DSQ: Calculating percents - GMAT Quantitative
Card 1 of 120
Jared, a jewelry salesman, makes a 10% commission on the selling price of all the jewelry he sells. Last month, he earned $4,000 in commission. What is the total selling price of the jewelry he sold this month?
1. His sales this month were 25% more than his sales last month.
2. He earned $5,000 in commission this month.
Jared, a jewelry salesman, makes a 10% commission on the selling price of all the jewelry he sells. Last month, he earned $4,000 in commission. What is the total selling price of the jewelry he sold this month?
1. His sales this month were 25% more than his sales last month.
2. He earned $5,000 in commission this month.
Tap to reveal answer
Each statement has enough information to calculate the answer.
Using statement 1, we know that he sold 25% more than last month. Given in the question, last month he earned $4,000. If $4,000 is 10% of the total price of his jewelry sold last month, we do some math (below) to find he sold $40,000 worth of jewelry. Let 
be the total price of jewelry sold last month. Then,
so
Increasing that by 25% we see that
NOTE: when multiplying the percents, make sure you use the decimal values.
Using statement 2, we know that we can just calculate the total selling price of the jewelry he sold this month based on the commission percentage. So, if we let 
equal the total price of jewelry sold this month, we get 
or
Therefore we see we can use either statement individually to find what we are looking for.
Each statement has enough information to calculate the answer.
Using statement 1, we know that he sold 25% more than last month. Given in the question, last month he earned $4,000. If $4,000 is 10% of the total price of his jewelry sold last month, we do some math (below) to find he sold $40,000 worth of jewelry. Let
Increasing that by 25% we see that
NOTE: when multiplying the percents, make sure you use the decimal values.
Using statement 2, we know that we can just calculate the total selling price of the jewelry he sold this month based on the commission percentage. So, if we let
or
Therefore we see we can use either statement individually to find what we are looking for.
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Mrs. Smith purchased groceries whose price, before tax, was $147.64. What was the tax rate on those groceries (nearest hundredth of a percent)?
-
The tax she paid was $9.23.
-
The total amount she paid was $156.87
Mrs. Smith purchased groceries whose price, before tax, was $147.64. What was the tax rate on those groceries (nearest hundredth of a percent)?
-
The tax she paid was $9.23.
-
The total amount she paid was $156.87
Tap to reveal answer
To determine the tax rate, you need to know the purchase price, which is given, and the amount of tax paid. The amount of tax is given in Statement 1. Statement 2 alone, however, also allows you to find the amount of tax; just subtract:
Either way, you can now find the tax rate:
To determine the tax rate, you need to know the purchase price, which is given, and the amount of tax paid. The amount of tax is given in Statement 1. Statement 2 alone, however, also allows you to find the amount of tax; just subtract:
Either way, you can now find the tax rate:
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What percent of students in a school are freshmen with glasses?
(1) Of the freshmen in the school, 10% wear glasses.
(2) Of the non-freshmen in the school, 20% wear glasses.
What percent of students in a school are freshmen with glasses?
(1) Of the freshmen in the school, 10% wear glasses.
(2) Of the non-freshmen in the school, 20% wear glasses.
Tap to reveal answer
To answer this question, it is necessary to know the total number of students in the school and the number of freshmen with glasses.
(1) This indicates that 10% of the freshmen have glasses; neither the total number of freshmen nor the total number of students in the school is provided rightarrow NOT sufficient.
(2) Provides the percent of non-freshmen who wear glasses (irrelevant to the question at hand). It does not provide the total number of students in the school or the number of freshmen with glasses rightarrow NOT sufficient.
From (1) and (2), the percent of non-freshmen with glasses is known and the percent of the freshmen with glasses is known, but not the percent of the school who are freshmen with glasses.
For example:
If there are 100 freshmen, including 10 freshmen with glasses, and 100 non-freshmen, including 20 non-freshmen with glasses, then $\frac{10}{200}$=5% of the school are freshmen with glasses.
