PROBLEM 1 :

Jamie counted the number of edges of a cube, Jimmy counted the number of corners, and Judy counted the number of faces. They then added the three numbers. What was the resulting sum?

(A) 12
(B) 16
(C) 20
(D) 22
(E) 26

ANSWER : (E) 26

PROBLEM 2 :

Which of the following numbers has the smallest prime factor?
(A) 55
(B) 57
(C) 58
(D) 59
(E) 61

ANSWER : (C) 58

PROBLEM 3 :

A burger at Ricky C's weighs 120 grams, of which 30 grams are filler. What percent of the burger is not filler?
(A) $60 \%$
(B) $65 \%$
(C) $70 \%$
(D) $75 \%$
(E) $90 \%$

ANSWER : (D) $75 \%$

PROBLEM 4 :

A group of children riding on bicycles and tricycles rode past Billy Bob's house. Billy Bob counted 7 children and 19 wheels. How many tricycles were there?

(A) 2
(B) 4
(C) 5
(D) 6
(E) 7

ANSWER : (C) 5

PROBLEM 5 :

If $20 \%$ of a number is 12 , what is $30 \%$ of the same number?
(A) 15
(B) 18
(C) 20
(D) 24
(E) 30

ANSWER : (B) 18

PROBLEM 6 :

Given the areas of the three squares in the figure, what is the area of the interior triangle?

(A) 13
(B) 30
(C) 60
(D) 300
(E) 1800

ANSWER : (B) 30

PROBLEM 7 :

Blake and Jenny each took four 100 -point tests. Blake averaged 78 on the four tests. Jenny scored 10 points higher than Blake on the first test, 10 points lower than him on the second test, and 20 points higher on both the third and fourth tests. What is the difference between Jenny's average and Blake's average on these four tests?
(A) 10
(B) 15
(C) 20
(D) 25
(E) 40

ANSWER : (A) 10

Problems 8, 9 and 10 use the data found in the accompanying paragraph and figures.

Four friends, Art, Roger, Paul and Trisha, bake cookies, and all cookies have the same thickness. The shapes of the cookies differ, as shown.

Art's cookies are trapezoids:

Roger's cookies are rectangles:

Paul's cookies are parallelograms:

Trisha's cookies are triangles:

Each friend uses the same amount of dough, and Art makes exactly 12 cookies.

PROBLEM 8 :

Who gets the fewest cookies from one batch of cookie dough?
(A) Art

(B) Paul

(C) Roger

(D) Trisha

(E) There is a tie for fewest.

ANSWER : (A) Art

PROBLEM 9 :

Art's cookies sell for $60 ¢$ each. To earn the same amount from a single batch, how much should one of Roger's cookies cost?
(A) $18 ¢$
(B) $25 ¢$
(C) $40 ¢$
(D) $75 ¢$
(E) $90 ¢$

ANSWER : (C) $40 ¢$

PROBLEM 10 :

How many cookies will be in one batch of Trisha's cookies?
(A) 10
(B) 12
(C) 16
(D) 18
(E) 24

ANSWER : (E) 24

PROBLEM 11 :

Business is a little slow at Lou's Fine Shoes, so Lou decides to have a sale. On Friday, Lou increases all of Thursday's prices by $10 \%$. Over the weekend, Lou advertises the sale: "Ten percent off the listed price. Sale starts Monday." How much does a pair of shoes cost on Monday that cost $\$ 40$ on Thursday?
(A) $\$ 36$
(B) $\$ 39.60$
(C) $\$ 40$
(D) $\$ 40.40$
(E) $\$ 44$

ANSWER : (B) $\$ 39.60$

PROBLEM 12 :

When a fair six-sided die is tossed on a table top, the bottom face cannot be seen. What is the probability that the product of the numbers on the five faces that can be seen is divisible by 6 ?
(A) $\frac{1}{3}$
(B) $\frac{1}{2}$
(C) $\frac{2}{3}$
(D) $\frac{5}{6}$
(E) 1

ANSWER : (E) 1

PROBLEM 13 :

Fourteen white cubes are put together to form the figure on the right. The complete surface of the figure, including the bottom, is painted red. The figure is then separated into individual cubes. How many of the individual cubes have exactly four red faces?

(A) 4
(B) 6
(C) 8
(D) 10
(E) 12

ANSWER : (B) 6

PROBLEM 14 :

In this addition problem, each letter stands for a different digit.

If $T=7$ and the letter $O$ represents an even number, what is the only possible value for $W$ ?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4

ANSWER : (D) 3

PROBLEM 15 :

A figure is constructed from unit cubes. Each cube shares at least one face with another cube. What is the minimum number of cubes needed to build a figure with the front and side views shown?

(A) 3

(B) 4

(C) 5

(D) 6

(E) 7

ANSWER : (B) 4

PROBLEM 16 :

Ali, Bonnie, Carlo and Dianna are going to drive together to a nearby theme park. The car they are using has four seats: one driver's seat, one front passenger seat and two back seats. Bonnie and Carlo are the only two who can drive the car. How many possible seating arrangements are there?
(A) 2
(B) 4
(C) 6
(D) 12
(E) 24

ANSWER : (D) 12

PROBLEM 17 :

The six children listed below are from two families of three siblings each. Each child has blue or brown eyes and black or blond hair. Children from the same family have at least one of these characteristics in common. Which two children are Jim's siblings?

(A) Nadeen and Austin
(B) Benjamin and Sue
(C) Benjamin and Austin
(D) Nadeen and Tevyn
(E) Austin and Sue

ANSWER : (E) Austin and Sue

PROBLEM 18 :

Each of the twenty dots on the graph below represents one of Sarah's classmates. Classmates who are friends are connected with a line segment. For her birthday party, Sarah is inviting only the following: all of her friends and all of those classmates who are friends with at least one of her friends. How many classmates will not be invited to Sarah's party?

(A) 1
(B) 4
(C) 5
(D) 6
(E) 7

ANSWER : (D) 6

PROBLEM 19 :

How many integers between 1000 and 2000 have all three of the numbers 15,20 and 25 as factors?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

ANSWER : (C) 3

PROBLEM 20 :

What is the measure of the acute angle formed by the hands of a clock at 4:20 a.m.?
(A) $0^{\circ}$
(B) $5^{\circ}$
(C) $8^{\circ}$
(D) $10^{\circ}$
(E) $12^{\circ}$

ANSWER : (D) $10^{\circ}$

PROBLEM 21 :

The area of trapezoid $A B C D$ is $164 \mathrm{~cm}^{2}$. The altitude is $8 \mathrm{~cm}, A B$ is 10 cm , and $C D$ is 17 cm . What is $B C$, in centimeters?

(A) 9
(B) 10
(C) 12
(D) 15
(E) 20

ANSWER : (B) 10

PROBLEM 22 :

The following figures are composed of squares and circles. Which figure has a shaded region with largest area?

(A) A only

(B) B only

(C) C only

(D) both A and B

(E) all are equal

ANSWER : (C) C only

PROBLEM 23 :

In the pattern below, the cat moves clockwise through the four squares and the mouse moves counterclockwise through the eight exterior segments of the four squares.

If the pattern is continued, where would the cat and mouse be after the 247th move?

ANSWER : (A)

PROBLEM 24 :

A ship travels from point $A$ to point $B$ along a semicircular path, centered at Island $X$. Then it travels along a straight path from $B$ to $C$. Which of these graphs best shows the ship's distance from Island $X$ as it moves along its course?

