Operations - GRE Quantitative Reasoning
Card 1 of 168
Of a group of 335 graduating high school atheletes, 106 played basketball, 137 ran track and field, and 51 participated in swimming. What is the maximum number of students that did both track and field and swimming upon graduation?
Of a group of 335 graduating high school atheletes, 106 played basketball, 137 ran track and field, and 51 participated in swimming. What is the maximum number of students that did both track and field and swimming upon graduation?
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Simply recognize that logically, the participation of either sport is non-exclusive, that is, just because people took track and field does not necessarily mean they did not take swimming as well. As such, those 51 who took swimming could have all potentially done track and field, which means all 51 students.
Simply recognize that logically, the participation of either sport is non-exclusive, that is, just because people took track and field does not necessarily mean they did not take swimming as well. As such, those 51 who took swimming could have all potentially done track and field, which means all 51 students.
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Of 300 students, 120 are enrolled in math club, 150 are enrolled in chess club, and 100 are enrolled in both. How many students are not members of either club?
Of 300 students, 120 are enrolled in math club, 150 are enrolled in chess club, and 100 are enrolled in both. How many students are not members of either club?
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There are 120 students in the math club and 150 students in the chess club, for a total membership of 270. However, 100 students are in both clubs, which means they are counted twice. You simply subtract 100 from 270, which will give you a total of 170 different students participating in both clubs. This means that the remaining 130 students do not participate in either club.
There are 120 students in the math club and 150 students in the chess club, for a total membership of 270. However, 100 students are in both clubs, which means they are counted twice. You simply subtract 100 from 270, which will give you a total of 170 different students participating in both clubs. This means that the remaining 130 students do not participate in either club.
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Choose the answer which best solves the following equation:
Choose the answer which best solves the following equation:
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When adding integers, one needs to pay close attention to the sign. When you add a negative integer, it's the same thing as subtracting that integer. Therefore:
When adding integers, one needs to pay close attention to the sign. When you add a negative integer, it's the same thing as subtracting that integer. Therefore:
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Choose the answer below which best solves the following equation:
Choose the answer below which best solves the following equation:
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The sum of any two negative numbers will be negative. Remember, also, that adding a negative number is like subtracting it. Therefore:
The sum of any two negative numbers will be negative. Remember, also, that adding a negative number is like subtracting it. Therefore:
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Of a group of 335 graduating high school atheletes, 106 played basketball, 137 ran track and field, and 51 participated in swimming. What is the maximum number of students that did both track and field and swimming upon graduation?
Of a group of 335 graduating high school atheletes, 106 played basketball, 137 ran track and field, and 51 participated in swimming. What is the maximum number of students that did both track and field and swimming upon graduation?
Tap to reveal answer
Simply recognize that logically, the participation of either sport is non-exclusive, that is, just because people took track and field does not necessarily mean they did not take swimming as well. As such, those 51 who took swimming could have all potentially done track and field, which means all 51 students.
Simply recognize that logically, the participation of either sport is non-exclusive, that is, just because people took track and field does not necessarily mean they did not take swimming as well. As such, those 51 who took swimming could have all potentially done track and field, which means all 51 students.
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Of 300 students, 120 are enrolled in math club, 150 are enrolled in chess club, and 100 are enrolled in both. How many students are not members of either club?
Of 300 students, 120 are enrolled in math club, 150 are enrolled in chess club, and 100 are enrolled in both. How many students are not members of either club?
Tap to reveal answer
There are 120 students in the math club and 150 students in the chess club, for a total membership of 270. However, 100 students are in both clubs, which means they are counted twice. You simply subtract 100 from 270, which will give you a total of 170 different students participating in both clubs. This means that the remaining 130 students do not participate in either club.
There are 120 students in the math club and 150 students in the chess club, for a total membership of 270. However, 100 students are in both clubs, which means they are counted twice. You simply subtract 100 from 270, which will give you a total of 170 different students participating in both clubs. This means that the remaining 130 students do not participate in either club.
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Choose the answer which best solves the following equation:
Choose the answer which best solves the following equation:
Tap to reveal answer
When adding integers, one needs to pay close attention to the sign. When you add a negative integer, it's the same thing as subtracting that integer. Therefore:
When adding integers, one needs to pay close attention to the sign. When you add a negative integer, it's the same thing as subtracting that integer. Therefore:
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Choose the answer below which best solves the following equation:
Choose the answer below which best solves the following equation:
Tap to reveal answer
The sum of any two negative numbers will be negative. Remember, also, that adding a negative number is like subtracting it. Therefore:
The sum of any two negative numbers will be negative. Remember, also, that adding a negative number is like subtracting it. Therefore:
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Of a group of 335 graduating high school atheletes, 106 played basketball, 137 ran track and field, and 51 participated in swimming. What is the maximum number of students that did both track and field and swimming upon graduation?
