Sets - ISEE Upper Level Quantitative Reasoning
Card 1 of 208
We can divide the natural numbers into four sets:
In which of these sets would 197 be a member?
We can divide the natural numbers into four sets:
In which of these sets would 197 be a member?
Tap to reveal answer
The sets are divided according to the remainder obtained when each element is divided by 4. 197 divided by 4 yields a remainder of 1; all of the elements of 
match this description, so 
.
The sets are divided according to the remainder obtained when each element is divided by 4. 197 divided by 4 yields a remainder of 1; all of the elements of
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We can divide the natural numbers into four sets:
In which of these sets would 197 be a member?
We can divide the natural numbers into four sets:
In which of these sets would 197 be a member?
Tap to reveal answer
The sets are divided according to the remainder obtained when each element is divided by 4. 197 divided by 4 yields a remainder of 1; all of the elements of match this description, so .
The sets are divided according to the remainder obtained when each element is divided by 4. 197 divided by 4 yields a remainder of 1; all of the elements of
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Which of the following can be the next number after 47 in the sequence below?
Which of the following can be the next number after 47 in the sequence below?
Tap to reveal answer
Each number in the set is the value of the preceding number multiplied by 2, plus 1:
Therefore, the next number in the set will be 47 times 2, plus 1. This gives us:
Each number in the set is the value of the preceding number multiplied by 2, plus 1:
Therefore, the next number in the set will be 47 times 2, plus 1. This gives us:
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We can divide the natural numbers into four sets:
In which of these sets would 197 be a member?
We can divide the natural numbers into four sets:
In which of these sets would 197 be a member?
Tap to reveal answer
The sets are divided according to the remainder obtained when each element is divided by 4. 197 divided by 4 yields a remainder of 1; all of the elements of match this description, so .
The sets are divided according to the remainder obtained when each element is divided by 4. 197 divided by 4 yields a remainder of 1; all of the elements of
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Which of the following can be the next number after 47 in the sequence below?
Which of the following can be the next number after 47 in the sequence below?
Tap to reveal answer
Each number in the set is the value of the preceding number multiplied by 2, plus 1:
Therefore, the next number in the set will be 47 times 2, plus 1. This gives us:
Each number in the set is the value of the preceding number multiplied by 2, plus 1:
Therefore, the next number in the set will be 47 times 2, plus 1. This gives us:
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Which of the following can be the next number after 47 in the sequence below?
Which of the following can be the next number after 47 in the sequence below?
Tap to reveal answer
Each number in the set is the value of the preceding number multiplied by 2, plus 1:
Therefore, the next number in the set will be 47 times 2, plus 1. This gives us:
Each number in the set is the value of the preceding number multiplied by 2, plus 1:
Therefore, the next number in the set will be 47 times 2, plus 1. This gives us:
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We can divide the natural numbers into four sets:
In which of these sets would 197 be a member?
We can divide the natural numbers into four sets:
In which of these sets would 197 be a member?
Tap to reveal answer
The sets are divided according to the remainder obtained when each element is divided by 4. 197 divided by 4 yields a remainder of 1; all of the elements of match this description, so .
The sets are divided according to the remainder obtained when each element is divided by 4. 197 divided by 4 yields a remainder of 1; all of the elements of
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Which of the following can be the next number after 47 in the sequence below?
Which of the following can be the next number after 47 in the sequence below?
Tap to reveal answer
Each number in the set is the value of the preceding number multiplied by 2, plus 1:
Therefore, the next number in the set will be 47 times 2, plus 1. This gives us:
Each number in the set is the value of the preceding number multiplied by 2, plus 1:
Therefore, the next number in the set will be 47 times 2, plus 1. This gives us:
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A pair of fair dice are tossed. Which is the greater quantity?
(a) The probability that the product of the two dice will be an even number
(b) 
A pair of fair dice are tossed. Which is the greater quantity?
(a) The probability that the product of the two dice will be an even number
(b)
Tap to reveal answer
The product of the two dice will be an odd number only if both dice are odd; the rolls favorable to that event are:
,
or nine out of the thirty-six possible rolls. This makes twenty-seven of the thirty-six equally probable rolls favorable to getting an even product. Since half of 36 is 18, the probability of getting an even product is greater than .
This makes (a) the greater quantity
The product of the two dice will be an odd number only if both dice are odd; the rolls favorable to that event are:
or nine out of the thirty-six possible rolls. This makes twenty-seven of the thirty-six equally probable rolls favorable to getting an even product. Since half of 36 is 18, the probability of getting an even product is greater than
This makes (a) the greater quantity
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A pair of fair dice are tossed. What is the probability that the product of the numbers of the faces is greater than or equal to 
?
A pair of fair dice are tossed. What is the probability that the product of the numbers of the faces is greater than or equal to ?
Tap to reveal answer
Out of a possible thirty-six rolls, the following result in a product of twenty or greater:
This is eight out of thirty-six, making the probability
.
Out of a possible thirty-six rolls, the following result in a product of twenty or greater:
This is eight out of thirty-six, making the probability
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A pair of fair dice are tossed. Which is the greater quantity?
(a) The probability that the product of the two dice will be an even number
(b)
A pair of fair dice are tossed. Which is the greater quantity?
