the total number of socks to find the probability of picking a blue sock:
Compare your answer with the correct one above
Light blue: Goodman
Orange: Ferris
Gray: Inman
Yellow: Jones
Dark blue: Harris
Refer to the diagram. If 3,145 people voted in the school board election, (the results of which are represented in the diagram), then approximately how many people voted for Inman?
Light blue: Goodman
Orange: Ferris
Gray: Inman
Yellow: Jones
Dark blue: Harris
Refer to the diagram. If 3,145 people voted in the school board election, (the results of which are represented in the diagram), then approximately how many people voted for Inman?
According to the legend, the gray sector represents the portion of the electorate who voted for Inman. This sector is about one-fifth of the circle, so, to find the best estimate of Inman's share of the vote, take one-fifth of 3,145 - or, equivalently, divide 3,145 by 5:
630 is the best estimate of the choices given.
According to the legend, the gray sector represents the portion of the electorate who voted for Inman. This sector is about one-fifth of the circle, so, to find the best estimate of Inman's share of the vote, take one-fifth of 3,145 - or, equivalently, divide 3,145 by 5:
630 is the best estimate of the choices given.
Compare your answer with the correct one above
In a room filled with 100 people, 52 are men and 40 are blonde. There were 16 blonde men in the room. How many non-blonde women were there? Use the following diagram.
In a room filled with 100 people, 52 are men and 40 are blonde. There were 16 blonde men in the room. How many non-blonde women were there? Use the following diagram.
Of the 
people, 
were either men or blonde or both. Therefore, 
are non-blonde and non-men (women).
Of the
Compare your answer with the correct one above
Define the universal set 
.
Define 
to be the set of prime numbers, 
to be the set of integers that end in 2, 5, or 8, and 
. If each number in the universal set were to be placed in its correct region in the above Venn diagram, how many integers would lie in the gray region?
Define the universal set
Define
The integers that go into the gray region are those that do not fall into any of the three sets 
, 
, or 
. We can eliminate the integers by taking the universal set and eliminating the elements that fall in any one of the three.
Out of the 50 integers from 1 to 50, we can eliminate the 20 that are in 
. This leaves 30 so far:
Now we can eliminate nine integers from 
- the ones that end in 2, 5, or 8. The 21 remaining numbers are
.
We now eliminate the primes from 
- 3, 7, 11, 13, 17, 19, 41, 43, 47. This leaves us with
,
a set with 12 elements.
The integers that go into the gray region are those that do not fall into any of the three sets
Out of the 50 integers from 1 to 50, we can eliminate the 20 that are in
Now we can eliminate nine integers from
We now eliminate the primes from
a set with 12 elements.
Compare your answer with the correct one above
The table below gives the population of the city of Renfrow for each of six census years.
Which decade saw a population decline?
The table below gives the population of the city of Renfrow for each of six census years.
Which decade saw a population decline?
The only census year in which Renfrow had fewer people than the previous one is 1970, so the correct choice is 1960-70.
The only census year in which Renfrow had fewer people than the previous one is 1970, so the correct choice is 1960-70.
Compare your answer with the correct one above
The table below gives the population of the city of Renfrow for each of six census years.
Which decade saw the greatest increase in population?
The table below gives the population of the city of Renfrow for each of six census years.
Which decade saw the greatest increase in population?
For each decade, we can subtract the population at the beginning of the decade from that at the end. We omit 1960-70 since there was a population decline.
1950-60 saw the greatest increase.
For each decade, we can subtract the population at the beginning of the decade from that at the end. We omit 1960-70 since there was a population decline.
1950-60 saw the greatest increase.
Compare your answer with the correct one above
The table below gives the population of the city of Renfrow for each of six census years.
The figures for subsequent years are not currently available but it is known that the increase over each decade since 1980 has been at least as great as the increase from 1970 to 1980. What was the minimum population in 2010?
The table below gives the population of the city of Renfrow for each of six census years.
The figures for subsequent years are not currently available but it is known that the increase over each decade since 1980 has been at least as great as the increase from 1970 to 1980. What was the minimum population in 2010?
The increase in population from 1970 to 1980 was 
. Since each of the three ten-year growths from 1980 to 2010 was at least that much, the minimum population of Renfrow in 2010 was 
The increase in population from 1970 to 1980 was
Compare your answer with the correct one above
The above is the menu at Monorail Sandwich Shop.