ANSWER : (B)

PROBLEM 25 :

In the figure, the area of square $W X Y Z$ is $25 \mathrm{~cm}^{2}$. The four smaller squares have sides 1 cm long, either parallel to or coinciding with the sides of the large square. In $\triangle A B C, A B=A C$, and when $\triangle A B C$ is folded over side $\overline{B C}$, point $A$ coincides with $O$, the center of square $W X Y Z$. What is the area of $\triangle A B C$, in square centimeters?

(A) $\frac{15}{4}$
(B) $\frac{21}{4}$
(C) $\frac{27}{4}$
(D) $\frac{21}{2}$
(E) $\frac{27}{2}$

ANSWER : (C) $\frac{27}{4}$

PROBLEM 1 :

A circle and two distinct lines are drawn on a sheet of paper. What is the largest possible number of points of intersection of these figures?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6

ANSWER : (D) 5

PROBLEM 2 :

How many different combinations of $\$ 5$ bills and $\$ 2$ bills can be used to make a total of $\$ 17$ ? Order does not matter in this problem.

(A) 2
(B) 3
(C) 4
(D) 5
(E) 6

ANSWER : (A) 2

PROBLEM 3 :

What is the smallest possible average of four distinct positive even integers?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7

ANSWER : (C) 5

PROBLEM 4 :

The year 2002 is a palindrome (a number that reads the same from left to right as it does from right to left). What is the product of the digits of the next year after 2002 that is a palindrome?
(A) 0
(B) 4
(C) 9
(D) 16
(E) 25

ANSWER : (B) 4

PROBLEM 5 :

Carlos Montado was born on Saturday, November 9, 2002. On what day of the week will Carlos be 706 days old?
(A) Monday
(B) Wednesday
(C) Friday
(D) Saturday (E) Sunday

ANSWER : (C) Friday

PROBLEM 6 :

A birdbath is designed to overflow so that it will be self-cleaning. Water flows in at the rate of 20 milliliters per minute and drains at the rate of 18 milliliters per minute. One of these graphs shows the volume of water in the birdbath during the filling time and continuing into the overflow time. Which one is it?

(A) A
(B) B
(C) C
(D) D
(E) E

ANSWER : (A) A

PROBLEM 7 :

The students in Mrs. Sawyer's class were asked to do a taste test of five kinds of candy. Each student chose one kind of candy. A bar graph of their preferences is shown. What percent of her class chose candy E?

(A) 5
(B) 12
(C) 15
(D) 16
(E) 20

ANSWER : (E) 20

Problems 8,9 and 10 use the data found in the accompanying paragraph and table:

Juan's Old Stamping Grounds :

Juan organizes the stamps in his collection by country and by the decade in which they were issued. The prices he paid for them at a stamp shop were: Brazil and France, $6 ¢$ each, Peru $4 \phi$ each, and Spain 5¢ each. (Brazil and Peru are South American countries and France and Spain are in Europe.)

PROBLEM 8 :

How many of his European stamps were issued in the '80s?\
(A) 9
(B) 15
(C) 18
(D) 24
(E) 42

ANSWER : (D) 24

PROBLEM 9 :

His South American stamps issued before the '70s cost him
(A) $\$ 0.40$
(B) $\$ 1.06$
(C) $\$ 1.80$
(D) $\$ 2.38$
(E) $\$ 2.64$

ANSWER : (B) $\$ 1.06$

PROBLEM 10 :

The average price of his '70s stamps is closest to
(A) $3.5 ¢$
(B) $4 ¢$
(C) $4.5 ¢$
(D) $5 ¢$
(E) $5.5 ¢$

ANSWER : (E) $5.5 ¢$

PROBLEM 11 :

A sequence of squares is made of identical square tiles. The edge of each square is one tile length longer than the edge of the previous square. The first three squares are shown. How many more tiles does the seventh square require than the sixth?

(A) 11
(B) 12
(C) 13
(D) 14
(E) 15

ANSWER : (C) 13

PROBLEM 12 :

A board game spinner is divided into three regions labeled $A, B$ and $C$. The probability of the arrow stopping on region $A$ is $\frac{1}{3}$ and on region $B$ is $\frac{1}{2}$. The probability of the arrow stopping on region $C$ is

(A) $\frac{1}{12}$
(B) $\frac{1}{6}$
(C) $\frac{1}{5}$
(D) $\frac{1}{3}$
(E) $\frac{2}{5}$

ANSWER : (B) $\frac{1}{6}$

PROBLEM 13 :

For his birthday, Bert gets a box that holds 125 jellybeans when filled to capacity. A few weeks later, Carrie gets a larger box full of jellybeans. Her box is twice as high, twice as wide and twice as long as Bert's. Approximately, how many jellybeans did Carrie get?
(A) 250
(B) 500
(C) 625
(D) 750
(E) 1000

ANSWER : (E) 1000

PROBLEM 14 :

A merchant offers a large group of items at $30 \%$ off. Later, the merchant takes $20 \%$ off these sale prices and claims that the final price of these items is $50 \%$ off the original price. The total discount is
(A) $35 \%$
(B) $44 \%$
(C) $50 \%$
(D) $56 \%$
(E) $60 \%$

ANSWER : (B) $44 \%$

PROBLEM 15 :

Which of the following polygons has the largest area?

(A) A
(B) B
(C) C
(D) D
(E) E

ANSWER : (E) E

PROBLEM 16 :

Right isosceles triangles are constructed on the sides of a $3-4-5$ right triangle, as shown. A capital letter represents the area of each triangle. Which one of the following is true?

(A) $X+Z=W+Y$
(B) $W+X=Z$
(C) $3 X+4 Y=5 Z$
(D) $X+W=\frac{1}{2}(Y+Z)$
(E) $X+Y=Z$

ANSWER : (E) $X+Y=Z$

PROBLEM 17 :

In a mathematics contest with ten problems, a student gains 5 points for a correct answer and loses 2 points for an incorrect answer. If Olivia answered every problem and her score was 29 , how many correct answers did she have?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9

ANSWER : (C) 7

PROBLEM 18 :

Gage skated 1 hr 15 min each day for 5 days and 1 hr 30 min each day for 3 days. How long would he have to skate the ninth day in order to average 85 minutes of skating each day for the entire time?
(A) 1 hr

(B) 1 hr 10 min

(C) 1 hr 20 min

(D) 1 hr 40 min

(E) 2 hr

ANSWER : (E) 2 hr

PROBLEM 19 :

How many whole numbers between 99 and 999 contain exactly one 0 ?
(A) 72
(B) 90
(C) 144
(D) 162
(E) 180

ANSWER : (D) 162

PROBLEM 20 :

The area of triangle $X Y Z$ is 8 square inches. Points $A$ and $B$ are midpoints of congruent segments $\overline{X Y}$ and $\overline{X Z}$. Altitude $\overline{X C}$ bisects $\overline{Y Z}$. The area (in square inches) of the shaded region is

(A) $1 \frac{1}{2}$
(B) 2
(C) $2 \frac{1}{2}$
(D) 3
(E) $3 \frac{1}{2}$

ANSWER : (D) 3

PROBLEM 21 :

Harold tosses a nickel four times. The probability that he gets at least as many heads as tails is
(A) $\frac{5}{16}$
(B) $\frac{3}{8}$
(C) $\frac{1}{2}$
(D) $\frac{5}{8}$
(E) $\frac{11}{16}$

ANSWER : (E) $\frac{11}{16}$

PROBLEM 22 :

Six cubes, each an inch on an edge, are fastened together, as shown. Find the total surface area in square inches. Include the top, bottom and sides.

