Proportion / Ratio / Rate - GRE Quantitative Reasoning
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When television remotes are shipped from a certain factory, 1 out of every 200 is defective. What is the ratio of defective to nondefective remotes?
When television remotes are shipped from a certain factory, 1 out of every 200 is defective. What is the ratio of defective to nondefective remotes?
One remote is defective for every 199 non-defective remotes.
One remote is defective for every 199 non-defective remotes.
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You are making a cake that requires, by volume, three times as much flour as sugar, twice as much sugar as milk, eight times more milk than baking powder and twice as much baking powder as salt. If you start with a teaspoon of salt, how many cups of flour do you need (there are 48 teaspoons in one cup)?
You are making a cake that requires, by volume, three times as much flour as sugar, twice as much sugar as milk, eight times more milk than baking powder and twice as much baking powder as salt. If you start with a teaspoon of salt, how many cups of flour do you need (there are 48 teaspoons in one cup)?
One teaspoon of salt requires 2 teaspoons of baking powder, which requires 16 teaspoons of milk and 32 teaspoons of sugar. 32 teaspoons of sugar requires 96 teaspoons of flour, which equals two cups of flour.
One teaspoon of salt requires 2 teaspoons of baking powder, which requires 16 teaspoons of milk and 32 teaspoons of sugar. 32 teaspoons of sugar requires 96 teaspoons of flour, which equals two cups of flour.
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You have a rope of some length, but 2/3rds of it is cut off and thrown away. 1/4th of the remaining rope is cut off and thrown away. What proportion of the original rope remains?
You have a rope of some length, but 2/3rds of it is cut off and thrown away. 1/4th of the remaining rope is cut off and thrown away. What proportion of the original rope remains?
If 2/3 is cut off and thrown away, that means 1/3 of the original length remains. Of this, 1/4 gets cut off and thrown away, meaning 3/4 of 1/3 still remains. Multiplying 3/4 * 1/3, we get 1/4.
If 2/3 is cut off and thrown away, that means 1/3 of the original length remains. Of this, 1/4 gets cut off and thrown away, meaning 3/4 of 1/3 still remains. Multiplying 3/4 * 1/3, we get 1/4.
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Quantitative Comparison
Alice has a puppy and a kitten. The puppy weighs 4 pounds and grows at a rate of 1 pound per month. The kitten weighs 2 pounds and grows at a rate of 2 pounds per month.
Quantity A: Weight of the puppy after 8 months
Quantity B: Weight of the kitten after 7 months
Quantitative Comparison
Alice has a puppy and a kitten. The puppy weighs 4 pounds and grows at a rate of 1 pound per month. The kitten weighs 2 pounds and grows at a rate of 2 pounds per month.
Quantity A: Weight of the puppy after 8 months
Quantity B: Weight of the kitten after 7 months
The puppy starts at 4 pounds and gains 1 pound per month for 8 months, so he weighs 4 + 8 = 12 pounds at the end of 8 months. The kitten starts at 2 pounds and gains 2 pounds per month for 7 months, so he weighs 2 + 14 = 16 pounds at the end of 7 months. Therefore Quantity B is greater.
The puppy starts at 4 pounds and gains 1 pound per month for 8 months, so he weighs 4 + 8 = 12 pounds at the end of 8 months. The kitten starts at 2 pounds and gains 2 pounds per month for 7 months, so he weighs 2 + 14 = 16 pounds at the end of 7 months. Therefore Quantity B is greater.
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In a solution, 
of the fluid is water, 
is wine, and 
is lemon juice. What is the ratio of lemon juice to water?
In a solution,
This problem is really an easy fraction division. You should first divide the lemon juice amount by the water amount:
Remember, to divide fractions, you multiply by the reciprocal:
This is the same as saying:
This problem is really an easy fraction division. You should first divide the lemon juice amount by the water amount:
Remember, to divide fractions, you multiply by the reciprocal:
This is the same as saying:
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You have a rope of some length, but 2/3rds of it is cut off and thrown away. 1/4th of the remaining rope is cut off and thrown away. What proportion of the original rope remains?
