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If 2 different representatives are to be selected at random from a group of 10 employees and if $p$ is the probability that both representatives selected will be women, is $p<\tfrac{1}{2}$ ?

(1) More than $\tfrac{1}{2}$ of the 10 employees are women.

(2) The probability that both representatives selected will be men is less

than $p<\tfrac{1}{10}$ .

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[GMAT-Math-7098-q-GEO]

In the figure shown, lines k and m str parallel to each other. Is x = z?

(1) x = w

(2) y = 180 - w

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[GMAT-Math-7100-q-GEO]

In the rectangular coordinate system above, if ΔOPQ and ΔQRS have equal area, what are the coordinates of point R?

(1) The coordinates of point P are (0,12).

(2) OP = OQ and QS = RS.

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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 perimeter of the entire quilt is 244 inches.

(2) The width of the border on all sides is 3 inches.

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Cost for a Sweater at a Thrift Shop
Days for Sale in Shop	Percent Markdown
5 − 7 days	10%
8 − 14 days	20%
15 − 21 days	30%
22 − 28 days	50%
Over 28 days	75%

The table above shows the pricing chart for a sweater at a local thrift shop. Suppose the original price for a sweater at the shop was $170. If a consumer purchased the sweater, how many days had it been for sale in the shop?

(1) The discount on the sweater was $51.

(2) If the consumer had waited one more day to purchase the sweater, the sweater would have been discounted an additional $34.

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Tuition Refund Deadlines
Deadline	Percent of Tuition Refunded
August 23	100%
Sept 7	90%
Sept 14	70%
Sept 21	25%

The table above shows the tuition refund schedule for canceling a class at a local college. If a student cancels a class with an original tuition cost of $3,200, on what day did the student cancel?

(1) The student was refunded $2,240.

(2) If the student canceled the class one day earlier, she would have been refunded an additional $640.

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	$A$	$B$	$C$	$D$	$E$
$A$	0	$y$	52	78	99
$B$	$y$	0	64	$x$	75
$C$	52	64	0	25	31
$D$	78	$x$	25	0	84
$E$	99	75	31	84	0

The table above shows the distance, in miles, by the most direct route, between any two of the five cities $A, B, C, D$ and $E$ . For example, the distance between City $B$ and City $C$ is $64$ miles. What is the value of $x$ ?

(1) By the most direct route, the distance between $A$ and $B$ is three times the distance between $A$ and $D$ .

(2) By the most direct route, the distance between $B$ and $D$ is four times the distance between $A$ and $B$ .

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If $x$ is an integer, is $x-|x| < 10^x$ ?

(1) $x=0$

(2) $x < 0$

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If $x$ is an integer, is $\frac{\left \vert x \right \vert}{x}<3^x$ ?

(1) $x > 0$

(2) $x=-3$

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Does the integer $p$ have at least three different positive prime factors?

(1) $\frac{p}{30}$ is an integer.

(2) $\frac{p}{40}$ is an integer.

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In the figure shown, lines $r$ and $s$ are parallel. Is $x=y$ ?

(1) $w+x=180$

(2) $w+z=180$

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What is the value of $x+y$ in the figure above?

(1) $w=75$

(2) $z=80$

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What is the value of $b-a$ in the figure above?

(1) $c=140$

(2) $d=130$

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In the rectangular coordinate system above, if $\Delta LMN$ and $\Delta NOP$ have equal area, what are the coordinates of point $L$ ?

(1) $\overline{LM}=\overline{MN}$ and $\overline{NP}=\overline{OP}$ .

(2) The coordinates of point $O$ are $(8,4)$ .

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In the $xy$ -plane, lines $f$ and $g$ intersect at the point $(1,2)$ . Is the $y$ -intercept of $f$ greater than the $y$ -intercept of $g$ ?

(1) The slope of $f$ is $-2$ .

(2) The slope of $g$ is negative.

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

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

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

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

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

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) $x+2=y$

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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 $m$ ?