(A) 18
(B) 24
(C) 26
(D) 30
(E) 36

ANSWER : (C) 26

PROBLEM 23 :

A corner of a tiled floor is shown. If the entire floor is tiled in this way and each of the four corners looks like this one, then what fraction of the tiled floor is made of darker tiles?

(A) $\frac{1}{3}$
(B) $\frac{4}{9}$
(C) $\frac{1}{2}$
(D) $\frac{5}{9}$
(E) $\frac{5}{8}$

ANSWER : (B) $\frac{4}{9}$

PROBLEM 24 :

Miki has a dozen oranges of the same size and a dozen pears of the same size. Miki uses her juicer to extract 8 ounces of pear juice from 3 pears and 8 ounces of orange juice from 2 oranges. She makes a pear-orange juice blend from an equal number of pears and oranges. What percent of the blend is pear juice?
(A) 30
(B) 40
(C) 50
(D) 60
(E) 70

ANSWER : (B) 40

PROBLEM 25 : Loki, Moe, Nick and Ott are good friends. Ott had no money, but the others did. Moe gave Ott one-fifth of his money, Loki gave Ott one-fourth of his money and Nick gave Ott one-third of his money. Each gave Ott the same amount of money. What fractional part of the group's money does Ott now have?\
(A) $\frac{1}{10}$
(B) $\frac{1}{4}$
(C) $\frac{1}{3}$
(D) $\frac{2}{5}$
(E) $\frac{1}{2}$

ANSWER : (B) $\frac{1}{4}$

PROBLEM 1 :

Aunt Anna is 42 years old. Caitlin is 5 years younger than Brianna, and Brianna is half as old as Aunt Anna. How old is Caitlin?
(A) 15
(B) 16
(C) 17
(D) 21
(E) 37

ANSWER : (B) 16

PROBLEM 2 :

Which of these numbers is less than its reciprocal?
(A) -2
(B) -1
(C) 0
(D) 1
(E) 2

ANSWER : (A) -2

PROBLEM 3 :

How many whole numbers lie in the interval between $\frac{5}{3}$ and $2 \pi$ ?
(A) 2
(B) 3
(C) 4
(D) 5
(E) infinitely many

ANSWER : (D) 5

PROBLEM 4 :

In 1960 only $5 \%$ of the working adults in Carlin City worked at home. By 1970 the "at-home" work force had increased to $8 \%$. In 1980 there were approximately $15 \%$ working at home, and in 1990 there were $30 \%$. The graph that best illustrates this is:

ANSWER : (E)

PROBLEM 5 :

Each principal of Lincoln High School serves exactly one 3 -year term. What is the maximum number of principals this school could have during an 8 -year period?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 8

ANSWER : (C) 4

PROBLEM 6 :

Figure $A B C D$ is a square. Inside this square three smaller squares are drawn with side lengths as labeled. the area of the shaded L-shaped region is

(A) 7
(B) 10
(C) 12.5
(D) 14
(E) 15

ANSWER :(A) 7

PROBLEM 7 :

What is the minimum possible product of three different numbers of the set ${-8,-6,-4,0,3,5,7}$ ?
(A) -336
(B) -280
(C) -210
(D) -192
(E) 0

ANSWER : (B) -280

PROBLEM 8 :

Three dice with faces numbered 1 through 6 are stacked as shown. Seven of the eighteen faces are visible, leaving eleven faces hidden(back, bottom, between). The total number of dots NOT visible in this view is

(A) 21
(B) 22
(C) 31
(D) 41
(E) 53

ANSWER : (D) 41

PROBLEM 9 :

Three-digit powers of 2 and 5 are used in this cross-number puzzle. What is the only possible digit for the outlined square?

(A) 0
(B) 2
(C) 4
(D) 6
(E) 8

ANSWER : (D)

PROBLEM 10 :

Ara and Shea were once the same height. Since then Shea has grown $20 \%$ while Ara has grown half as many inches as Shea. Shea is now 60 inches tall. How tall, in inches, is Ara now?
(A) 48
(B) 51
(C) 52
(D) 54
(E) 55

ANSWER : (E) 55

PROBLEM 11 :

The number 64 has the property that it is divisible by its units digit. How many whole numbers between 10 and 50 have this property?
(A) 15
(B) 16
(C) 17
(D) 18
(E) 20

ANSWER : (C) 17

PROBLEM 12 :

A block wall 100 feet long and 7 feet high will be constructed using blocks that are 1 foot high and either 2 feet long or 1 foot long (no blocks may be cut). The vertical joins in the blocks must be staggered as shown, and the wall must be even on the ends. What is the smallest number of blocks needed to build this wall?

(A) 344
(B) 347
(C) 350
(D) 353
(E) 356

ANSWER : (D) 353

PROBLEM 13 :

In triangle $C A T$, we have $\angle A C T=\angle A T C$ and $\angle C A T=36^{\circ}$. If $\overline{T R}$ bisects $\angle A T C$, then $\angle C R T=$

(A) $16^{\circ}$
(B) $51^{\circ}$
(C) $72^{\circ}$
(D) $90^{\circ}$
(E) $108^{\circ}$

ANSWER : (C) $72^{\circ}$

PROBLEM 14 :

What is the units digit of $19^{19}+99^{99}$ ?
(A) 0
(B) 1
(C) 2
(D) 8
(E) 9

ANSWER : (D) 8

PROBLEM 15 :

Triangle $A B C, A D E$, and $E F G$ are all equilateral. Points $D$ and $G$ are midpoints of $\overline{A C}$ and $\overline{A E}$, respectively. If $A B=4$, what is the perimeter of figure $A B C D E F G$ ?

(A) 12
(B) 13
(C) 15
(D) 18
(E) 21

ANSWER : (C) 15

PROBLEM 16 :

In order for Mateen to walk a kilometer $(1000 \mathrm{~m})$ in his rectangular backyard, he must walk the length 25 times or walk its perimeter 10 times. What is the area of Mateen's backyard in square meters?
(A) 40
(B) 200
(C) 400
(D) 500
(E) 1000

ANSWER : (C) 400

PROBLEM 17 :

The operation $\otimes$ is defined for all nonzero numbers by $a \otimes b=\frac{a^{2}}{b}$. Determine $[(1 \otimes 2) \otimes 3]-[1 \otimes(2 \otimes 3)]$.
(A) $-\frac{2}{3}$
(B) $-\frac{1}{4}$
(C) 0
(D) $\frac{1}{4}$
(E) $\frac{2}{3}$

ANSWER : (A) $-\frac{2}{3}$

PROBLEM 18 :

Consider these two geoboard quadrilaterals. Which of the following statements is true?

(A) The area of quadrilateral I is more than the area of quadri- • lateral II.
(B) The area of quadrilateral I is less than the area of quadrilateral II.
(C) The quadrilaterals have the same area and the same perimeter.
(D) The quadrilaterals have the same area, but the perimeter of I is more than the perimeter of II.
(E) The quadrilaterals have the same area, but the perimeter of I is less than the perimeter of II.

ANSWER : (E) The quadrilaterals have the same area, but the perimeter of I is less than the perimeter of II.

PROBLEM 19 :

Three circular arcs of radius 5 units bound the region shown. $\operatorname{Arcs} A B$ and $A D$ are quarter-circles, and $\operatorname{arc} B C D$ is a semicircle. What is the area, in square units, of the region?