You have a rope of some length, but 2/3rds of it is cut off and thrown away. 1/4th of the remaining rope is cut off and thrown away. What proportion of the original rope remains?
If 2/3 is cut off and thrown away, that means 1/3 of the original length remains. Of this, 1/4 gets cut off and thrown away, meaning 3/4 of 1/3 still remains. Multiplying 3/4 * 1/3, we get 1/4.
If 2/3 is cut off and thrown away, that means 1/3 of the original length remains. Of this, 1/4 gets cut off and thrown away, meaning 3/4 of 1/3 still remains. Multiplying 3/4 * 1/3, we get 1/4.
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In a solution, of the fluid is water, is wine, and is lemon juice. What is the ratio of lemon juice to water?
In a solution,
This problem is really an easy fraction division. You should first divide the lemon juice amount by the water amount:
Remember, to divide fractions, you multiply by the reciprocal:
This is the same as saying:
This problem is really an easy fraction division. You should first divide the lemon juice amount by the water amount:
Remember, to divide fractions, you multiply by the reciprocal:
This is the same as saying:
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There are 
philosophy books and 
history books on a shelf. The number of philosophy books is doubled. What is the ratio of philosophy books to history books after this?
There are
First, compute the new number of philosophy books. This will be 
.
The ratio of philosophy books to history books is thus:
This can be reduced by dividing the numerator and the denominator by 
:
Therefore, the ratio is 
.
First, compute the new number of philosophy books. This will be
The ratio of philosophy books to history books is thus:
This can be reduced by dividing the numerator and the denominator by
Therefore, the ratio is
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A used car lot has 
total vehicles to be sold. 
of the vehicles are 4-wheel drive and the rest are 2-wheel drive. What is the ratio of 2-wheel drive to 4-wheel drive vehicles on the lot?
A used car lot has
27 of the 72 cars are 4-wheel drive, we can write this as a proportion.
The proportion of the 4-wheel drive cars to the total number of vehicles.
Therefore, to find the proportion of 2-wheel drive cars is,
Therefore the ratio of 2-wheel drive:4-wheel drive vehicles is 5:3.
27 of the 72 cars are 4-wheel drive, we can write this as a proportion.
The proportion of the 4-wheel drive cars to the total number of vehicles.
Therefore, to find the proportion of 2-wheel drive cars is,
Therefore the ratio of 2-wheel drive:4-wheel drive vehicles is 5:3.
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On a desk, there are 
papers for every 
paper clips and 
papers for every 
greeting card. What is the ratio of paper clips to total items on the desk?
On a desk, there are
Begin by making your life easier: presume that there are 
papers on the desk. Immediately, we know that there are 
paper clips. Now, if there are 
papers, you know that there also must be 
greeting cards. Technically you figure this out by using the ratio:
By cross-multiplying you get:
Solving for 
, you clearly get 
.
(Many students will likely see this fact without doing the algebra, however. The numbers are rather simple.)
Now, this means that our desk has on it:
papers
paper clips
greeting cards
Therefore, you have 
total items. Based on this, your ratio of paper clips to total items is:
, which is the same as 
.
Begin by making your life easier: presume that there are
By cross-multiplying you get:
Solving for
(Many students will likely see this fact without doing the algebra, however. The numbers are rather simple.)
Now, this means that our desk has on it:
Therefore, you have
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In a garden, there are 
pansies, 
lilies, 
roses, and 
petunias. What is the ratio of petunias to the total number of flowers in the garden?
In a garden, there are
To begin, you need to do a simple addition to find the total number of flowers in the garden:
Now, the ratio of petunias to the total number of flowers in the garden can be represented by a simple division of the number of petunias by 
. This is:
Next, reduce the fraction by dividing out the common 
from the numerator and the denominator:
This is the same as 
.
To begin, you need to do a simple addition to find the total number of flowers in the garden:
Now, the ratio of petunias to the total number of flowers in the garden can be represented by a simple division of the number of petunias by
Next, reduce the fraction by dividing out the common
This is the same as
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In a classroom of 
students, each student takes a language class (and only one—nobody studies two languages). 
take Latin, 
take Greek, 
take Anglo-Saxon, and the rest take Old Norse. What is the ratio of students taking Old Norse to students taking Greek?