If there are 300 freshmen, including 30 freshmen with glasses and 100 non-freshmen, including 20 non-freshmen with glasses, then $\frac{30}{400}$=7.5% of the school are freshmen with glasses.
Both statements together are not sufficient.
To answer this question, it is necessary to know the total number of students in the school and the number of freshmen with glasses.
(1) This indicates that 10% of the freshmen have glasses; neither the total number of freshmen nor the total number of students in the school is provided rightarrow NOT sufficient.
(2) Provides the percent of non-freshmen who wear glasses (irrelevant to the question at hand). It does not provide the total number of students in the school or the number of freshmen with glasses rightarrow NOT sufficient.
From (1) and (2), the percent of non-freshmen with glasses is known and the percent of the freshmen with glasses is known, but not the percent of the school who are freshmen with glasses.
For example:
If there are 100 freshmen, including 10 freshmen with glasses, and 100 non-freshmen, including 20 non-freshmen with glasses, then $\frac{10}{200}$=5% of the school are freshmen with glasses.
If there are 300 freshmen, including 30 freshmen with glasses and 100 non-freshmen, including 20 non-freshmen with glasses, then $\frac{30}{400}$=7.5% of the school are freshmen with glasses.
Both statements together are not sufficient.
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In 2013 there are 300 employees at Company ABC. If the number of employees at Company ABC increased by 200% from 1993 to 2013, by what percent did the number of employees at Company ABC increase from 2003 to 2013?
(1) In 2003 there were 160 employees at Company ABC.
(2) From 1993 to 2003 the number of employees increased by 60% at Company ABC.
In 2013 there are 300 employees at Company ABC. If the number of employees at Company ABC increased by 200% from 1993 to 2013, by what percent did the number of employees at Company ABC increase from 2003 to 2013?
(1) In 2003 there were 160 employees at Company ABC.
(2) From 1993 to 2003 the number of employees increased by 60% at Company ABC.
Tap to reveal answer
For statement (1), since we know the numbers of employees in 2003 and 2013, we can directly calculate the percentage change: 
.
For statement (2), since we know the percentage change from 1993 to 2013 and the percentage change from 1993 to 2003, we can set the percentage change from 2003 to 2013 to be 
and then calculate 
from the following:
.
Solve 
and we can get 
.
For statement (1), since we know the numbers of employees in 2003 and 2013, we can directly calculate the percentage change:
For statement (2), since we know the percentage change from 1993 to 2013 and the percentage change from 1993 to 2003, we can set the percentage change from 2003 to 2013 to be
Solve
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Data sufficiency question- do not actually solve the question
How many male students are in a class?
1. There are 42 students in the class.
2. 55 percent of the students are female.
Data sufficiency question- do not actually solve the question
How many male students are in a class?
1. There are 42 students in the class.
2. 55 percent of the students are female.
Tap to reveal answer
In order to calculate the number of males in the class, you need to know the total number of students and the number of females (which can be calculated using the percentage).
In order to calculate the number of males in the class, you need to know the total number of students and the number of females (which can be calculated using the percentage).
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Data sufficiency question- do not actually solve the question
There are 20 cats in an animal shelter. How many black, female cats are in the shelter?
1. 14 of the cats are male
2. 25 percent of the cats are black
Data sufficiency question- do not actually solve the question
There are 20 cats in an animal shelter. How many black, female cats are in the shelter?
1. 14 of the cats are male
2. 25 percent of the cats are black
Tap to reveal answer
The information provided will allow you to calculate the number of females and the number of black cats, but there is not enough information to quantify the number of black, female cats
The information provided will allow you to calculate the number of females and the number of black cats, but there is not enough information to quantify the number of black, female cats
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A certain pet store sells cats and dogs. The number of dogs is 250% greater than the number of cats. How many cats are in the store?
1. There are 40 dogs in the store.
2. There are 56 cats and dogs in the store.
A certain pet store sells cats and dogs. The number of dogs is 250% greater than the number of cats. How many cats are in the store?