(A) 25
(B) $10+5 \pi$
(C) 50
(D) $50+5 \pi$
(E) $25 \pi$

ANSWER : (C) 50

PROBLEM 20 :

You have nine coins: a collection of pennies, nickels, dimes, and quarters having a total value of $\$ 1.02$, with at least one coin of each type. How many dimes must you have?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

ANSWER : (A) 1

PROBLEM 21 :

Keiko tosses one penny and Ephraim tosses two pennies. The probability that Ephraim gets the same number of heads that Keiko gets is
(A) $\frac{1}{4}$
(B) $\frac{3}{8}$
(C) $\frac{1}{2}$
(D) $\frac{2}{3}$
(E) $\frac{3}{4}$

ANSWER : (B) $\frac{3}{8}$

PROBLEM 22 :

A cube has edge length 2. Suppose that we glue a cube of edge length 1 on top of the big cube so that one of its faces rests entirely on the top face of the larger cube. The percent increase in the surface area (sides, top, and bottom) from the original cube to the new solid formed is closest to:

(A) 10
(B) 15
(C) 17
(D) 21
(E) 25

ANSWER : (C) 17

PROBLEM 23 :

There is a list of seven numbers. The average of the first four numbers is 5 , and the average of the last four numbers is 8 . If the average of all seven numbers is $6 \frac{4}{7}$, then the number common to both sets of four numbers is
(A) $5 \frac{3}{7}$
(B) 6
(C) $6 \frac{4}{7}$
(D) 7
(E) $7 \frac{3}{7}$

ANSWER : (B) 6

PROBLEM 24 :

If $\angle A=20^{\circ}$ and $\angle A F G=\angle A G F$, Then $\angle B+\angle D=$

(A) $48^{\circ}$
(B) $60^{\circ}$
(C) $72^{\circ}$
(D) $80^{\circ}$
(E) $90^{\circ}$

ANSWER : (D) $80^{\circ}$

PROBLEM 25 :

The area of rectangle $A B C D$ is 72 . If point $A$ and the midpoints of $\overline{B C}$ and $\overline{C D}$ are joined to form a triangle, the area of that triangle is

(A) 21
(B) 27
(C) 30
(D) 36
(E) 40

ANSWER : (B) 27

PROBLEM 1 :

Casey's shop class is making a golf trophy. He has to paint 300 dimples on a golf ball. If it takes him 2 seconds to paint one dimple, how many minutes will he need to do his job?

(A) 4
(B) 6
(C) 8
(D) 10
(E) 12

ANSWER : (D) 10

PROBLEM 2 :

I'm thinking of two whole numbers. Their product is 24 and their sum is 11 . What is the larger number?
(A) 3
(B) 4
(C) 6
(D) 8
(E) 12

ANSWER : (D) 8

PROBLEM 3 :

Granny Smith has $\$ 63$. Elberta has $\$ 2$ more than Anjou and Anjou has onethird as much as Granny Smith. How many dollars does Elberta have?
(A) 17
(B) 18
(C) 19
(D) 21
(E) 23

ANSWER : (E) 23

PROBLEM 4 :

The digits $1,2,3,4$ and 9 are each used once to form the smallest possible even five-digit number. The digit in the tens place is
(A) 1
(B) 2
(C) 3
(D) 4
(E) 9

ANSWER : (E) 9

PROBLEM 5 :

On a dark and stormy night Snoopy suddenly saw a flash of lightning. Ten seconds later he heard the sound of thunder. The speed of sound is 1088 feet per second and one mile is 5280 feet. Estimate, to the nearest half-mile, how far Snoopy was from the flash of lightning.
(A) 1
(B) $1 \frac{1}{2}$
(C) 2
(D) $2 \frac{1}{2}$
(E) 3

ANSWER : (C) 2

PROBLEM 6 :

Six trees are equally spaced along one side of a straight road. The distance from the first tree to the fourth is 60 feet. What is the distance in feet between the first and last trees?
(A) 90
(B) 100
(C) 105
(D) 120
(E) 140

ANSWER : (B) 100

Problems 7, 8 and 9 are about these kites.

PROBLEM 7 :

To promote her school's annual Kite Olympics, Genevieve makes a small kite and a large kite for a bulletin board display. The kites look like the one in the diagram. For her small kite Genevieve draws the kite on a one-inch grid. For the large kite she triples both the height and width of the entire grid.
What is the number of square inches in the area of the small kite?
(A) 21
(B) 22
(C) 23
(D) 24
(E) 25

ANSWER : (A) 21

PROBLEM 8 :

Genevieve puts bracing on her large kite in the form of a cross connecting opposite corners of the kite. How many inches of bracing material does she need?
(A) 30
(B) 32
(C) 35
(D) 38
(E) 39

ANSWER : (E) 39

PROBLEM 9 :

The large kite is covered with gold foil. The foil is cut from a rectangular piece that just covers the entire grid. How many square inches of waste material are cut off from the four corners?
(A) 63
(B) 72
(C) 180
(D) 189
(E) 264

ANSWER : (D) 189

PROBLEM 10 :

A collector offers to buy state quarters for $2000 \%$ of their face value. At that rate how much will Bryden get for his four state quarters?
(A) 20 dollars
(B) 50 dollars
(C) 200 dollars
(D) 500 dollars
(E) 2000 dollars

ANSWER : (A) 20 dollars

PROBLEM 11 :

Points $A, B, C$ and $D$ have these coordinates: $A(3,2), B(3,-2), C(-3,-2)$ and $D(-3,0)$. The area of quadrilateral $A B C D$ is

(A) 12
(B) 15
(C) 18
(D) 21
(E) 24

ANSWER : (C) 18

PROBLEM 12 :

If $a \otimes b=\frac{a+b}{a-b}$, then $(6 \otimes 4) \otimes 3==$
(A) 4
(B) 13
(C) 15
(D) 30
(E) 72

ANSWER : (A) 4

PROBLEM 13 :

Of the 36 students in Richelle's class, 12 prefer chocolate pie, 8 prefer apple, and 6 prefer blueberry. Half of the remaining students prefer cherry pie and half prefer lemon. For Richelle's pie graph showing this data, how many degrees should she use for cherry pie?
(A) 10
(B) 20
(C) 30
(D) 50
(E) 72

ANSWER : (D) 50

PROBLEM 14 :

Tyler has entered a buffet line in which he chooses one kind of meat, two different vegetables and one dessert. If the order of food items is not important, how many different meals might he choose?

• Meat: beef, chicken, pork
• Vegetables: baked beans, corn, potatoes, tomatoes
• Dessert: brownies, chocolate cake, chocolate pudding, ice cream
  (A) 4
  (B) 24
  (C) 72
  (D) 80
  (E) 144

ANSWER : (C) 72

PROBLEM 15 :

Homer began peeling a pile of 44 potatoes at the rate of 3 potatoes per minute. Four minutes later Christen joined him and peeled at the rate of 5 potatoes per minute. When they finished, how many potatoes had Christen peeled?
(A) 20
(B) 24
(C) 32
(D) 33
(E) 40

ANSWER : (A) 20

PROBLEM 16 :

A square piece of paper, 4 inches on a side, is folded in half vertically. Both layers are then cut in half parallel to the fold. Three new rectangles are formed, a large one and two small ones. What is the ratio of the perimeter of one of the small rectangles to the perimeter of the large rectangle?

(A) $\frac{1}{3}$
(B) $\frac{1}{2}$
(C) $\frac{3}{4}$
(D) $\frac{4}{5}$
(E) $\frac{5}{6}$

ANSWER : (E) $\frac{5}{6}$

PROBLEM 17 :

For the game show Who Wants To Be A Millionaire?, the dollar values of each question are shown in the following table (where $\mathrm{K}=1000$ ).