Of a group of 335 graduating high school atheletes, 106 played basketball, 137 ran track and field, and 51 participated in swimming. What is the maximum number of students that did both track and field and swimming upon graduation?
Tap to reveal answer
Simply recognize that logically, the participation of either sport is non-exclusive, that is, just because people took track and field does not necessarily mean they did not take swimming as well. As such, those 51 who took swimming could have all potentially done track and field, which means all 51 students.
Simply recognize that logically, the participation of either sport is non-exclusive, that is, just because people took track and field does not necessarily mean they did not take swimming as well. As such, those 51 who took swimming could have all potentially done track and field, which means all 51 students.
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Of 300 students, 120 are enrolled in math club, 150 are enrolled in chess club, and 100 are enrolled in both. How many students are not members of either club?
Of 300 students, 120 are enrolled in math club, 150 are enrolled in chess club, and 100 are enrolled in both. How many students are not members of either club?
Tap to reveal answer
There are 120 students in the math club and 150 students in the chess club, for a total membership of 270. However, 100 students are in both clubs, which means they are counted twice. You simply subtract 100 from 270, which will give you a total of 170 different students participating in both clubs. This means that the remaining 130 students do not participate in either club.
There are 120 students in the math club and 150 students in the chess club, for a total membership of 270. However, 100 students are in both clubs, which means they are counted twice. You simply subtract 100 from 270, which will give you a total of 170 different students participating in both clubs. This means that the remaining 130 students do not participate in either club.
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Choose the answer which best solves the following equation:
Choose the answer which best solves the following equation:
Tap to reveal answer
When adding integers, one needs to pay close attention to the sign. When you add a negative integer, it's the same thing as subtracting that integer. Therefore:
When adding integers, one needs to pay close attention to the sign. When you add a negative integer, it's the same thing as subtracting that integer. Therefore:
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Choose the answer below which best solves the following equation:
Choose the answer below which best solves the following equation:
Tap to reveal answer
The sum of any two negative numbers will be negative. Remember, also, that adding a negative number is like subtracting it. Therefore:
The sum of any two negative numbers will be negative. Remember, also, that adding a negative number is like subtracting it. Therefore:
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Which of the following integers is divisible by 
?
Which of the following integers is divisible by
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In order to find a number divisible by 6, you must find a number divisible by both of its factors — 2 and 3. Only even numbers are divisible by 2, so 81 is eliminated. In order to be divisible by 3, the sum of the digits has to be divisible by 3.
The sum of the digits of 316 is 3 + 1 + 6 = 10.
For 240, the sum is 2 + 4 = 6.
For 118, the sum is 1 + 1 + 8 = 10.
Only 6 is divisible by 3.
In order to find a number divisible by 6, you must find a number divisible by both of its factors — 2 and 3. Only even numbers are divisible by 2, so 81 is eliminated. In order to be divisible by 3, the sum of the digits has to be divisible by 3.
The sum of the digits of 316 is 3 + 1 + 6 = 10.
For 240, the sum is 2 + 4 = 6.
For 118, the sum is 1 + 1 + 8 = 10.
Only 6 is divisible by 3.
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Which of the following rules makes the expression 
an integer?
Which of the following rules makes the expression
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4 is already an integer, so we need to make sure x/10 is an integer too.
Multiples of 5 won't work. For example, 5 is a multiple of 5 but 5/10 isn't an integer. Similarly, if x/10 leaves a remainder of 5, x/10 isn't an integer. For example, 15/10 leaves a remainder of 5 and isn't an integer.
If x/10 has no remainder, then it must be an integer. For example, 10/10 and 20/10 both leave no remainders and simplify to the integers 1 and 2, respectively.
4 is already an integer, so we need to make sure x/10 is an integer too.
Multiples of 5 won't work. For example, 5 is a multiple of 5 but 5/10 isn't an integer. Similarly, if x/10 leaves a remainder of 5, x/10 isn't an integer. For example, 15/10 leaves a remainder of 5 and isn't an integer.
If x/10 has no remainder, then it must be an integer. For example, 10/10 and 20/10 both leave no remainders and simplify to the integers 1 and 2, respectively.
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Apples are sold by whole bushels. You cannot purchase part of a bushel. There are 126 apples in a bushel.
Sam is a caterer who needs to bake 300 pies to sell at the county fair. If it takes 4 apples to make a pie, how many bushels must Sam order to ensure he has enough apples for his pies?
Apples are sold by whole bushels. You cannot purchase part of a bushel. There are 126 apples in a bushel.
Sam is a caterer who needs to bake 300 pies to sell at the county fair. If it takes 4 apples to make a pie, how many bushels must Sam order to ensure he has enough apples for his pies?
Tap to reveal answer
Because Sam needs to make 300 pies, and each pie needs 4 apples, the number of apples he needs is
300 x 4 = 1200.
To determine how many bushels Sam needs, divide the total number of apples by the number of apples sold in a bushel.
