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Ready4	Does the integer $n$ have at least three different positive prime factors? (1) $\frac{n}{8}$ is an integer (2) $\frac{n}{6}$ is an integer
Ready4	Does the positive integer $x$ have at least two different positive prime factors? (1) $\frac{x}{4}$ is an integer. (2) $\frac{x}{25}$ is an integer.
Ready4	Running at their respective constant rates, Machine A takes 4 days longer to produce $n$ widgets than Machine B. At these rates, if the two machines together produce $\frac{10}{7}n$ widgets in 3 days, how many days would it take Machine A alone to produce $3n$ widgets?
Ready4	In the figure shown, angles $n$ , $q$ , and $r$ make up three of the interior angles of quadrilateral $ABCD$ . Is $n=r$ ? (1) Lines $h$ and $k$ are parallel. (2) $p+q=180$
Ready4	In the rectangular coordinate system above, if $\Delta HIJ$ and $\Delta JKL$ have equal area, what are the coordinates of point $L$ ? (1) The coordinates of point $J$ are $(6,0)$ . (2) $\overline{JK}=2\overline{LK}$
Ready4	The sequence $a_1, a_2, a_3, ..., a_n, ...$ is defined such that for all integers $n \geq 1$ : $a_n = \frac{1}{n+1}-\frac{1}{n+2}$ If $k$ is a positive integer, is the sum of the first $k$ terms of the sequence greater than $\frac{5}{12}$ ? (1) $k < 17$ (2) $k > 11$
Ready4	If two different students are to be selected at random from a group of $10$ male and female students, and if $p$ is the probability that one male and one female student will be selected, is $p>\frac{1}{3}$ ? (1) More than $\frac{1}{2}$ of the $10$ students are female. (2) The probability that both students selected will be female is greater than $\frac{1}{3}$ and less than $\frac{1}{2}$ .
Ready4	If arc $XYZ$ above is a semicircle, what is the length of diameter $\overline{XZ}$ ? (1) $m=16$ (2) $\overline{YZ}=4\sqrt{5}$
Ready4	If $x$ and $y$ are positive integers, is $\frac{x}{y} < \frac{5}{7}$ ? (1) $\frac{x}{y} < 0.714$ (2) $\frac{y}{x} > 1.414$
Ready4	$A=\{2,3,x,y\}$ $B=\{x,y,5,6,7\}$ Two integers will be randomly selected, one integer from set $A$ and one integer from set $B$ . What is the probability that the sum of the two integers will equal $7$ ? (1) $x=3$ (2) $y=4$
Ready4	The inside of a rectangular carton is $36$ inches long, $30$ inches wide, and $6$ inches high. The carton is filled to capacity with $x$ identical cylindrical cans of soda that stand upright in rows and columns, as indicated in the figure above. If the cans are $6$ inches high, what is the value of $x$ ? (1) Each of the cans has a radius of $3$ inches. (2) Six of the cans fit exactly along the length of the carton.
Ready4	The inside of a rectangular carton is $44$ centimeters long, $28$ centimeters wide, and $5$ centimeters high. The carton is filled to capacity with $y$ identical cylindrical cans of tomato paste that stand upright in rows and columns, as indicated in the figure above. If the cans are $5$ centimeters high, what is the value of $y$ ? (1) Each of the cans has a radius of $2$ centimeters. (2) Seven of the cans fit exactly along the width of the carton.
Ready4	If arc $ABC$ above is a semicircle, what is the length of segment $\overline{AB}$ ? (1) $\overline{BC}=5$ (2) $\overline{AC}=13$
Ready4	If arc $WXY$ above is a semicircle, what is the length of $\overline{XY}$ ? (1) $\overline{WY}=17$ (2) $\overline{WX}=15$
Ready4	A machine makes widgets and gizmos. If it takes 6 minutes to make each widget and 10 minutes to make each gizmo, what is the total number of minutes it takes to make a batch of widgets and gizmos? (1) A batch has 50 more widgets than gizmos. (2) The ratio of the number of widgets to the number of gizmos in a batch is 3 to 1.
Ready4	How many different prime numbers are factors of the positive integer $k$ ? (1) Three different prime numbers are factors of $5k$ . (2) Three different prime numbers are factors of $k^2$ .
Ready4	If $xy \neq 0$ , is $\frac{1}{x}+\frac{1}{y}=10$ ? (1) $x+y=10xy$ (2) $x=y$
Ready4	If $ab \neq 0$ , is $\frac{1}{a}- \frac{1}{b}=10$ ? (1) $b=2a$ (2) $b-a=10ab$
Ready4	On a certain date, Sashi invested $1,000 at $x$ percent simple annual interest and a different amount at $y$ percent simple annual interest. What amount did Sashi invest at $y$ percent simple annual interest? (1) Sashi invested $1,000 at 2 percent simple annual interest and the other amount at 3 percent simple interest. (2) The total amount of interest earned by Sashi's two investments in one year was $100.
Ready4	A tortoise moves at a constant speed of 15 feet per minute. If the tortoise moves across a field, is the distance that the tortoise moves less than 0.1 mile? (1 mile = 5,280 feet) (1) It takes the tortoise less than 0.6 hour to move across the field. (2) It takes the tortoise more than 0.5 hour to move across the field.