1. There are 40 dogs in the store.
2. There are 56 cats and dogs in the store.
Tap to reveal answer
Statement 1: sufficient
Statement 2: sufficient
Statement 1: sufficient
Statement 2: sufficient
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A distributor ordered 3,250 chairs. 2,315 chairs were delivered. What percentage of the chairs have not yet been delivered?
A distributor ordered 3,250 chairs. 2,315 chairs were delivered. What percentage of the chairs have not yet been delivered?
Tap to reveal answer
First let's find the number of chairs not delivered:
Therefore the fraction of chairs not delivered is 
.
Divide the numerator by the denominator to convert this fraction into a decimal:
Multiply by 100 to turn this decimal into a percentage:
First let's find the number of chairs not delivered:
Therefore the fraction of chairs not delivered is
Divide the numerator by the denominator to convert this fraction into a decimal:
Multiply by 100 to turn this decimal into a percentage:
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What percent of a company's employees are women with a college degree?
(1) Of the women employed in the company, 
do not have a college degree.
(2) Of the men employed in the company, 
have a college degree.
What percent of a company's employees are women with a college degree?
(1) Of the women employed in the company,
(2) Of the men employed in the company,
Tap to reveal answer
Statement (1) indicates the percentage of women who do not have a college degree. From that statement, we know that 60% of the women in the company have a college degree. However, we do not know the total number of employees or the total number of women in the company. Therefore, statement (1) alone is not sufficient.
Statement (2) indicates the percentage of men who have a college degree but from that statement we cannot find the total number of employees or the total number of women with a college degree.
We need the total number of women and the total number of employees in order to calculate the percentage of employees who are women with a college degree. We show it with the following example:
If we assume that there are 100 women and 100 men working in the company, we can attempt to find the percentage of employees who are women with a college degree in the following way:
So in that example, 30% of the employees are women with a college degree.
However if we change the number of women to 500 and the number of men to 600, the percentage of employees who are women with a college degree is:
The percentage of employees who are women with a college degree becomes 25%.
Therefore both statements together are not sufficient.
Statement (1) indicates the percentage of women who do not have a college degree. From that statement, we know that 60% of the women in the company have a college degree. However, we do not know the total number of employees or the total number of women in the company. Therefore, statement (1) alone is not sufficient.
Statement (2) indicates the percentage of men who have a college degree but from that statement we cannot find the total number of employees or the total number of women with a college degree.
We need the total number of women and the total number of employees in order to calculate the percentage of employees who are women with a college degree. We show it with the following example:
If we assume that there are 100 women and 100 men working in the company, we can attempt to find the percentage of employees who are women with a college degree in the following way:
So in that example, 30% of the employees are women with a college degree.
However if we change the number of women to 500 and the number of men to 600, the percentage of employees who are women with a college degree is:
The percentage of employees who are women with a college degree becomes 25%.
Therefore both statements together are not sufficient.
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is 
of 
, and 
is 
of 
.
True or false: 
.
Statement 1: 
.
Statement 2: 
True or false:
Statement 1:
Statement 2:
Tap to reveal answer
is 60% of 
, meaning that 
, or, equivalently, 
.
From Statement 1 alone, since 
, it follows that
This is enough to prove that 
.
is 60% of 
, so 
.
From Statement 2 alone, since 
, it follows that
.
This is enough to prove that 
.
From Statement 1 alone, since
This is enough to prove that
From Statement 2 alone, since
This is enough to prove that
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is 30% of 
, and 60% of 
. 
and 
are positive integers.
True or false: 
is a positive integer.
Statement 1: 
is a multiple of 5.
Statement 2: 
is a multiple of 5.
True or false:
Statement 1:
Statement 2:
Tap to reveal answer
Statement 1 alone is inconclusive. For example, if 
, then 
is 30% of 10 - that is,
,
an integer.
But if 
, then 
is 30% of 15 - that is,
,
not an integer.
If Statement 2 alone is assumed, then 
for some integer 
. 60% of this is
.
is three times an integer and is itself an integer.