In a classroom of
To begin, you need to calculate how many students are taking Old Norse. This is:
Now, the ratio of students taking Old Norse to students taking Greek is the same thing as the fraction of students taking Old Norse to students taking Greek, or:
Next, just reduce this fraction to its lowest terms by dividing the numerator and denominator by their common factor of 
:
This is the same as 
.
To begin, you need to calculate how many students are taking Old Norse. This is:
Now, the ratio of students taking Old Norse to students taking Greek is the same thing as the fraction of students taking Old Norse to students taking Greek, or:
Next, just reduce this fraction to its lowest terms by dividing the numerator and denominator by their common factor of
This is the same as
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Express 
as a ratio.
Express
A ratio is two numbers separated by a colon. When expressing fractions as a ratio, the numerator is the number to the left of the colon while the denominator is to the right of the colon. The answer is 
A ratio is two numbers separated by a colon. When expressing fractions as a ratio, the numerator is the number to the left of the colon while the denominator is to the right of the colon. The answer is
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Express 
as an integer ratio.
Express
To find an integer ratio, let's find the fractions with a common denominator. This will be 
. Then, we multiply the left by 
and the right by 
to get fractions of 
and 
. With the same denominators, we just have numerators to compare. Ratio is then 
.
To find an integer ratio, let's find the fractions with a common denominator. This will be
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If there are fifteen girls and six boys in a class, what is the ratio of boys to girls?
If there are fifteen girls and six boys in a class, what is the ratio of boys to girls?
Let's convert the words into numbers. Since there are 
girls and 
boys, we need ratio of boys to girls. The ratio should be 
.
Let's convert the words into numbers. Since there are
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If the ratio of girls to boys is 
, what could be the number of children in the class?
If the ratio of girls to boys is
If there are 
girls and 
boys, that means we have 
students in the class. To continue to have this ratio, we need an answer than is a multiple of 
.
is a multiple of 
which is the right answer.
If there are
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An espresso drink has a ratio of 
ounces of espresso to water. If Amanda wants her drink to be 
espresso, how much water was added?
An espresso drink has a ratio of
In the problem, the drink is 
espresso since the overall weight of the drink is 
ounces. If we are reducing the concentration of espresso to 
, then we can create an equation to figure out the addition of water.
represents the addition of water.
Cross-multiply.
Subtract 
on both sides.
In the problem, the drink is
Cross-multiply.
Subtract
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What is the ratio of square numbers to cubic numbers from 
noninclusive?
What is the ratio of square numbers to cubic numbers from
Let's list a bunch of square numbers from 
noninclusive.
doesn,t count since it's not included HOWEVER: 
count.
Let's list a bunch of cubic numbers from 
noninclusive.
doesn,t count since it's not included HOWEVER: 
count.
There are four square numbers to two cubic numbers. The ratio becomes 
or 
.
Let's list a bunch of square numbers from
Let's list a bunch of cubic numbers from
There are four square numbers to two cubic numbers. The ratio becomes
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If 
apples equal 
bananas and 
bananas equal 
carrots, what is the ratio of an apple to a carrot?
If
To get the apple to carrot ratio, we need to equal out the bananas. The least common denominator of 
and 
is 
. So if 
apples equal 
bananas, then 
bananas equal 
apples. Also, if 
bananas equal 
carrots, then 
bananas equal 
carrots. Since now the total bananas are equal, we can find the ratio of apples to carrots. We have 
as the final answer.
To get the apple to carrot ratio, we need to equal out the bananas. The least common denominator of
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If Jill, Jack and John found 
and decided to split it 
respectively, how much more did Jack get than John?
If Jill, Jack and John found
If Jill, Jack and John get 
, that means there are 
parts.
Because they found 
, each part gets 
or 
.
Jack gets 
or 
.
John gets 
or 
.
Since the question is asking how much more did Jack get than John, we subtract 
and 
to get 
.
If Jill, Jack and John get
Because they found
Jack gets
John gets
Since the question is asking how much more did Jack get than John, we subtract
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