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Chapter 10

Math Fundamentals

Educators


Problem 1

If a prime number, $p,$ is squared and the result is added to the next prime number greater than $p$ which of the following integers could be the resulting sum?
Indicate all such integers.
a. 3
b. 4
c. 7
d. 14
e. 58
f. 60
g. 65
h. 69

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Problem 2

A bookstore will only order books that come in complete cases. Each case has 150 books and $\operatorname{costs} \$ 1,757$
Quantity $\mathbf{A}$
The number of books that can be ordered for $\$ 10,550$
Quantity_B
The number of books that can be ordered for $\$ 12,290$
a. Quantity A is greater.
b. Quantity B is greater.
c. The two quantities are equal.
d. The relationship cannot be determined from the information given

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Problem 3

If the product of two distinct integers is $91,$ then which of the following values could represent the sum of the two integers? Indicate all possible values.
a. -92
b. -91
c. 7
d. 13
e. 20

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Problem 4

What is the value of the ones digit for the sum of all of the distinct prime integers less than $20 ?$
a. 4
b. 5
c. 6
d. 7
e. 8

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Problem 5

During a sale, a store decreases the prices on all of its scarves by 25 to 50 percent. If all of the scarves in the store were originally priced at $\$ 20,$ which of the following prices could be the sale price of a scarf?
Indicate all such prices.
a. $\$ 8$
b. $\$ 10$
c. $\$ 12$
d. $\$ 14$
e. $\$ 16$

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Problem 6

On Monday, 40 of the 160 available books in a library's collection were borrowed. On Tuesday, half of the books borrowed on Monday were returned and on Wednesday half of the remaining borrowed books from Monday were returned. On Thursday, the library receives 30 more available books, and a sixth of the remaining borrowed books from Monday are returned. On Friday, 30 more books are borrowed and on Saturday 35 more books are borrowed. If no other books were borrowed, returned, or received during the week, what is the percent change of the available books at the end of the day Monday to the available books at the end of the day on Saturday?

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Problem 7

Quantity_A
$4\left(\frac{1}{2} x+2 y\right)$
Quantity B
\[2 x+8 y\]
a. Quantity A is greater.
b. Quantity B is greater.
c. The two quantities are equal.
d. The relationship cannot be determined from the information given

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Problem 8

Quantity $\mathbf{A}$
The greatest number of distinct nonnegative consecutive integers whose sum is less than 22
Quantity_B
6
a. Quantity A is greater
b. Quantity B is greater
c. The two quantities are equal.
d. The relationship cannot be determined from the information given.

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Problem 9

If $x$ is the remainder when a multiple of 4 is divided by $6,$ and $y$ is the remainder when a multiple of 2 is divided by $3,$ what is the greatest possible value of $x+y ?$
a. 2
b. 3
c. 5
d. 6
e. 9

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Problem 10

What is the value of the expression $12-\left(\frac{6}{3}-4 \times 3\right)-8 \times 3 ?$
a. -46
b. -30
c. -18
d. -6
e. -2

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