Statement 1 alone is inconclusive. For example, if
an integer.
But if
not an integer.
If Statement 2 alone is assumed, then
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is 30% of 
, and 
is 30% of 
. 
is an integer. True or false: 
is an integer.
Statement 1: 
is an integer.
Statement 2: 
is divisible by 100.
Statement 1:
Statement 2:
Tap to reveal answer
Assume Statement 1 alone.
If 
is 30% of 
and 
is 30% of 
, then:
and
or
is an integer; for 
to be an integer, 
must be divisible by 100. This makes Statement 2 a consequence of Statement 1, so we can now test Statement 2 alone.
If 
is divisible by 100, then for some integer 
, 
. 30% of this is 
. 
is 30 times some integer, and is therefore an integer itself.
Either statement alone answers the question.
Assume Statement 1 alone.
If
and
or
If
Either statement alone answers the question.
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is 20% of 
, and 
is 20% of 
. 
is an integer. True or false: 
is an integer.
Statement 1: 
is not an integer.
Statement 2: 
is divisible by 72.
Statement 1:
Statement 2:
Tap to reveal answer
Assume both statements are true.
Case 1: 
.
Then 
is 20% of this, so
is 20% of 
, so
Case 2: 
Then 
is 20% of this, so
is 20% of 
, so
In both situations, the conditions of the problem, as well as both statements, are true, but in one case, 
is not an integer and in the other case, 
is an integer. The statements together are inconclusive.
Assume both statements are true.
Case 1:
Then
Case 2:
Then
In both situations, the conditions of the problem, as well as both statements, are true, but in one case,
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is 25% of 
, which is 25% of 
. 
is a positive integer.
True of false: 
is an integer.
Statement 1: 
is a prime number.
Statement 2: 
is an odd number.
True of false:
Statement 1:
Statement 2:
Tap to reveal answer
is 25% of 
, so
.
Similarly, 
.
Therefore,
,
or, equivalently,
or
.
If 
is an integer, then 16 is a factor of 
. This contradicts both Statement 1, since 16 is composite, making 
composite, and Statement 2, since this makes 
a multiple of 
- that is, even. Either statement alone answers the question in the negative.
Similarly,
Therefore,
or, equivalently,
or
If
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Three candidates - Rodger, Stephanie, and Tina - ran for student body president. By the rules, the candidate who wins more than half the ballots cast wins the election outright; if no candidate wins more than half, there must be a runoff between the two top vote-getters. You may assume that no other names were written in.
Was there an outright winner, or will there be a runoff?
Statement 1: Rodger won 100 more votes than Stephanie and 210 more votes than Tina.
Statement 2: Tina won 25.9% of the votes.
Three candidates - Rodger, Stephanie, and Tina - ran for student body president. By the rules, the candidate who wins more than half the ballots cast wins the election outright; if no candidate wins more than half, there must be a runoff between the two top vote-getters. You may assume that no other names were written in.
Was there an outright winner, or will there be a runoff?
Statement 1: Rodger won 100 more votes than Stephanie and 210 more votes than Tina.
Statement 2: Tina won 25.9% of the votes.
Tap to reveal answer
For one candidate to have won the election outright, (s)he must win more than 50% of the votes.
Statement 1 alone does not prove there was an outright winner. For example, if Rodger got 211 votes, then Stephanie got 111 votes, and Tina got 1 vote; this makes Rodger's share of the votes
,
making Rodger the outright winner. But if Rodger got 500 votes, then Stephanie got 400 votes, and Tina got 290; Rodger got the most votes, but his share is
,
not the required share of the vote.
Statement 2 alone does not prove this either, since 74.1% of the vote was won by either Rodger or Stephanie, but it is not specified how this is distributed; Roger or Stephanie could have won 51%, with the remaining 23.1% won by the other, resulting in an outright winner. However, it is also possible that each won half this, or about 37%, resulting in a runoff between the two.
Now assume both statements are true. Let 
be the number of votes won by Tina. Then Rodger won 
votes and Stephanie won 
, or 
, votes. The total votes are
.
