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Short Story	$S1$	$S2$	$S3$	$S4$	$S5$	$S6$
Fraction of the Total Reading Assignment	$\frac{1}{3}$	$\frac{1}{4}$	$\frac{1}{6}$	$\frac{1}{9}$	$\frac{1}{12}$	$\frac{1}{18}$

Hannah was given an assignment to read $6$ short stories this week. She does her reading on Wednesday and Thursday. Her teacher labeled the stories $S1$ , $S2$ , $S3$ , $S4$ , $S5$ , and $S6$ . The table shows the percentage of each story as a fraction of the total number of pages of the entire reading assignment. If Hannah read more than $\frac{1}{2}$ of the entire assignment on Wednesday and she always completed a short story in one sitting, did she read $S6$ on Wednesday?

(1) Hannah read $S1$ and $S4$ on Thursday.

(2) Hannah read $S2$ and $S5$ on Wednesday.

Ready4

Box	$B1$	$B2$	$B3$	$B4$	$B5$	$B6$
Fraction of the Total Value of Rachel's Order	$\frac{1}{4}$	$\frac{5}{24}$	$\frac{3}{16}$	$\frac{1}{6}$	$\frac{1}{8}$	$\frac{1}{16}$

Rachel submitted an order for several items from a popular online retail site. Her items were packaged in 6 separate boxes and were delivered on Monday and Tuesday of this past week. Each box was labeled $B1$ , $B2$ , $B3$ , $B4$ , $B5$ , or $B6$ . The table shows the value of each box as a fraction of the total value of Rachel's order. If the delivery on Monday had a value greater than $\frac{1}{2}$ of the total value of Rachel's order, was box $B4$ delivered on Monday?

(1) $B3$ and $B5$ were delivered on Monday.

(2) $B1$ and $B2$ were delivered on Tuesday.

Ready4

In the figure above, what is the value of $m+n$ ?

(1) $p=15$

(2) $\Delta ABC$ and $\Delta DBC$ are both isosceles and $q=40$

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In the figure above, what is the value of $a+b$ ?

(1) $b=88$

(2) $\Delta WYZ$ and $\Delta XYZ$ are both isosceles and $\text{m}\angle XYW=15^{\circ}$

Ready4

In the figure above, what is the value of $x+y$ ?

(1) $x=86$

(2) $\Delta MNO$ and $\Delta MPO$ are both isosceles triangles and $\angle PMO=32^{\circ}$

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The inside of a rectangular carton is $45$ centimeters long, $30$ centimeters wide, and $10$ centimeters high. The carton is filled to capacity with $m$ identical cylindrical cans of vegetables that stand upright in rows and columns, as indicated in the figure above. If the cans are $10$ centimeters high, what is the value of $m$ ?

(1) Each of the cans has a volume of $62.5\pi$ cubic centimeters.

(2) The area of the base of the rectangular carton is $1{,}350$ square centimeters.

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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.

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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

$P=\{1,3,x,y\}$

$Q=\{2,x,y,8\}$

Two integers will be randomly selected, one from set $P$ and one from set $Q$ . What is the probability that the sum of the two integers will equal $12$ ?

(1) $x+y=10$

(2) $x+2=y$

Ready4

$S=\{2,4,a,b,12\}$

$T=\{a,b,10\}$

Two integers will be randomly selected, one from set $S$ and one from set $T$ . What is the probability that the sum of the two integers will be odd?

(1) $a=5$

(2) $b$ is even.

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$A=\{2,3,x,y\}$

$B=\{x,y,5,6,7\}$

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

If $m$ and $n$ are positive integers, is $\frac{m}{n} < \frac{13}{15}$ ?

(1) $\frac{n}{m} > 1.154$

(2) $\frac{m}{n} < 0.876$

Ready4

If $x$ and $y$ are positive integers, is $\frac{x}{y} < \frac{5}{7}$ ?

(1) $\frac{x}{y} < 0.714$

(2) $\frac{y}{x} > 1.414$

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If $x$ and $y$ are positive integers, is $9x < 7y$ ?

(1) $\frac{x}{y} < 0.777$

(2) $\frac{y}{x} > 1.286$

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

(1) $m=16$

(2) $\overline{YZ}=4\sqrt{5}$

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

(1) $m=9$

(2) $n=1$

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If $2$ different animals are to be selected at random from a group of $16$ cats and dogs, and if $p$ is the probability that one cat and one dog will be selected, is $p > \frac{1}{2}$ ?

(1) At most $6$ animals are dogs.

(2) The probability that both animals selected will be cats is greater than $\frac{1}{2}$ .

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 $2$ different houses are to be selected at random from a group of $12$ houses on a street and if $p$ is the probability that both houses selected will have even address numbers, is $p < \frac{1}{2}$ ?

(1) More than $\frac{1}{2}$ of the $12$ houses have even numbers.

(2) The probability that both houses selected will have odd numbers is less than $\frac{1}{4}$ .

Ready4

The sequence $t_1, t_2, t_3,...,t_n,...$ such that $t_n = \frac{1}{n - 1} - \frac{1}{n}$ for all integers $n > 1$ . If $k$ is a positive integer greater than $1$ , is the sum of the first $k$ terms of the sequence less than $\frac{11}{12}$ ?

(1) $k < 13$

(2) $k > 9$