Between which two questions is the percent increase of the value the smallest?
(A) From 1 to 2v
(B) From 2 to 3
(C) From 3 to 4
(D) From 11 to 12
(E) From 14 to 15

ANSWER : (B) From 2 to 3

PROBLEM 18 :

Two dice are thrown. What is the probability that the product of the two numbers is a multiple of 5 ?
(A) $\frac{1}{36}$
(B) $\frac{1}{18}$
(C) $\frac{1}{6}$
(D) $\frac{11}{36}$
(E) $\frac{1}{3}$

ANSWER : (D) $\frac{11}{36}$

PROBLEM 19 :

Car M traveled at a constant speed for a given time. This is shown by the dashed line. Car N traveled at twice the speed for the same distance. If Car N's speed and time are shown as solid line, which graph illustrates this?

ANSWER : (D)

PROBLEM 20 :

Kaleana shows her test score to Quay, Marty and Shana, but the others keep theirs hidden. Quay thinks, "At least two of us have the same score." Marty thinks, "I didn't get the lowest score." Shana thinks, "I didn't get the highest score." List the scores from lowest to highest for Marty (M), Quay (Q) and Shana (S).
(A) $S, Q, M$
(B) Q,M,S
(C) Q,S,M
(D) $M, S, Q$
(E) $S, M, Q$

ANSWER : (A) $S, Q, M$

PROBLEM 21 :

The mean of a set of five different positive integers is 15 . The median is 18 . The maximum possible value of the largest of these five integers is
(A) 19
(B) 24
(C) 32
(D) 35
(E) 40

ANSWER : (D) 35

PROBLEM 22 :

On a twenty-question test, each correct answer is worth 5 points, each unanswered question is worth 1 point and each incorrect answer is worth 0 points. Which of the following scores is NOT possible?
(A) 90
(B) 91
(C) 92
(D) 95
(E) 97

ANSWER : (E) 97

PROBLEM 23 :

Points $R, S$ and $T$ are vertices of an equilateral triangle, and points $X, Y$ and $Z$ are midpoints of its sides. How many noncongruent triangles can be drawn using any three of these six points as vertices?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 20

ANSWER : (D) 4

PROBLEM 24 :

Each half of this figure is composed of 3 red triangles, 5 blue triangles and 8 white triangles. When the upper half is folded down over the centerline, 2 pairs of red triangles coincide, as do 3 pairs of blue triangles. There are 2 red-white pairs. How many white pairs coincide?

(A) 4
(B) 5
(C) 6
(D) 7
(E) 9

ANSWER : (B) 5

PROBLEM 25 :

There are 24 four-digit whole numbers that use each of the four digits 2,4 , 5 and 7 exactly once. Only one of these four-digit numbers is a multiple of another one. Which of the following is it?
(A) 5724
(B) 7245
(C) 7254

(D) 7425

(E) 7542

ANSWER : (D) 7425

PROBLEM 1 :

The eight-pointed star, shown in the figure below, is a popular quilting pattern. What percent of the entire $4 \times 4$ grid is covered by the star?

(A) 40
(B) 50
(C) 60
(D) 75
(E) 80

ANSWER :

(B) 50

PROBLEM 2 :

The table below shows the ancient Egyptian hieroglyphs that were used to represent different numbers.

For example, the number 32 was represented by the hieroglyphs $\cap \cap \cap |$. What number is represented by the following combination of hieroglyphs?

(A) 1,423
(B) 10,423
(C) 14,023
(D) 14,203
(E) 14,230

ANSWER :

(B) 10,423

PROBLEM 3 :

Buffalo Shuffle-o is a card game in which all the cards are distributed evenly among all players at the start of the game. When Annika and 3 of her friends play Buffalo Shuffle-o, each player is dealt 15 cards. Suppose 2 more friends join the next game. How many cards will be dealt to each player?

(A) 8
(B) 9
(C) 10
(D) 11
(E) 12

ANSWER :

(C) 10

PROBLEM 4 :

Lucius is counting backward by 7 s . His first three numbers are 100,93 , and 86 . What is his 10 th number?
(A) 30
(B) 37
(C) 42
(D) 44
(E) 47

ANSWER :

(B) 37

PROBLEM 5 :

Betty drives a truck to deliver packages in a neighborhood whose street map is shown below. Betty starts at the factory (labled $F$ ) and drives to location $A$, then $B$, then $C$, before returning to $F$. What is the shortest distance, in blocks, she can drive to complete the route?

(A) 20
(B) 23
(C) 24
(D) 26
(E) 28

ANSWER :

(C) 24

PROBLEM 6 :

Sekou writes the numbers $15,16,17,18,19$. After he erases one of his numbers, the sum of the remaining four numbers is a multiple of 4 . Which number did he erase?
(A) 15
(B) 16
(C) 17
(D) 18
(E) 19

ANSWER :

(C) 17

PROBLEM 7 :

On the most recent exam on Prof. Xochi's class,

• 5 students earned a score of at least $95 \%$,
• 13 students earned a score of at least $90 \%$,
• 27 students earned a score of at least $85 \%$,
• 50 students earned a score of at least $80 \%$,

How many students earned a score of at least $80 \%$ and less than $90 \%$ ?
(A) 8
(B) 14
(C) 22
(D) 37
(E) 45

ANSWER :

(D) 37

PROBLEM 8 :

Isaiah cuts open a cardboard cube along some of its edges to form the flat shape shown on the right, which has an area of 18 square centimeters. What is the volume of the cube in cubic centimeters?

(A) $3 \sqrt{3}$
(B) 6
(C) 9
(D) $6 \sqrt{3}$
(E) $9 \sqrt{3}$

ANSWER :

(A) $3 \sqrt{3}$

PROBLEM 9 :

Ningli looks at the 6 pairs of numbers directly across from each other on a clock. She takes the average of each pair of numbers. What is the average of the resulting 6 numbers?

(A) 5
(B) 6.5
(C) 8
(D) 9.5
(E) 12

ANSWER :

(B) 6.5

PROBLEM 10 :

In the figure below, $A B C D$ is a rectangle with sides of length $A B=5$ inches and $A D=3$ inches. Rectangle $A B C D$ is rotated $90^{\circ}$ clockwise around the midpoint of side $D C$ to give a second rectangle. What is the total area, in square inches, covered by the two overlapping rectangles?

(A) 21
(B) 22.25
(C) 23
(D) 23.75
(E) 25

ANSWER :

(D) 23.75

PROBLEM 11 :

A tetromino consists of four squares connected along their edges. There are five possible tetromino shapes, $I, O, L, T$, and $S$, shown below, which can be rotated or flipped over. Three tetrominoes are used to completely cover a $3 \times 4$ rectangle. At least one of the tiles is an $S$ tile. What are the other two tiles?

(A) $I$ and $L$
(B) $I$ and $T$
(C) $L$ and $L$
(D) $L$ and $S$
(E) $O$ and $T$

ANSWER :

(C) $L$ and $L$

PROBLEM 12 :

The region shown below consists of 24 squares, each with side length 1 centimeter. What is the area, in square centimeters, of the largest circle that can fit inside the region, possibly touching the boundaries?

(A) $3 \pi$
(B) $4 \pi$
(C) $5 \pi$
(D) $6 \pi$
(E) $8 \pi$

ANSWER :

(C) $5 \pi$

PROBLEM 13 :

Each of the even numbers $2,4,6, \ldots, 50$ is divided by 7 . The remainders are recorded. Which histogram displays the number of times each remainder occurs?