Today, Monorail is running a special - buy three sandwiches and get a large soda free. A boss treats her employees to lunch; she orders three beef sandwiches, two turkey sandwiches, two ham sandwiches, and seven large sodas. There is no sales tax. If the boss hands the clerk a $100 bill, how much change will she get back?
The above is the menu at Monorail Sandwich Shop.
Today, Monorail is running a special - buy three sandwiches and get a large soda free. A boss treats her employees to lunch; she orders three beef sandwiches, two turkey sandwiches, two ham sandwiches, and seven large sodas. There is no sales tax. If the boss hands the clerk a $100 bill, how much change will she get back?
The boss orders seven sandwiches, so two of the sodas will be free. Therefore, she will pay for three beef sandwiches, two turkey sandwiches, two ham sandwiches, and five large sodas. Their total price:
The change from a $100 bill is
.
The boss orders seven sandwiches, so two of the sodas will be free. Therefore, she will pay for three beef sandwiches, two turkey sandwiches, two ham sandwiches, and five large sodas. Their total price:
The change from a $100 bill is
Compare your answer with the correct one above
The above is the menu at Monorail Sandwich Shop.
Today, Monorail is running a special - buy any two sandwiches and get an additonal sandwich of equal or lesser value for free, with a limit of two free sandwiches per customer per day.
A father wants to buy some sandwiches for his family. He orders two beef sandwiches, three chicken sandwiches, and four veggie sandwiches. Disregarding sales tax, what is the least possible amount he will pay for them?
The above is the menu at Monorail Sandwich Shop.
Today, Monorail is running a special - buy any two sandwiches and get an additonal sandwich of equal or lesser value for free, with a limit of two free sandwiches per customer per day.
A father wants to buy some sandwiches for his family. He orders two beef sandwiches, three chicken sandwiches, and four veggie sandwiches. Disregarding sales tax, what is the least possible amount he will pay for them?
In descending order of cost, he is ordering sandwiches that cost the following:
Note that the father will get one chicken sandwich free with the two beef sandwiches, and that he will get one veggie sandwich free with the other two chicken sandwiches. Therefore, he will pay for the other seven sandwiches:
In descending order of cost, he is ordering sandwiches that cost the following:
Note that the father will get one chicken sandwich free with the two beef sandwiches, and that he will get one veggie sandwich free with the other two chicken sandwiches. Therefore, he will pay for the other seven sandwiches:
Compare your answer with the correct one above
The above is the menu at Monorail Sandwich Shop.
Monorail is running a special today - for each sandwich you buy, you can purchase one large soda for ninety cents or get one small soda for free.
Kevin purchases three beef sandwiches, two large sodas, and two small sodas. Disregarding tax, how much will he pay?
The above is the menu at Monorail Sandwich Shop.
Monorail is running a special today - for each sandwich you buy, you can purchase one large soda for ninety cents or get one small soda for free.
Kevin purchases three beef sandwiches, two large sodas, and two small sodas. Disregarding tax, how much will he pay?
Kevin will pay $5.89 each for the three beef sandwiches. He will pay $0.90 for each of the two large sodas and get one of the small sodas for free; he will pay the full price of $1.09 for one small soda. Therefore, Kevin will pay
Kevin will pay $5.89 each for the three beef sandwiches. He will pay $0.90 for each of the two large sodas and get one of the small sodas for free; he will pay the full price of $1.09 for one small soda. Therefore, Kevin will pay
Compare your answer with the correct one above
The above is the menu at Monorail Sandwich Shop. The sales tax is 8%, and with the purchase of two sandwiches, a customer gets one free soda of any size.
Charlie wants to purchase four turkey sandwiches. He only has $30 on him and he has no checks, debit cards, or credit cards. How many large sodas can he get with the sandwiches and stay within his budget?
The above is the menu at Monorail Sandwich Shop. The sales tax is 8%, and with the purchase of two sandwiches, a customer gets one free soda of any size.
Charlie wants to purchase four turkey sandwiches. He only has $30 on him and he has no checks, debit cards, or credit cards. How many large sodas can he get with the sandwiches and stay within his budget?
If 
is the maximum price of the sandwiches before tax, then the price after tax is 
. Charlie can spend at most $30 after sales tax of 8% is counted, so we can set up the equation:
The four turkey sandwiches cost 
, leaving
to buy drinks.
buys one large soda.
, so 
allows for the purchase of two. Also, with the four sandwiches, he gets two free sodas, so he can get a total of four sodas.
If
The four turkey sandwiches cost
to buy drinks.
