Ratio & Proportions - GMAT Quantitative
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A furlong is a measure of length used in horse racing. Eight furlongs are equal to one mile.
Express 20 furlongs in feet.
A furlong is a measure of length used in horse racing. Eight furlongs are equal to one mile.
Express 20 furlongs in feet.
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Divide 20 furlongs by 8 furlongs per mile, then multiply by 5,280 feet per mile.
Divide 20 furlongs by 8 furlongs per mile, then multiply by 5,280 feet per mile.
A fathom is a unit of underwater depth equal to six feet.
Express two miles in fathoms.
A fathom is a unit of underwater depth equal to six feet.
Express two miles in fathoms.
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Multiply 2 miles by 5,280 feet per mile, then divide by 6 feet per fathom:
Multiply 2 miles by 5,280 feet per mile, then divide by 6 feet per fathom:
The ratio 4 to $\frac{1}{4}$ is equal to which of the following ratios?
The ratio 4 to $\frac{1}{4}$ is equal to which of the following ratios?
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The ratio 4 to $\frac{1}{4}$ is equal to $\frac{4}{frac{1}${4}} which is 4left ( $\frac{4}{1}$ right )= 16.
16 can be written as the ratio 16 to 1.
The ratio 4 to $\frac{1}{4}$ is equal to $\frac{4}{frac{1}${4}} which is 4left ( $\frac{4}{1}$ right )= 16.
16 can be written as the ratio 16 to 1.
The annual budget for a road construction project is $25,200 budgeted equally over 12 months. If by the end of the third month the actual expenses have been $7,420, how much has the construction project gone over budget?
The annual budget for a road construction project is $25,200 budgeted equally over 12 months. If by the end of the third month the actual expenses have been $7,420, how much has the construction project gone over budget?
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The monthly budget is found by:
$\frac{25,200}{12}$=2,100
which for 3 months is a budget of:
2,100cdot 3= 6,300
To find out how much they are over budget the budgeted amount is subtracted from the actual expenses.
7,420 - 6,300 = 1,120
The monthly budget is found by:
$\frac{25,200}{12}$=2,100
which for 3 months is a budget of:
2,100cdot 3= 6,300
To find out how much they are over budget the budgeted amount is subtracted from the actual expenses.
7,420 - 6,300 = 1,120
The ratio 3 to $\frac{1}{2}$ is equal to the ratio:
The ratio 3 to $\frac{1}{2}$ is equal to the ratio:
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The ratio 3 to $\frac{1}{2}$ is the same as $\frac{3}{frac{1}${2}}=3times $\frac{2}{1}$=6,
which equals a ratio of 6 to 1.
Also, if you double both sides of the ratio, you get 6 to 1.
The ratio 3 to $\frac{1}{2}$ is the same as $\frac{3}{frac{1}${2}}=3times $\frac{2}{1}$=6,
which equals a ratio of 6 to 1.
Also, if you double both sides of the ratio, you get 6 to 1.
Nishita has necklaces, bracelets, and rings in a ratio of 7:5:4. If she has 64 jewelry items total, how many bracelets does she have?
Nishita has necklaces, bracelets, and rings in a ratio of 7:5:4. If she has 64 jewelry items total, how many bracelets does she have?
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bracelets: 
bracelets:
In a certain classroom all of the students are either sophomores or juniors. The number of boys and girls in the classroom are equal. Of the girls, 
are sophomores, and there are 24 junior boys. If the number of junior boys in the classroom are in the same proportion to the total amount of boys as the number of sophomore girls are to the total number of girls, how many students are in the classroom?
In a certain classroom all of the students are either sophomores or juniors. The number of boys and girls in the classroom are equal. Of the girls,
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This question seems convoluted but is actually more simple than it seems. We are told that the number of girls and boys in the classroom are equal and that 
of the girls are sophomores. We are then told that 24 of the boys are juniors, and that they represent a proportion of total boys equal to the proportion of sophomore girls to total girls. This means that:
==> 
where 
is the total number of boys.
If we know that the number of boys and girls in the class are equal, then the total number of students in the class = 112.
This question seems convoluted but is actually more simple than it seems. We are told that the number of girls and boys in the classroom are equal and that
If we know that the number of boys and girls in the class are equal, then the total number of students in the class = 112.
A box contains red and blue marbles. The probablity of picking a red is 
. There are 30 blue marbles. How many total marbles are there?
A box contains red and blue marbles. The probablity of picking a red is
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If 
are red, then 
are blue, and the number of blue marbles can be written as
Plug in the number of blue marbles, 30, and solve for the total marbles.
If
Plug in the number of blue marbles, 30, and solve for the total marbles.
On a map, one and a half inches represents sixty actual miles. In terms of 
, what distance in actual miles is represented by 
inches on the map?
On a map, one and a half inches represents sixty actual miles. In terms of
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Let 
be the number of actual miles. Then the proportion statement to be set up, with each ratio being number of actual miles to number of map inches, is:
Simplify the left expression and solve for 
Let
Simplify the left expression and solve for
The Kingdom of Zenda uses an unusual currency system. It takes 16 kronkheits to make a grotnik and 12 grotniks to make a gazoo.