Since Tina won 25.9% of the vote, we can set up an equation:
This can be solved for 
. From this, the number of votes each candidate got, the votes cast, and, finally, the percent of the vote each won can be calculated.
For one candidate to have won the election outright, (s)he must win more than 50% of the votes.
Statement 1 alone does not prove there was an outright winner. For example, if Rodger got 211 votes, then Stephanie got 111 votes, and Tina got 1 vote; this makes Rodger's share of the votes
making Rodger the outright winner. But if Rodger got 500 votes, then Stephanie got 400 votes, and Tina got 290; Rodger got the most votes, but his share is
not the required share of the vote.
Statement 2 alone does not prove this either, since 74.1% of the vote was won by either Rodger or Stephanie, but it is not specified how this is distributed; Roger or Stephanie could have won 51%, with the remaining 23.1% won by the other, resulting in an outright winner. However, it is also possible that each won half this, or about 37%, resulting in a runoff between the two.
Now assume both statements are true. Let
Since Tina won 25.9% of the vote, we can set up an equation:
This can be solved for
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Jared, a jewelry salesman, makes a 10% commission on the selling price of all the jewelry he sells. Last month, he earned $4,000 in commission. What is the total selling price of the jewelry he sold this month?
1. His sales this month were 25% more than his sales last month.
2. He earned $5,000 in commission this month.
Jared, a jewelry salesman, makes a 10% commission on the selling price of all the jewelry he sells. Last month, he earned $4,000 in commission. What is the total selling price of the jewelry he sold this month?
1. His sales this month were 25% more than his sales last month.
2. He earned $5,000 in commission this month.
Tap to reveal answer
Each statement has enough information to calculate the answer.
Using statement 1, we know that he sold 25% more than last month. Given in the question, last month he earned $4,000. If $4,000 is 10% of the total price of his jewelry sold last month, we do some math (below) to find he sold $40,000 worth of jewelry. Let be the total price of jewelry sold last month. Then,
so
Increasing that by 25% we see that
NOTE: when multiplying the percents, make sure you use the decimal values.
Using statement 2, we know that we can just calculate the total selling price of the jewelry he sold this month based on the commission percentage. So, if we let equal the total price of jewelry sold this month, we get
or
Therefore we see we can use either statement individually to find what we are looking for.
Each statement has enough information to calculate the answer.
Using statement 1, we know that he sold 25% more than last month. Given in the question, last month he earned $4,000. If $4,000 is 10% of the total price of his jewelry sold last month, we do some math (below) to find he sold $40,000 worth of jewelry. Let
Increasing that by 25% we see that
NOTE: when multiplying the percents, make sure you use the decimal values.
Using statement 2, we know that we can just calculate the total selling price of the jewelry he sold this month based on the commission percentage. So, if we let
or
Therefore we see we can use either statement individually to find what we are looking for.
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Mrs. Smith purchased groceries whose price, before tax, was $147.64. What was the tax rate on those groceries (nearest hundredth of a percent)?
-
The tax she paid was $9.23.
-
The total amount she paid was $156.87
Mrs. Smith purchased groceries whose price, before tax, was $147.64. What was the tax rate on those groceries (nearest hundredth of a percent)?
-
The tax she paid was $9.23.
-
The total amount she paid was $156.87
Tap to reveal answer
To determine the tax rate, you need to know the purchase price, which is given, and the amount of tax paid. The amount of tax is given in Statement 1. Statement 2 alone, however, also allows you to find the amount of tax; just subtract:
Either way, you can now find the tax rate:
To determine the tax rate, you need to know the purchase price, which is given, and the amount of tax paid. The amount of tax is given in Statement 1. Statement 2 alone, however, also allows you to find the amount of tax; just subtract:
Either way, you can now find the tax rate:
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What percent of students in a school are freshmen with glasses?
(1) Of the freshmen in the school, 10% wear glasses.
(2) Of the non-freshmen in the school, 20% wear glasses.
What percent of students in a school are freshmen with glasses?
