How to find the missing part of a list - ISEE Upper Level Quantitative Reasoning

Card 0 of 208

Question

We can divide the natural numbers into four sets:

$A = \left \{ 1, 5, 9, 13, 17, ... \right \}$

$B= \left \{ 2, 6, 10, 14, 18...\right \}$

$C = \left \{ 3, 7, 11, 15, 19...\right \}$

$D = \left \{ 4, 8, 12, 16, 20...\right \}$

In which of these sets would 197 be a member?

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 $197 \in A$ .

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Question

We can divide the natural numbers into four sets:

$A = \left \{ 1, 5, 9, 13, 17, ... \right \}$

$B= \left \{ 2, 6, 10, 14, 18...\right \}$

$C = \left \{ 3, 7, 11, 15, 19...\right \}$

$D = \left \{ 4, 8, 12, 16, 20...\right \}$

In which of these sets would 197 be a member?

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 $197 \in A$ .

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Question

Which of the following can be the next number after 47 in the sequence below?

$\{2, 5, 11, 23, 47...\}\textup{\ ?}$

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:

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Question

We can divide the natural numbers into four sets:

$A = \left \{ 1, 5, 9, 13, 17, ... \right \}$

$B= \left \{ 2, 6, 10, 14, 18...\right \}$

$C = \left \{ 3, 7, 11, 15, 19...\right \}$

$D = \left \{ 4, 8, 12, 16, 20...\right \}$

In which of these sets would 197 be a member?

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 $197 \in A$ .

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Question

Which of the following can be the next number after 47 in the sequence below?

$\{2, 5, 11, 23, 47...\}\textup{\ ?}$

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:

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Question

Which of the following can be the next number after 47 in the sequence below?

$\{2, 5, 11, 23, 47...\}\textup{\ ?}$

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:

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Question

We can divide the natural numbers into four sets:

$A = \left \{ 1, 5, 9, 13, 17, ... \right \}$

$B= \left \{ 2, 6, 10, 14, 18...\right \}$

$C = \left \{ 3, 7, 11, 15, 19...\right \}$

$D = \left \{ 4, 8, 12, 16, 20...\right \}$

In which of these sets would 197 be a member?

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 $197 \in A$ .

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Question

Which of the following can be the next number after 47 in the sequence below?

$\{2, 5, 11, 23, 47...\}\textup{\ ?}$

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:

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Question

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) $\frac{1}{2}$

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:

$\left \{ (1,1) , (1,3), (1,5), (3,1) , (3,3), (3,5),(5,1) , (5,3), (5,5) \right \}$ ,

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 $\frac{1}{2}$ .

This makes (a) the greater quantity

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Question

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 ?

Answer

Out of a possible thirty-six rolls, the following result in a product of twenty or greater:

$\left\{ (4, 5), (4, 6), (5, 4), (5, 5), (5, 6), (6, 4), (6, 5), (6, 6) \right\}$

This is eight out of thirty-six, making the probability

$\frac{8}{36} = \frac {2}{9}$ .

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Question

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) $\frac{1}{2}$

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:

$\left \{ (1,1) , (1,3), (1,5), (3,1) , (3,3), (3,5),(5,1) , (5,3), (5,5) \right \}$ ,

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 $\frac{1}{2}$ .

This makes (a) the greater quantity

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Question

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 ?

Answer

Out of a possible thirty-six rolls, the following result in a product of twenty or greater:

$\left\{ (4, 5), (4, 6), (5, 4), (5, 5), (5, 6), (6, 4), (6, 5), (6, 6) \right\}$

This is eight out of thirty-six, making the probability

$\frac{8}{36} = \frac {2}{9}$ .

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Question

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) $\frac{1}{2}$

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:

$\left \{ (1,1) , (1,3), (1,5), (3,1) , (3,3), (3,5),(5,1) , (5,3), (5,5) \right \}$ ,

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 $\frac{1}{2}$ .

This makes (a) the greater quantity

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Question

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 ?

Answer

Out of a possible thirty-six rolls, the following result in a product of twenty or greater:

$\left\{ (4, 5), (4, 6), (5, 4), (5, 5), (5, 6), (6, 4), (6, 5), (6, 6) \right\}$

This is eight out of thirty-six, making the probability

$\frac{8}{36} = \frac {2}{9}$ .

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Question

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) $\frac{1}{2}$

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:

$\left \{ (1,1) , (1,3), (1,5), (3,1) , (3,3), (3,5),(5,1) , (5,3), (5,5) \right \}$ ,

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 $\frac{1}{2}$ .

This makes (a) the greater quantity

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Question

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 ?

Answer

Out of a possible thirty-six rolls, the following result in a product of twenty or greater:

$\left\{ (4, 5), (4, 6), (5, 4), (5, 5), (5, 6), (6, 4), (6, 5), (6, 6) \right\}$

This is eight out of thirty-six, making the probability

$\frac{8}{36} = \frac {2}{9}$ .