ANSWER :

(A)

PROBLEM 14 :

A number $N$ is inserted into the list $2,6,7,7,28$. The mean is now twice as great as the median. What is $N$ ?
(A) 7
(B) 14
(C) 20
(D) 28
(E) 34

ANSWER :

(E) 34

PROBLEM 15 :

Kei draws a 6 -by- 6 grid. He colors 13 of the unit squares silver and the remaining squares gold. Kei then folds the grid in half vertically, forming pairs of overlapping unit squares. Let $m$ and $M$ equal the least and greatest possible number of gold-on-gold pairs, respectively. What is the value of $m+M$ ?

(A) 12
(B) 14
(C) 16
(D) 18
(E) 20

ANSWER :

(C) 16

PROBLEM 16 :

Five distinct integers from 1 to 10 are chosen, and five distinct integers from 11 to 20 are chosen. No two numbers differ by exactly 10 . What is the sum of the ten chosen numbers?
(A) 95
(B) 100
(C) 105
(D) 110
(E) 115

ANSWER :

(C) 105

PROBLEM 17 :

In the land of Markovia, there are three cities: $A, B$, and $C$. There are 100 people who live in $A, 120$ who live in $B$, and 160 who live in $C$. Everyone works in one of the three cities, and a person may work in the same city where they live. In the figure below, an arrow pointing from one city to another is labeled with the fraction of people living in the first city who work in the second city. (For example, $\frac{1}{4}$ of the people who live in $A$ work in $B$.) How many people work in $A$ ?

(A) 55
(B) 60
(C) 85
(D) 115
(E) 160

ANSWER :

(D) 115

PROBLEM 18 :

The circle shown below on the left has a radius of 1 unit. The region between the circle and the inscribed square is shaded. In the circle shown on the right, one quarter of the region between the circle and the inscribed square is shaded. The shaded regions in the two circles have the same area. What is the radius $R$, in units, of the circle on the right?

(A) $\sqrt{2}$
(B) 2
(C) $2 \sqrt{2}$
(D) 4
(E) $4 \sqrt{2}$

ANSWER :

(B) 2

PROBLEM 19 :

Two towns, $A$ and $B$, are connected by a straight road that is 15 miles long. Travelling from city $A$ to town $B$, the speed limit changes every 5 miles: from 25 to 40 to 20 miles per hour (mph). Two cars, one at town $A$ and one at town $B$, start moving toward each other at the same time. They drive at exactly the speed limit in each portion of the road. How far from town $A$, in miles, will the two cars meet?

(A) 7.75
(B) 8
(C) 8.25
(D) 8.5
(E) 8.75

ANSWER :

(D) 8.5

PROBLEM 20 :

Sarika, Dev, and Rajiv are sharing a large block of cheese. They take turns cutting off half of what remains and eating it: first Sarika eats half of the cheese, then Dev eats half of the remaining half, then Rajiv eats half of what remains, then back to Sarika, and so on. They stop when the cheese is too small to see. About what fraction of the original block of cheese does Sarika eat in total?
(A) $\frac{4}{7}$
(B) $\frac{3}{5}$
(C) $\frac{2}{3}$
(D) $\frac{3}{4}$
(E) $\frac{7}{8}$

ANSWER :

(A) $\frac{4}{7}$.

PROBLEM 21 :

The Konigsberg School has assigned grades 1 through 7 to pods $A$ through $G$, one grade per pod. Some of the pods are connected by walkways, as shown in the figure below. The school noticed that each pair of connected pods has been assigned grades differing by 2 or more grade levels. (For example, grades 1 and 2 will not be in pods directly connected by a walkway.) What is the sum of the grade levels assigned to pods $C, E$, and $F$ ?

(A) 12
(B) 13
(C) 14
(D) 15
(E) 16

ANSWER :

(A) 12

PROBLEM 22 :

A classroom has a row of 35 coat hooks. Paulina likes coats to be equally spaced, so that there is the same number of empty hooks before the first coat, after the last coat, and between every coat and the next one. Suppose there is at least 1 coat and at least 1 empty hook. How many different numbers of coats can satisfy Paulina's pattern?

(A) 2
(B) 4
(C) 5
(D) 7
(E) 9

ANSWER :

(D) 7

PROBLEM 23 :

How many four-digit numbers have all three of the following properties?
(I) The tens and ones digit are both 9 .
(II) The number is 1 less than a perfect square.
(III) The number is the product of exactly two prime numbers.
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4

ANSWER :

(B) 1

PROBLEM 24 :

In trapezoid $A B C D$, angles $B$ and $C$ measure $60^{\circ}$ and $A B=D C$. The side lengths are all positive integers, and the perimeter of $A B C D$ is 30 units. How many non-congruent trapezoids satisfy all of these conditions?

(A) 0
(B) 1
(C) 2
(D) 3
(E) 4

ANSWER :

(E) 4

PROBLEM 25 :

Makayla finds all the possible ways to draw a path in a $5 \times 5$ diamond-shaped grid. Each path starts at the bottom of the grid and ends at the top, always moving one unit northeast or northwest. She computes the area of the region between each path and the right side of the grid. Two examples are shown in the figures below. What is the sum of the areas determined by all possible paths?

(A) 2520
(B) 3150
(C) 3840
(D) 4730
(E) 5050

ANSWER :

(B) 3150

PROBLEM 1 :

The Math Team designed a logo shaped like a multiplication symbol, shown below on a grid of 1-inch squares. What is the area of the logo in square inches?

(A) 10
(B) 12
(C) 13
(D) 14
(E) 15

ANSWER :

(A) 10

PROBLEM 2 :

Consider these two operations:

$$
\begin{aligned}
a \bullet b & =a^2-b^2 \
a \star b & =(a-b)^2
\end{aligned}
$$

What is the output of $(5 \diamond 3) \star 6$ ?
(A) -20
(B) 4
(C) 16
(D) 100
(E) 220

ANSWER :

(D) 100

PROBLEM 3 :

When three positive integers $a, b$, and $c$ are multiplied together, their product is 100 . Suppose $a<b<c$. In how many ways can the numbers be chosen?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4

ANSWER :

(E) 4

PROBLEM 4 :

The letter $\mathbf{M}$ in the figure below is first reflected over the line $q$ and then reflected over the line $p$. What is the resulting image?

ANSWER :

(E)

PROBLEM 5 :

Anna and Bella are celebrating their birthdays together. Five years ago, when Bella turned 6 years old, she received a newborn kitten as a birthday present. Today the sum of the ages of the two children and the kitten is 30 years. How many years older than Bella is Anna?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

ANSWER :

(C) 3

PROBLEM 6 :

Three positive integers are equally spaced on a number line. The middle number is 15 , and the largest number is 4 times the smallest number. What is the smallest of these three numbers?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8

ANSWER :

(C) 6

PROBLEM 7 :

When the World Wide Web first became popular in the 1990 s, download speeds reached a maximum of about 56 kilobits per second.
Approximately how many minutes would the download of a 4.2 -megabyte song have taken at that speed? (Note that there are 8000 kilobits in a megabyte.)
(A) 0.6
(B) 10
(C) 1800
(D) 7200
(E) 36000

ANSWER :

(B) 10

PROBLEM 8 :

What is the value of

$$
\frac{1}{3} \cdot \frac{2}{4} \cdot \frac{3}{5} \cdots \frac{18}{20} \cdot \frac{19}{21} \cdot \frac{20}{22} ?
$$

(A) $\frac{1}{462}$
(B) $\frac{1}{231}$
(C) $\frac{1}{132}$
(D) $\frac{2}{213}$
(E) $\frac{1}{22}$

ANSWER :

(B) $\frac{1}{231}$.

