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Ready4

In the $xy$ -plane, is point $Q$ closer to $(10,3)$ than to $(3,10)$ ?

(1) $Q$ lies on the line $y=x$

(2) $Q$ lies on the line $y=-x$

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Consider a two digit number $xy$ where $x$ is the tens digit and $y$ is the units digit. Can we divide $xy$ by $15$ ?

(1) $xy$ is a multiple of $5$

(2) $x+y=9$

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When $x$ is divided by $4$ , the remainder is $3$ . Is $x$ divisible by $9$ ?

(1) $x$ is an odd number

(2) $x+3$ is a multiple of $5$

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If $a$ , $b$ , and $c$ are integers, is $abc$ odd?

(1) $ab$ is odd

(2) $bc$ is odd

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If x is an integer, what is the value of x?

(1) x² > 0

(2) x⁵ < 0

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Set $E$ contains five distinct positive integers $\{ x, 4, 2, 6, y\}$ . Is the mean of set $E$ greater than its median?

(1) The largest integer in set $E$ is $6$

(2) The smallest integer in set $E$ is $2$

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If $w$ represents the tens digit in

$a=2{,}125{,}4w6$

what is the value of $w$ ?

(1) $a$ is divisible by 6

(2) $a$ is divisible by 4

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If $a$ and $b$ are both positive integers, then is $\frac{10a+b}{5}$ also an integer?

(1) $a$ is divisible by 5

(2) $b$ is divisible by 5

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Is $(\frac{a}{b}) > 1$ ?

(1) $\frac{\left |a \right |}{\left |b \right |}><font color='#FE8080'>1</font>$

(2) $(\frac{a}{b}) > 0$

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If x is a two-digit integer, and a is the tens digit and b is the units digit, what is x?

(1) a + b = 10

(2) a − b = 8

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	$A$	$B$	$C$	$D$
$A$	0	81	$x$	$y$
$B$	81	0	58	43
$C$	$x$	58	0	25
$D$	$y$	43	25	0

The table above shows the distance, in miles, by the most direct route, between any two of the four cities $A, B, C$ and $D$ . For example, the distance between City $B$ and City $D$ is $43$ 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 $C$ is half the distance between $A$ and $C$ .

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	W	X	Y	Z
W	0	83	45	$y$
X	83	0	$b$	43
Y	45	$b$	0	$a$
Z	$y$	43	$a$	0

The table above shows the distance, in miles, by the most direct route between any two of the four cities W, X, Y, and Z. For example, the distance between City W and City X is 83 miles. What is the value of $a$ ?

(1) By the most direct route, the distance between W and X is one-third of the distance between Y and Z.

(2) By the most direct route, the distance between W and Y is four times the distance between X and Y.

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Each hour, a radio station plays 600 seconds worth of both 30-second and 60-second commercials. At least one commercial of each length is played. How many 60-second commercials are played each hour?

(1) Fewer than 5 commercials that are 30 seconds are played each hour.

(2) More than 8 commercials that are 60 seconds are played each hour.

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Enough small and large pizzas are ordered for $30$ party guests that are expected to eat $3$ slices each. Each small pizza has $6$ slices and each large pizza has $8$ slices. How many small pizzas are ordered?