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Question

Which of the following is an example of two sets and such that $A \cap B = \varnothing$ ?

Answer

$\varnothing$ refers to the empty set, the set with no elements; $A \cap B = \varnothing$ 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:

$A = \left \{ \Delta , \Gamma , \Theta , \underline{\Lambda} , \Sigma \right \}$

$B = \left \{ \Omega , \Psi , \Phi , \Pi , \underline{\Lambda} \right \}$

$A = \left \{ \textrm{Lincoln, Washington, Jefferson, Jackson, \underline{Madison}}\right \}$

$B = \left \{ \textrm{ Monroe, Kennedy, \underline{Madison}, McKinley , Taft} \right \}$

$A = \left \{ a,v,\underline{r}, w,s,y\right \}$

$B = \left \{ k, p, \underline{r}, q,x\right \}$

$A = \left \{ \underline{2}, 8, 4, 1, 10\right \}$

$B = \left \{ 5, 9, 7, \underline{2}, 0\right \}$

$A = \left \{ \textrm{John, Mary, Fred, Stan, Harry } \right \}$ and $B = \left \{ \textrm{Greg, Larry, Phil, Andy, Joanne }\right \}$ do not have an element in common, so this is the right choice.

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Question

Which of the following is an example of two sets and such that $A \cap B = \varnothing$ ?

Answer

$\varnothing$ refers to the empty set, the set with no elements; $A \cap B = \varnothing$ 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:

$A = \left \{ \Delta , \Gamma , \Theta , \underline{\Lambda} , \Sigma \right \}$

$B = \left \{ \Omega , \Psi , \Phi , \Pi , \underline{\Lambda} \right \}$

$A = \left \{ \textrm{Lincoln, Washington, Jefferson, Jackson, \underline{Madison}}\right \}$

$B = \left \{ \textrm{ Monroe, Kennedy, \underline{Madison}, McKinley , Taft} \right \}$

$A = \left \{ a,v,\underline{r}, w,s,y\right \}$

$B = \left \{ k, p, \underline{r}, q,x\right \}$

$A = \left \{ \underline{2}, 8, 4, 1, 10\right \}$

$B = \left \{ 5, 9, 7, \underline{2}, 0\right \}$

$A = \left \{ \textrm{John, Mary, Fred, Stan, Harry } \right \}$ and $B = \left \{ \textrm{Greg, Larry, Phil, Andy, Joanne }\right \}$ do not have an element in common, so this is the right choice.

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Question

Which of the following is an example of two sets and such that $A \cap B = \varnothing$ ?

Answer

$\varnothing$ refers to the empty set, the set with no elements; $A \cap B = \varnothing$ 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:

$A = \left \{ \Delta , \Gamma , \Theta , \underline{\Lambda} , \Sigma \right \}$

$B = \left \{ \Omega , \Psi , \Phi , \Pi , \underline{\Lambda} \right \}$

$A = \left \{ \textrm{Lincoln, Washington, Jefferson, Jackson, \underline{Madison}}\right \}$

$B = \left \{ \textrm{ Monroe, Kennedy, \underline{Madison}, McKinley , Taft} \right \}$

$A = \left \{ a,v,\underline{r}, w,s,y\right \}$

$B = \left \{ k, p, \underline{r}, q,x\right \}$

$A = \left \{ \underline{2}, 8, 4, 1, 10\right \}$

$B = \left \{ 5, 9, 7, \underline{2}, 0\right \}$

$A = \left \{ \textrm{John, Mary, Fred, Stan, Harry } \right \}$ and $B = \left \{ \textrm{Greg, Larry, Phil, Andy, Joanne }\right \}$ do not have an element in common, so this is the right choice.

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Question

Which of the following is an example of two sets and such that $A \cap B = \varnothing$ ?

Answer

$\varnothing$ refers to the empty set, the set with no elements; $A \cap B = \varnothing$ 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:

$A = \left \{ \Delta , \Gamma , \Theta , \underline{\Lambda} , \Sigma \right \}$

$B = \left \{ \Omega , \Psi , \Phi , \Pi , \underline{\Lambda} \right \}$

$A = \left \{ \textrm{Lincoln, Washington, Jefferson, Jackson, \underline{Madison}}\right \}$

$B = \left \{ \textrm{ Monroe, Kennedy, \underline{Madison}, McKinley , Taft} \right \}$

$A = \left \{ a,v,\underline{r}, w,s,y\right \}$

$B = \left \{ k, p, \underline{r}, q,x\right \}$

$A = \left \{ \underline{2}, 8, 4, 1, 10\right \}$

$B = \left \{ 5, 9, 7, \underline{2}, 0\right \}$

$A = \left \{ \textrm{John, Mary, Fred, Stan, Harry } \right \}$ and $B = \left \{ \textrm{Greg, Larry, Phil, Andy, Joanne }\right \}$ do not have an element in common, so this is the right choice.

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