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Ready4

If $a, b$ and $c$ are positive integers such that $a$ is a multiple of $b$ , and $b$ is a factor of $c$ , which of the following is NOT necessarily an integer?

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If $p, q,$ $r$ are positive integers such that $p$ is a divisor of $q$ , and $r$ is a multiple of $p$ , which of the following is NOT necessarily an integer?

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If $n$ is a positive integer and $n^2$ is divisible by 98, then the largest positive integer that must divide $n$ is

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Kassi works $h$ hours a day for $d$ days and earns $x$ dollars per hour. If she puts $p$ percent of her earnings into savings, which of the following represents Kassi's earnings after savings?

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The function $h$ is defined for each positive three-digit integer $n$ by $h(n) = 2^{a}5^{b}7^{c}$ where $a, b$ and $c$ are the hundreds, tens, and units digits of $n$ respectively. If $p$ and $q$ are three-digit positive integers such that $h(p) = 25 \cdot h(q)$ , then what is the value of $p-q$ ?

Ready4

If $10 > \frac{3-x}{2}$ , which of the following must be true?

I. $17 < x$

II. $-(x+17)$ is negative.

III. $| x+5 | > 12$

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A bookstore that sells print books and ebooks reported that revenue from print book sales in 2016 was up 8 percent from 2015 and revenue from ebook sales in 2016 was down 7 percent from 2015. If total revenues from print book sales and ebook sales in 2016 were up 2 percent from 2015, what is the ratio of revenues from print book sales to ebook sales in 2015?

Ready4

The rectangular picture shown in the figure above has a frame of uniform width. What is the area of the portion of the picture that excludes the frame?

(1) The perimeter of the framed picture is 56 inches.

(2) The width of the frame on all sides is 2 inches.

Ready4

The rectangular quilt shown in the figure above has a border of uniform width. What is the area of the portion of the quilt that excludes the border?

(1) The width of the border on all sides is 4 inches.

(2) The perimeter of the entire quilt, including the border, is 220 inches. The length of the entire quilt is 20 inches longer than the width of the entire quilt.

Ready4

If arc $XYZ$ above is a semicircle, what is the length of diameter $\overline{XZ}$ ?

(1) $XY=12$

(2) $YZ=5$

Ready4


Cruise Cancellation Fees
Days Prior to Departure	Percent of Package Price
61 or more	10%
46 − 60	25%
31 − 45	40%
6 − 30	60%
5 or fewer	100%

The table above shows the cancellation fee schedule that a cruise company uses to determine the fee charged to a tourist who cancels a trip prior to departure. If a tourist canceled a trip with a package price of $3,800 and a departure date of August 5, on what day was the trip canceled?

(1) The cancellation fee was $950.

(2) If the trip had been canceled one day later, the cancellation fee would have been $570 more.

Ready4

The subsets of the set $\{p,q,r\}$ are:

$\{p\}$ , $\{q\}$ , $\{r\}$ , $\{p,q\}$ ,

$\{p,r\}$ , $\{q,r\}$ , $\{p,q,r\}$ ,

and $\{\ \}$ (the empty subset)

How many subsets of the set $\{p,q,r,s\}$ contain both $p$ and $q$ ?

Ready4

There are 8 popsicles in a box, of which 6 are red and 2 are purple. How many possible selections of 3 popsicles from the box contain at least one red popsicle and at least one purple popsicle?

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There are 9 keys on a keychain, of which 5 are for exterior locks and 4 are for interior locks. How many possible selections of 5 keys from the keychain contain at least one key for an exterior lock and at least one key for an interior lock?

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$2x+y=12$ $\left | y \right |\leq 12$

For how many ordered pairs $(x,y)$ that are solutions of the system above are $x$ and $y$ both integers?

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Today, Rose is twice as old as Sam and Sam is 3 years younger than Tina. If Rose, Sam and Tina are all alive 4 years from today, which of the following must be true on that day?

I. Rose is twice as old as Sam

II. Sam is 3 years younger than Tina.

III. Rose is older than Tina.

Ready4

If x is an integer and y = 3x + 2, which of the following CANNOT be a divisor of y?

Ready4

If positive integers x and y are not both odd, which of the following must be even?

Ready4

In the figure above, if z = 50, then x + y =

Ready4

In the figure above, point $O$ is the center of the circle and $OC = AC = AB$ . What is the value of $x$ ?