1200 / 126 = 9.524
Because apples are sold by the whole bushel, Sam cannot order part of a bushel. In order to make sure he has sufficient apples, he will need to order 10 bushels.
Because Sam needs to make 300 pies, and each pie needs 4 apples, the number of apples he needs is
300 x 4 = 1200.
To determine how many bushels Sam needs, divide the total number of apples by the number of apples sold in a bushel.
1200 / 126 = 9.524
Because apples are sold by the whole bushel, Sam cannot order part of a bushel. In order to make sure he has sufficient apples, he will need to order 10 bushels.
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The remainder of 
is 
.
Quantity A:
Quantity B:
The remainder of
Quantity A:
Quantity B:
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If the remainder of 
is 
, we know that 
could be:
Since this generates an entire list of values, we cannot know which quantity is larger.
Do not be tricked by the question, which is trying to get you to say that they are equal!
If the remainder of
Since this generates an entire list of values, we cannot know which quantity is larger.
Do not be tricked by the question, which is trying to get you to say that they are equal!
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The remainder of 
is 
.
The remainder of 
is 
.
Which of the following is a potential value for 
?
The remainder of
The remainder of
Which of the following is a potential value for
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Begin by writing out a few possible values for 
and 
.
Since the remainder of 
is 
, we can list:
Since the remainder of 
is 
, we can list:
Since 
(which is 
) is your smallest possible value, you know that 
and 
are not options. You cannot derive either 
or 
from the values given.
Therefore, the only option that is left is 
, which is equal to 
.
Begin by writing out a few possible values for
Since the remainder of
Since the remainder of
Since
Therefore, the only option that is left is
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Which of the following integers is divisible by ?
Which of the following integers is divisible by
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In order to find a number divisible by 6, you must find a number divisible by both of its factors — 2 and 3. Only even numbers are divisible by 2, so 81 is eliminated. In order to be divisible by 3, the sum of the digits has to be divisible by 3.
The sum of the digits of 316 is 3 + 1 + 6 = 10.
For 240, the sum is 2 + 4 = 6.
For 118, the sum is 1 + 1 + 8 = 10.
Only 6 is divisible by 3.
In order to find a number divisible by 6, you must find a number divisible by both of its factors — 2 and 3. Only even numbers are divisible by 2, so 81 is eliminated. In order to be divisible by 3, the sum of the digits has to be divisible by 3.
The sum of the digits of 316 is 3 + 1 + 6 = 10.
For 240, the sum is 2 + 4 = 6.
For 118, the sum is 1 + 1 + 8 = 10.
Only 6 is divisible by 3.
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Which of the following rules makes the expression an integer?
Which of the following rules makes the expression
Tap to reveal answer
4 is already an integer, so we need to make sure x/10 is an integer too.
Multiples of 5 won't work. For example, 5 is a multiple of 5 but 5/10 isn't an integer. Similarly, if x/10 leaves a remainder of 5, x/10 isn't an integer. For example, 15/10 leaves a remainder of 5 and isn't an integer.
If x/10 has no remainder, then it must be an integer. For example, 10/10 and 20/10 both leave no remainders and simplify to the integers 1 and 2, respectively.
4 is already an integer, so we need to make sure x/10 is an integer too.
Multiples of 5 won't work. For example, 5 is a multiple of 5 but 5/10 isn't an integer. Similarly, if x/10 leaves a remainder of 5, x/10 isn't an integer. For example, 15/10 leaves a remainder of 5 and isn't an integer.
If x/10 has no remainder, then it must be an integer. For example, 10/10 and 20/10 both leave no remainders and simplify to the integers 1 and 2, respectively.
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Apples are sold by whole bushels. You cannot purchase part of a bushel. There are 126 apples in a bushel.
Sam is a caterer who needs to bake 300 pies to sell at the county fair. If it takes 4 apples to make a pie, how many bushels must Sam order to ensure he has enough apples for his pies?
Apples are sold by whole bushels. You cannot purchase part of a bushel. There are 126 apples in a bushel.
Sam is a caterer who needs to bake 300 pies to sell at the county fair. If it takes 4 apples to make a pie, how many bushels must Sam order to ensure he has enough apples for his pies?
Tap to reveal answer
Because Sam needs to make 300 pies, and each pie needs 4 apples, the number of apples he needs is
300 x 4 = 1200.
To determine how many bushels Sam needs, divide the total number of apples by the number of apples sold in a bushel.
1200 / 126 = 9.524
Because apples are sold by the whole bushel, Sam cannot order part of a bushel. In order to make sure he has sufficient apples, he will need to order 10 bushels.
Because Sam needs to make 300 pies, and each pie needs 4 apples, the number of apples he needs is
300 x 4 = 1200.
To determine how many bushels Sam needs, divide the total number of apples by the number of apples sold in a bushel.
1200 / 126 = 9.524
Because apples are sold by the whole bushel, Sam cannot order part of a bushel. In order to make sure he has sufficient apples, he will need to order 10 bushels.
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