At current, $1 can be exchanged for 8 grotniks and 8 kronkheits. For how much American currency can a visitor from Zenda exchange a 100-gazoo bill, to the nearest cent?
The Kingdom of Zenda uses an unusual currency system. It takes 16 kronkheits to make a grotnik and 12 grotniks to make a gazoo.
At current, $1 can be exchanged for 8 grotniks and 8 kronkheits. For how much American currency can a visitor from Zenda exchange a 100-gazoo bill, to the nearest cent?
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$1 can be exchanged for 8 grotniks and 8 kronkheits, or, equivalently, 8.5 grotniks (8 kronkheits is one-half of a grotnik). 100 gazoos is equal to 
grotniks. Therefore, if 
is the number of dollars that can be exchanged for the 100-gazoo bill, we can set up the proportion:
Solve for 
:
That is, the 100-gazoo bill can be exchanged for $141.18.
$1 can be exchanged for 8 grotniks and 8 kronkheits, or, equivalently, 8.5 grotniks (8 kronkheits is one-half of a grotnik). 100 gazoos is equal to
Solve for
That is, the 100-gazoo bill can be exchanged for $141.18.
The Duchy of Grand Fenwick uses an unusual currency system. It takes 24 tiny fenwicks to make a big fenwick.
At current exchange rates, 1 big fenwick can be exchanged for $3.26 American currency. For how much in Grand Fenwick currency can an American tourist exchange $300 (rounded to the nearest tiny fenwick)?
The Duchy of Grand Fenwick uses an unusual currency system. It takes 24 tiny fenwicks to make a big fenwick.
At current exchange rates, 1 big fenwick can be exchanged for $3.26 American currency. For how much in Grand Fenwick currency can an American tourist exchange $300 (rounded to the nearest tiny fenwick)?
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$3.26 can be exchanged for 1 big fenwick, or, equivalently, 24 tiny fenwicks. We can set up a proportion statement, where 
is the number of tiny fenwicks for which $300 can be exchanged:
Solve for 
:
The answer is 2,209 tiny fenwicks, which can be counted up with division:
or 92 big fenwicks and 1 tiny fenwick.
$3.26 can be exchanged for 1 big fenwick, or, equivalently, 24 tiny fenwicks. We can set up a proportion statement, where
Solve for
The answer is 2,209 tiny fenwicks, which can be counted up with division:
or 92 big fenwicks and 1 tiny fenwick.
Five different pizza places offer five different specials. Assuming that all of these pizzas are of the same thickness and that all are of the same quality, which of the following is the best buy?
Five different pizza places offer five different specials. Assuming that all of these pizzas are of the same thickness and that all are of the same quality, which of the following is the best buy?
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Since all of the pizzas are of the same thickness and quality, to determine the best bargain, calculate the price per square inch of each. The least amount will mark the best bargain.
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A round pizza 10 inches in diameter for $5.99:
The area of the pizza in square inches is 
The cost per square inch: 
or 7.6 cents
A round pizza 12 inches in diameter for $8.99
The area of the pizza in square inches is 
The cost per square inch: 
or 7.9 cents
A 9 inch by 9 inch square pizza for $6.99
The area of the pizza in square inches is 
The cost per square inch: 
or 8.6 cents
A 10 inch by 10 inch square pizza for $7.99
The area of the pizza in square inches is 
The cost per square inch: 
or 8.0 cents
A 12 inch by 8 inch rectangular pizza for $9.99:
The area of the pizza in square inches is 
The cost per square inch: 
or 10.4 cents
The round pizza 10 inches in diameter for $5.99 is the best buy.
Since all of the pizzas are of the same thickness and quality, to determine the best bargain, calculate the price per square inch of each. The least amount will mark the best bargain.
Edit this later
A round pizza 10 inches in diameter for $5.99:
The area of the pizza in square inches is
The cost per square inch:
A round pizza 12 inches in diameter for $8.99
The area of the pizza in square inches is
The cost per square inch:
A 9 inch by 9 inch square pizza for $6.99
The area of the pizza in square inches is
The cost per square inch:
A 10 inch by 10 inch square pizza for $7.99
The area of the pizza in square inches is
The cost per square inch:
A 12 inch by 8 inch rectangular pizza for $9.99:
The area of the pizza in square inches is
The cost per square inch:
The round pizza 10 inches in diameter for $5.99 is the best buy.
127 people signed up for a subscription service. 45 signed up for weekly deliveries, 34 for monthly deliveries, and the rest for annual deliveries. What is the ratio of weekly subscribers to annual subscribers?
127 people signed up for a subscription service. 45 signed up for weekly deliveries, 34 for monthly deliveries, and the rest for annual deliveries. What is the ratio of weekly subscribers to annual subscribers?
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Let's first find the number of annual subscribers:
The ratio of weekly subscribers to annual subscribers is therefore 
.