PROBLEM 9 :

A cup of boiling water $\left(212^{\circ} \mathrm{F}\right)$ is placed to cool in a room whose temperature remains constant at $68^{\circ} \mathrm{F}$. Suppose the difference between the water temperature and the room temperature is halved every 5 minutes. What is the water temperature, in degrees Fahrenheit, after 15 minutes?
(A) 77
(B) 86
(C) 92
(D) 98
(E) 104

ANSWER :

(B) 86

PROBLEM 10 :

One sunny day, Ling decided to take a hike in the mountains. She left her house at 8 AM , drove at a constant speed of 45 miles per hour, and arrived at the hiking trail at 10 AM . After hiking for 3 hours, Ling drove home at a constant speed of 60 miles per hour. Which of the following graphs best illustrates the distance between Ling's car and her house over the course of her trip?

ANSWER :

(E)

PROBLEM 11 :

Henry the donkey has a very long piece of pasta. He takes a number of bites of pasta, each time eating 3 inches of pasta from the middle of one piece. In the end, he has 10 pieces of pasta whose total length is 17 inches. How long, in inches, was the piece of pasta he started with?
(A) 34
(B) 38
(C) 41
(D) 44
(E) 47

ANSWER :

(D) 44

PROBLEM 12 :

The arrows on the two spinners shown below are spun. Let the number $N$ equal 10 times the number on Spinner A , added to the number on Spinner B. What is the probability that $N$ is a perfect square number?

(A) $\frac{1}{16}$
(B) $\frac{1}{8}$
(C) $\frac{1}{4}$
(D) $\frac{3}{8}$
(E) $\frac{1}{2}$

ANSWER :

(B) $\frac{1}{8}$

PROBLEM 13 :

How many positive integers can fill the blank in the sentence below?
"One positive integer is ____ more than twice another, and the sum of the two numbers is $28 . "$

(A) 6
(B) 7
(C) 8
(D) 9
(E) 10

ANSWER :

(D) 9

PROBLEM 14 :

In how many ways can the letters in BEEKEEPER be rearranged so that two or more Es do not appear together?
(A) 1
(B) 4
(C) 12
(D) 24
(E) 120

ANSWER :

(D) 24

PROBLEM 15 :

Laszlo went online to shop for black pepper and found thirty different black pepper options varying in weight and price, shown in the scatter plot below. In ounces, what is the weight of the pepper that offers the lowest price per ounce?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

ANSWER :

(C) 3

PROBLEM 16 :

Four numbers are written in a row. The average of the first two is 21 , the average of the middle two is 26 , and the average of the last two is 30 . What is the average of the first and last of the numbers?
(A) 24
(B) 25
(C) 26
(D) 27
(E) 28

ANSWER :

(B) 25

PROBLEM 17 :

If $n$ is an even positive integer, the double factorial notation $n!!$ represents the product of all the even integers from 2 to $n$. For example, $8!!=2 \cdot 4 \cdot 6 \cdot 8$. What is the units digit of the following sum?

$$
2!!+4!!+6!!+\cdots+2018!!+2020!!+2022!!
$$

(A) 0
(B) 2
(C) 4
(D) 6
(E) 8

ANSWER :

(B) 2

PROBLEM 18 :

The midpoints of the four sides of a rectangle are $(-3,0),(2,0),(5,4)$, and $(0,4)$. What is the area of the rectangle?
(A) 20
(B) 25
(C) 40
(D) 50
(E) 80

ANSWER :

(C) 40

PROBLEM 19 :

Mr. Ramos gave a test to his class of 20 students. The dot plot below shows the distribution of test scores.

Later Mr. Ramos discovered that there was a scoring error on one of the questions. He regraded the tests, awarding some of the students 5 extra points, which increased the median test score to 85 . What is the minimum number of students who received extra points?
(Note that the median test score equals the average of the 2 scores in the middle if the 20 test scores are arranged in increasing order.)
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6

ANSWER :

(C) 4

PROBLEM 20 :

The grid below is to be filled with integers in such a way that the sum of the numbers in each row and the sum of the numbers in each column are the same. Four numbers are missing. The number $x$ in the lower left corner is larger than the other three missing numbers. What is the smallest possible value of $x$ ?

(A) -1
(B) 5
(C) 6
(D) 8
(E) 9

ANSWER :

(D) 8

PROBLEM 21 :

Steph scored 15 baskets out of 20 attempts in the first half of a game, and 10 baskets out of 10 attempts in the second half. Candace took 12 attempts in the first half and 18 attempts in the second. In each half, Steph scored a higher percentage of baskets than Candace. Surprisingly they ended with the same overall percentage of baskets scored. How many more baskets did Candace score in the second half than in the first?

(A) 7
(B) 8
(C) 9
(D) 10
(E) 11

ANSWER :

(C) 9

PROBLEM 22 :

A bus takes 2 minutes to drive from one stop to the next, and waits 1 minute at each stop to let passengers board. Zia takes 5 minutes to walk from one bus stop to the next. As Zia reaches a bus stop, if the bus is at the previous stop or has already left the previous stop, then she will wait for the bus. Otherwise she will start walking toward the next stop. Suppose the bus and Zia start at the same time toward the library, with the bus 3 stops behind. After how many minutes will Zia board the bus?

(A) 17
(B) 19
(C) 20
(D) 21
(E) 23

ANSWER :

(A) 17

PROBLEM 23 :

A △ or $\bigcirc$ is placed in each of the nine squares in a 3 -by- 3 grid. Shown below is a sample configuration with three $\triangle s$ in a line.

How many configurations will have three △ s in a line and three □ s in a line?
(A) 39
(B) 42
(C) 78
(D) 84
(E) 96

ANSWER :

D) 84

PROBLEM 24 :

The figure below shows a polygon $A B C D E F G H$, consisting of rectangles and right triangles. When cut out and folded on the dotted lines, the polygon forms a triangular prism. Suppose that $A H=E F=8$ and $G H=14$. What is the volume of the prism?

(A) 112
(B) 128
(C) 192
(D) 240
(E) 288

ANSWER :

(C) 192

PROBLEM 25 :

A cricket randomly hops between 4 leaves, on each turn hopping to one of the other 3 leaves with equal probability. After 4 hops what is the probability that the cricket has returned to the leaf where it started?

(A) $\frac{2}{9}$
(B) $\frac{19}{80}$
(C) $\frac{20}{81}$
(D) $\frac{1}{4}$
(E) $\frac{7}{27}$

ANSWER :

(E) $\frac{7}{27}$

PROBLEM 1 :

Which of the following values is largest?
(A) $2+0+1+7$
(B) $2 \times 0+1+7$
(C) $2+0 \times 1+7$
(D) $2+0+1 \times 7$
(E) $2 \times 0 \times 1 \times 7$

ANSWER : (A) $2+0+1+7$

PROBLEM 2 :

Alicia, Brenda, and Colby were the candidates in a recent election for student president. The pie chart below shows how the votes were distributed among the three candidates. If Brenda received 36 votes, then how many votes were cast all together?

