How to divide integers - GRE Quantitative Reasoning
Card 1 of 40
Which of the following integers is divisible by 
?
Which of the following integers is divisible by
Tap to reveal answer
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.
← Didn't Know|Knew It →
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.
← Didn't Know|Knew It →
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.
← Didn't Know|Knew It →
The remainder of 
is 
.
Quantity A:
Quantity B:
The remainder of
Quantity A:
Quantity B:
Tap to reveal answer
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!
← Didn't Know|Knew It →
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
Tap to reveal answer
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
← Didn't Know|Knew It →
Which of the following integers is divisible by ?
Which of the following integers is divisible by
Tap to reveal answer
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.
← Didn't Know|Knew It →
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.
← Didn't Know|Knew It →
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.
← Didn't Know|Knew It →
The remainder of is .
Quantity A:
Quantity B:
The remainder of
Quantity A:
Quantity B:
Tap to reveal answer
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!
← Didn't Know|Knew It →
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
Tap to reveal answer
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
← Didn't Know|Knew It →
Which of the following integers is divisible by ?
Which of the following integers is divisible by
Tap to reveal answer
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.
← Didn't Know|Knew It →
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.
← Didn't Know|Knew It →
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.
← Didn't Know|Knew It →
The remainder of is .
Quantity A:
Quantity B:
The remainder of
Quantity A:
Quantity B:
Tap to reveal answer
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!
← Didn't Know|Knew It →
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
Tap to reveal answer
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
← Didn't Know|Knew It →
Which of the following integers is divisible by ?
Which of the following integers is divisible by
Tap to reveal answer
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.
← Didn't Know|Knew It →
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.
← Didn't Know|Knew It →
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.
← Didn't Know|Knew It →
The remainder of is .
Quantity A:
Quantity B:
The remainder of
Quantity A:
Quantity B:
Tap to reveal answer
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!
← Didn't Know|Knew It →
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
Tap to reveal answer
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
← Didn't Know|Knew It →