Let's first find the number of annual subscribers:
The ratio of weekly subscribers to annual subscribers is therefore
A clothing store is having a sales for the holiday season. They mark down all items by 
. What is the sales price of a suit whose original price is 
?
A clothing store is having a sales for the holiday season. They mark down all items by
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We start by finding the value of the mark down:
Therefore, the mark down is 43.8% or 0.438, which means that the new price of the suit is:
We start by finding the value of the mark down:
Therefore, the mark down is 43.8% or 0.438, which means that the new price of the suit is:
Noah and Lilly both work for Company ABC. Lilly earns 
more than Noah, and each year every employee gets a 
salary increase. In 2012, Noah's salary was 
.
What was Lilly's salary in 2013?
Noah and Lilly both work for Company ABC. Lilly earns
What was Lilly's salary in 2013?
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We start by finding Lilly's salary in 2012:
$60,000 x 1.20 = $60,000 + $12,000 = $72,000
Then we account for the annual 10% increase to find Lilly's salary in 2013:
$72,000 x 1.10 = $72,000 + $7,200 = $79,200
So Lilly's salary in 2013 was $79,200.
We start by finding Lilly's salary in 2012:
$60,000 x 1.20 = $60,000 + $12,000 = $72,000
Then we account for the annual 10% increase to find Lilly's salary in 2013:
$72,000 x 1.10 = $72,000 + $7,200 = $79,200
So Lilly's salary in 2013 was $79,200.
Company 
sells 
liters of soda for 
, and Company 
sells 
liters of soda for 
.
If the amount of soda sold per dollar is the same for each company, what is 
?
Company
If the amount of soda sold per dollar is the same for each company, what is
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Since the amount of soda per dollar is the same for each company, we can equate the 2 ratios
And solve
(Cross multiply)
Since the amount of soda per dollar is the same for each company, we can equate the 2 ratios
And solve
Ms. Lopez earned $236.25 after working 15 hours last week. At this rate, how much will she have earned if she works 25 hours?
Ms. Lopez earned $236.25 after working 15 hours last week. At this rate, how much will she have earned if she works 25 hours?
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The first thing we must do is set up our equation. We do this by writing our earnings to hours worked ratio:
where 
represents her earnings after working 25 hours.
We can then solve this equation for 
.
Then, 
The first thing we must do is set up our equation. We do this by writing our earnings to hours worked ratio:
where
We can then solve this equation for
Then,
George just finished the first week of his new job. He calculated that if he works 50 hours in two weeks, his biweekly paycheck will be $812.50. If he has worked a total of 27 hours so far, how much additional money must he earn in order to reach $812.50?
George just finished the first week of his new job. He calculated that if he works 50 hours in two weeks, his biweekly paycheck will be $812.50. If he has worked a total of 27 hours so far, how much additional money must he earn in order to reach $812.50?
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He has worked 27 hours out of the 50 hours calculated. As such, we are asked how much he will earn after working the remaining 23 hours.
We can first find his hourly pay and then calculate his earnings for 23 hours.
where 
represents his hourly earnings
He earns $16.25 an hour
We can now calculate how much he earns for the remaining 23 hours:
So, George needs $373.75.
He has worked 27 hours out of the 50 hours calculated. As such, we are asked how much he will earn after working the remaining 23 hours.
We can first find his hourly pay and then calculate his earnings for 23 hours.
where
He earns $16.25 an hour
We can now calculate how much he earns for the remaining 23 hours:
So, George needs $373.75.
A small company's workforce consists of store employees, store managers, and corporate managers in the ratio 10:3:1. How many employees are either corporate managers or store managers if the company has a total of 
employees?
A small company's workforce consists of store employees, store managers, and corporate managers in the ratio 10:3:1. How many employees are either corporate managers or store managers if the company has a total of
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Let 
be the number of store employees, 
the number of store managers, and 
the number of corporate managers.
, so the number of store employees is 
.
, so the number of store managers is 
.
, so the number of corporate managers is 
.
Therefore, the number of employees who are either store managers or corporate managers is 
.
Let
Therefore, the number of employees who are either store managers or corporate managers is
A scale model of the newest Mars rover has a wheel radius of 
and its antennae are each 
long. If the radius of the wheel on the actual rover is 
, what is the length of the antennae on the actual rover?
A scale model of the newest Mars rover has a wheel radius of
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Setting up a proportion here is the way to go. To make our proportion even easier to solve, set it up in such a way that your unknown (antennae length for the actual rover) is in the numerator. Recall that in a proportion, we want to have similar parts together. In this case, we will keep the wheel radii on the left and the antennae lengths on the right.
By leaving our unknown on top, we can solve this in one fell swoop. Simply multiply both sides by 
and simplify to get the answer.
Setting up a proportion here is the way to go. To make our proportion even easier to solve, set it up in such a way that your unknown (antennae length for the actual rover) is in the numerator. Recall that in a proportion, we want to have similar parts together. In this case, we will keep the wheel radii on the left and the antennae lengths on the right.
By leaving our unknown on top, we can solve this in one fell swoop. Simply multiply both sides by