(a) The probability that the product of the two dice will be an even number
(b)
Tap to reveal answer
The product of the two dice will be an odd number only if both dice are odd; the rolls favorable to that event are:
,
or nine out of the thirty-six possible rolls. This makes twenty-seven of the thirty-six equally probable rolls favorable to getting an even product. Since half of 36 is 18, the probability of getting an even product is greater than .
This makes (a) the greater quantity
The product of the two dice will be an odd number only if both dice are odd; the rolls favorable to that event are:
or nine out of the thirty-six possible rolls. This makes twenty-seven of the thirty-six equally probable rolls favorable to getting an even product. Since half of 36 is 18, the probability of getting an even product is greater than
This makes (a) the greater quantity
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A pair of fair dice are tossed. What is the probability that the product of the numbers of the faces is greater than or equal to ?
A pair of fair dice are tossed. What is the probability that the product of the numbers of the faces is greater than or equal to ?
Tap to reveal answer
Out of a possible thirty-six rolls, the following result in a product of twenty or greater:
This is eight out of thirty-six, making the probability
.
Out of a possible thirty-six rolls, the following result in a product of twenty or greater:
This is eight out of thirty-six, making the probability
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A pair of fair dice are tossed. Which is the greater quantity?
(a) The probability that the product of the two dice will be an even number
(b)
A pair of fair dice are tossed. Which is the greater quantity?
(a) The probability that the product of the two dice will be an even number
(b)
Tap to reveal answer
The product of the two dice will be an odd number only if both dice are odd; the rolls favorable to that event are:
,
or nine out of the thirty-six possible rolls. This makes twenty-seven of the thirty-six equally probable rolls favorable to getting an even product. Since half of 36 is 18, the probability of getting an even product is greater than .
This makes (a) the greater quantity
The product of the two dice will be an odd number only if both dice are odd; the rolls favorable to that event are:
or nine out of the thirty-six possible rolls. This makes twenty-seven of the thirty-six equally probable rolls favorable to getting an even product. Since half of 36 is 18, the probability of getting an even product is greater than
This makes (a) the greater quantity
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A pair of fair dice are tossed. What is the probability that the product of the numbers of the faces is greater than or equal to ?
A pair of fair dice are tossed. What is the probability that the product of the numbers of the faces is greater than or equal to ?
Tap to reveal answer
Out of a possible thirty-six rolls, the following result in a product of twenty or greater:
This is eight out of thirty-six, making the probability
.
Out of a possible thirty-six rolls, the following result in a product of twenty or greater:
This is eight out of thirty-six, making the probability
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A pair of fair dice are tossed. Which is the greater quantity?
(a) The probability that the product of the two dice will be an even number
(b)
A pair of fair dice are tossed. Which is the greater quantity?
(a) The probability that the product of the two dice will be an even number
(b)
Tap to reveal answer
The product of the two dice will be an odd number only if both dice are odd; the rolls favorable to that event are:
,
or nine out of the thirty-six possible rolls. This makes twenty-seven of the thirty-six equally probable rolls favorable to getting an even product. Since half of 36 is 18, the probability of getting an even product is greater than .
This makes (a) the greater quantity
The product of the two dice will be an odd number only if both dice are odd; the rolls favorable to that event are:
or nine out of the thirty-six possible rolls. This makes twenty-seven of the thirty-six equally probable rolls favorable to getting an even product. Since half of 36 is 18, the probability of getting an even product is greater than
This makes (a) the greater quantity
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A pair of fair dice are tossed. What is the probability that the product of the numbers of the faces is greater than or equal to ?
A pair of fair dice are tossed. What is the probability that the product of the numbers of the faces is greater than or equal to ?
Tap to reveal answer
Out of a possible thirty-six rolls, the following result in a product of twenty or greater:
This is eight out of thirty-six, making the probability
.
Out of a possible thirty-six rolls, the following result in a product of twenty or greater:
This is eight out of thirty-six, making the probability
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Which of the following is an example of two sets 
and 
such that 
?
Which of the following is an example of two sets
Tap to reveal answer
refers to the empty set, the set with no elements; 
if and only if the two sets have no elements in common. In four of these cases, 
and 
share an element, which in each of these four choices is underlined:
and 
do not have an element in common, so this is the right choice.
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Which of the following is an example of two sets and such that ?
Which of the following is an example of two sets
Tap to reveal answer
refers to the empty set, the set with no elements; if and only if the two sets have no elements in common. In four of these cases, and share an element, which in each of these four choices is underlined:
and do not have an element in common, so this is the right choice.
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Which of the following is an example of two sets and such that ?
Which of the following is an example of two sets
Tap to reveal answer
refers to the empty set, the set with no elements; if and only if the two sets have no elements in common. In four of these cases, and share an element, which in each of these four choices is underlined:
and do not have an element in common, so this is the right choice.
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Which of the following is an example of two sets and such that ?
Which of the following is an example of two sets
Tap to reveal answer
refers to the empty set, the set with no elements; if and only if the two sets have no elements in common. In four of these cases, and share an element, which in each of these four choices is underlined:
and do not have an element in common, so this is the right choice.
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