(1) Of the freshmen in the school, 10% wear glasses.
(2) Of the non-freshmen in the school, 20% wear glasses.
Tap to reveal answer
To answer this question, it is necessary to know the total number of students in the school and the number of freshmen with glasses.
(1) This indicates that 10% of the freshmen have glasses; neither the total number of freshmen nor the total number of students in the school is provided rightarrow NOT sufficient.
(2) Provides the percent of non-freshmen who wear glasses (irrelevant to the question at hand). It does not provide the total number of students in the school or the number of freshmen with glasses rightarrow NOT sufficient.
From (1) and (2), the percent of non-freshmen with glasses is known and the percent of the freshmen with glasses is known, but not the percent of the school who are freshmen with glasses.
For example:
If there are 100 freshmen, including 10 freshmen with glasses, and 100 non-freshmen, including 20 non-freshmen with glasses, then $\frac{10}{200}$=5% of the school are freshmen with glasses.
If there are 300 freshmen, including 30 freshmen with glasses and 100 non-freshmen, including 20 non-freshmen with glasses, then $\frac{30}{400}$=7.5% of the school are freshmen with glasses.
Both statements together are not sufficient.
To answer this question, it is necessary to know the total number of students in the school and the number of freshmen with glasses.
(1) This indicates that 10% of the freshmen have glasses; neither the total number of freshmen nor the total number of students in the school is provided rightarrow NOT sufficient.
(2) Provides the percent of non-freshmen who wear glasses (irrelevant to the question at hand). It does not provide the total number of students in the school or the number of freshmen with glasses rightarrow NOT sufficient.
From (1) and (2), the percent of non-freshmen with glasses is known and the percent of the freshmen with glasses is known, but not the percent of the school who are freshmen with glasses.
For example:
If there are 100 freshmen, including 10 freshmen with glasses, and 100 non-freshmen, including 20 non-freshmen with glasses, then $\frac{10}{200}$=5% of the school are freshmen with glasses.
If there are 300 freshmen, including 30 freshmen with glasses and 100 non-freshmen, including 20 non-freshmen with glasses, then $\frac{30}{400}$=7.5% of the school are freshmen with glasses.
Both statements together are not sufficient.
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In 2013 there are 300 employees at Company ABC. If the number of employees at Company ABC increased by 200% from 1993 to 2013, by what percent did the number of employees at Company ABC increase from 2003 to 2013?
(1) In 2003 there were 160 employees at Company ABC.
(2) From 1993 to 2003 the number of employees increased by 60% at Company ABC.
In 2013 there are 300 employees at Company ABC. If the number of employees at Company ABC increased by 200% from 1993 to 2013, by what percent did the number of employees at Company ABC increase from 2003 to 2013?
(1) In 2003 there were 160 employees at Company ABC.
(2) From 1993 to 2003 the number of employees increased by 60% at Company ABC.
Tap to reveal answer
For statement (1), since we know the numbers of employees in 2003 and 2013, we can directly calculate the percentage change: .
For statement (2), since we know the percentage change from 1993 to 2013 and the percentage change from 1993 to 2003, we can set the percentage change from 2003 to 2013 to be and then calculate from the following:
.
Solve and we can get .
For statement (1), since we know the numbers of employees in 2003 and 2013, we can directly calculate the percentage change:
For statement (2), since we know the percentage change from 1993 to 2013 and the percentage change from 1993 to 2003, we can set the percentage change from 2003 to 2013 to be
Solve
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Data sufficiency question- do not actually solve the question
How many male students are in a class?
1. There are 42 students in the class.
2. 55 percent of the students are female.
Data sufficiency question- do not actually solve the question
How many male students are in a class?
1. There are 42 students in the class.
2. 55 percent of the students are female.
Tap to reveal answer
In order to calculate the number of males in the class, you need to know the total number of students and the number of females (which can be calculated using the percentage).
In order to calculate the number of males in the class, you need to know the total number of students and the number of females (which can be calculated using the percentage).
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