Compare your answer with the correct one above
Five candidates ran for the office of student body president at Garfield High School. According to the rules, the student who gets the most votes wins the office, with ties resulting in a runoff. However, Garfield has an unusual rule that states that seniors' votes count double.
This table shows how freshmen, sophomores, and juniors voted:
This table shows how seniors voted:
Who won the election?
Five candidates ran for the office of student body president at Garfield High School. According to the rules, the student who gets the most votes wins the office, with ties resulting in a runoff. However, Garfield has an unusual rule that states that seniors' votes count double.
This table shows how freshmen, sophomores, and juniors voted:
This table shows how seniors voted:
Who won the election?
For each candidate, add the number of freshman, sophomore, and junior votes to twice the number of senior votes:
Jones won the election.
For each candidate, add the number of freshman, sophomore, and junior votes to twice the number of senior votes:
Jones won the election.
Compare your answer with the correct one above
Five candidates ran for the office of student body president at Buchanan High School. According to the rules, the student who gets a majority of the votes wins the office; if no student wins a majority, then there will be a runoff between the top two vote-getters. However, Buchanan has an unusual rule that states that seniors' votes count double.
This table shows how freshmen, sophomores, and juniors voted:
This table shows how seniors voted:
Who won the election?
Five candidates ran for the office of student body president at Buchanan High School. According to the rules, the student who gets a majority of the votes wins the office; if no student wins a majority, then there will be a runoff between the top two vote-getters. However, Buchanan has an unusual rule that states that seniors' votes count double.
This table shows how freshmen, sophomores, and juniors voted:
This table shows how seniors voted:
Who won the election?
For each candidate, add the number of freshman, sophomore, and junior votes to twice the number of senior votes:
Jones got the most votes. However, he clearly did not win a majority, so he and the second-highest vote-getter, Trask, will face each other in a runoff.
For each candidate, add the number of freshman, sophomore, and junior votes to twice the number of senior votes:
Jones got the most votes. However, he clearly did not win a majority, so he and the second-highest vote-getter, Trask, will face each other in a runoff.
Compare your answer with the correct one above
The above table shows the initial count of the votes for a school election. According to the rules, the students who finish first, second, and third become President, Vice-President, and Secretary-Treasurer, respectively. In the event of any tie, a runoff election will be held.
After the initial count, it is discovered that some ballots were left out of the count by mistake. These votes were distributed as follows:
Who was elected Vice-President?
The above table shows the initial count of the votes for a school election. According to the rules, the students who finish first, second, and third become President, Vice-President, and Secretary-Treasurer, respectively. In the event of any tie, a runoff election will be held.
After the initial count, it is discovered that some ballots were left out of the count by mistake. These votes were distributed as follows:
Who was elected Vice-President?
The revised vote count is as follows:
Trask finished second with 116, so he was elected Vice-President.
The revised vote count is as follows:
Trask finished second with 116, so he was elected Vice-President.
Compare your answer with the correct one above
Public domain map from The World Factbook, Central Intelligence Agency.
Flight 984 departed from London (green circle) when it was 6:12 PM there. It arrived in Chicago, IL (red circle) 8 hours, 30 minutes later. What time was it in Chicago upon the flight's arrival there?
(You may assume that Daylight Savings Time is not in effect.)
Public domain map from The World Factbook, Central Intelligence Agency.
Flight 984 departed from London (green circle) when it was 6:12 PM there. It arrived in Chicago, IL (red circle) 8 hours, 30 minutes later. What time was it in Chicago upon the flight's arrival there?
(You may assume that Daylight Savings Time is not in effect.)
Refer to the time zone differences printed at the top of the map. The time zone for Chicago is marked 
; the time zone for London is marked 0. This means that London is 
hours ahead of Chicago, so we need to adjust accordingly.
The flight departed from London when it was 6:12 PM in London, so we subtract six hours from this to get 12:12 PM, the time it was in Chicago. Now we can add 8 hours, 30 minutes, first rewriting 12:12 PM as 0:12:
The flight landed in Chicago when it was 9:42 PM there.
Refer to the time zone differences printed at the top of the map. The time zone for Chicago is marked
The flight departed from London when it was 6:12 PM in London, so we subtract six hours from this to get 12:12 PM, the time it was in Chicago. Now we can add 8 hours, 30 minutes, first rewriting 12:12 PM as 0:12:
The flight landed in Chicago when it was 9:42 PM there.
Compare your answer with the correct one above