(A) 70
(B) 84
(C) 100
(D) 106
(E) 120

ANSWER :(E) 120

PROBLEM 3 :

What is the value of the expression $\sqrt{16 \sqrt{8 \sqrt{4}}}$ ?
(A) 4
(B) $4 \sqrt{2}$
(C) 8
(D) $8 \sqrt{2}$
(E) 16

ANSWER : (C) 8

PROBLEM 4 :

When 0.000315 is multiplied by $7,928,564$ the product is closest to which of the following?
(A) 210
(B) 240
(C) 2100
(D) 2400
(E) 24000

ANSWER : (D) 2400

PROBLEM 5 :

What is the value of the expression $\frac{1 \cdot 2 \cdot 3 \cdot 4 \cdot 5 \cdot 6 \cdot 7 \cdot 8}{1+2+3+4+5+6+7+8}$ ?
(A) 1020
(B) 1120
(C) 1220
(D) 2240
(E) 3360

ANSWER : (B) 1120

PROBLEM 6 :

If the degree measures of the angles of a triangle are in the ratio $3: 3: 4$, what is the degree measure of the largest angle of the triangle?
(A) 18
(B) 36
(C) 60
(D) 72
(E) 90

ANSWER : (D) 72

PROBLEM 7 :

Let $\boldsymbol{Z}$ be a 6 -digit positive integer, such as 247247 , whose first three digits are the same as its last three digits taken in the same order. Which of the following numbers must also be a factor of $Z$ ?
(A) 11
(B) 19
(C) 101
(D) 111
(E) 1111

ANSWER : (A) 11

PROBLEM 8 :

Malcolm wants to visit Isabella after school today and knows the street where she lives but doesn't know her house number. She tells him, "My house number has two digits, and exactly three of the following four statements about it are true."
(1) It is prime.

(2) It is even.
(3) It is divisible by 7 .
(4) One of its digits is 9 .

This information allows Malcolm to determine Isabella's house number. What is its units digit?
(A) 4
(B) 6
(C) 7
(D) 8
(E) 9

ANSWER : (D) 8

PROBLEM 9 :

All of Marcy's marbles are blue, red, green, or yellow. One third of her marbles are blue, one fourth of them are red, and six of them are green. What is the smallest number of yellow marbles that Marcy could have?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

ANSWER : (D) 4

PROBLEM 10 :

A box contains five cards, numbered $1,2,3,4$, and 5 . Three cards are selected randomly without replacement from the box. What is the probability that 4 is the largest value selected?
(A) $\frac{1}{10}$
(B) $\frac{1}{5}$
(C) $\frac{3}{10}$
(D) $\frac{2}{5}$
(E) $\frac{1}{2}$

ANSWER : (D) $\frac{2}{5}$

PROBLEM 11 :

A square-shaped floor is covered with congruent square tiles. If the total number of tiles that lie on the two diagonals is 37 , how many tiles cover the floor?
(A) 148
(B) 324
(C) 361
(D) 1296
(E) 1369

ANSWER : (C) 361

PROBLEM 12 :

The smallest positive integer greater than 1 that leaves a remainder of 1 when divided by 4,5 , and 6 lies between which of the following pairs of numbers?
(A) 2 and 19
(B) 20 and 39
(C) 40 and 59
(D) 60 and 79
(E) 80 and 124

ANSWER : (D) 60 and 79

PROBLEM 13 :

Peter, Emma, and Kyler played chess with each other. Peter won 4 games and lost 2 games. Emma won 3 games and lost 3 games. If Kyler lost 3 games, how many games did he win?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4

ANSWER : (B) 1

PROBLEM 14 :

Chloe and Zoe are both students in Ms. Demeanor's math class. Last night they each solved half of the problems in their homework assignment alone and then solved the other half together. Chloe had correct answers to only $80 \%$ of the problems she solved alone, but overall $88 \%$ of her answers were correct. Zoe had correct answers to $90 \%$ of the problems she solved alone. What was Zoe's overall percentage of correct answers?
(A) 89
(B) 92
(C) 93
(D) 96
(E) 98

ANSWER : (C) 93

PROBLEM 15 :

In the arrangement of letters and numerals below, by how many different paths can one spell AMC8? Beginning at the A in the middle, a path allows only moves from one letter to an adjacent (above, below, left, or right, but not diagonal) letter. One example of such a path is traced in the picture.

(A) 8
(B) 9
(C) 12
(D) 24
(E) 36

ANSWER : (D) 24

PROBLEM 16 :

In the figure below, choose point $D$ on $\overline{B C}$ so that $\triangle A C D$ and $\triangle A B D$ have equal perimeters. What is the area of $\triangle A B D$ ?

(A) $\frac{3}{4}$
(B) $\frac{3}{2}$
(C) 2
(D) $\frac{12}{5}$
(E) $\frac{5}{2}$

ANSWER : (D) $\frac{12}{5}$

PROBLEM 17 :

Starting with some gold coins and some empty treasure chests, I tried to put 9 gold coins in each treasure chest, but that left 2 treasure chests empty. So instead I put 6 gold coins in each treasure chest, but then I had 3 gold coins left over. How many gold coins did I have?
(A) 9
(B) 27
(C) 45
(D) 63
(E) 81

ANSWER : (C) 45

PROBLEM 18 :

In the non-convex quadrilateral $A B C D$ shown below, $\angle B C D$ is a right angle, $A B=12, B C=4, C D=3$, and $A D=13$.

What is the area of quadrilateral $A B C D$ ?
(A) 12
(B) 24
(C) 26
(D) 30
(E) 36

ANSWER : (B) 24

PROBLEM 19 :

For any positive integer $M$, the notation $M!$ denotes the product of the integers 1 through $M$. What is the largest integer $n$ for which $5^n$ is a factor of the sum $98!+99!+100!$ ?
(A) 23
(B) 24
(C) 25
(D) 26
(E) 27

ANSWER : (D) 26

PROBLEM 20 :

An integer between 1000 and 9999 , inclusive, is chosen at random. What is the probability that it is an odd integer whose digits are all distinct?
(A) $\frac{14}{75}$
(B) $\frac{56}{225}$
(C) $\frac{107}{400}$
(D) $\frac{7}{25}$
(E) $\frac{9}{25}$

ANSWER : (B) $\frac{56}{225}$

PROBLEM 21 :

Suppose $a, b$, and are nonzero real numbers, and . What are the possible value(s) for $\frac{a}{|a|}+\frac{b}{|b|}+\frac{c}{|c|}+\frac{a b c}{|a b c|}$ ?
(A) 0
(B) 1 and - 1
(C) 2 and - 2
(D) 0,2, and - 2
(E) 0 , 1 , and -1

ANSWER : (A) 0

PROBLEM 22 :

In the right triangle $A B C, A C=12, B C=5$, and angle $C$ is a right angle. A semicircle is inscribed in the triangle as shown. What is the radius of the semicircle?

(A) $\frac{7}{6}$
(B) $\frac{13}{5}$
(C) $\frac{59}{18}$
(D) $\frac{10}{3}$
(E) $\frac{60}{13}$

ANSWER : (D) $\frac{10}{3}$

PROBLEM 23 :

Each day for four days, Linda traveled for one hour at a speed that resulted in her traveling one mile in an integer number of minutes. Each day after the first, her speed decreased so that the number of minutes to travel one mile increased by 5 minutes over the preceding day. Each of the four days, her distance traveled was also an integer number of miles. What was the total number of miles for the four trips?
(A) 10
(B) 15
(C) 25
(D) 50
(E) 82

ANSWER : (C) 25

PROBLEM 24 :

Mrs. Sanders has three grandchildren, who call her regularly. One calls her every three days, one calls her every four days, and one calls her every five days. All three called her on December 31, 2021. On how many days during the next year did she not receive a phone call from any of her grandchildren?
(A) 78
(B) 80
(C) 144
(D) 146
(E) 152

ANSWER : (D) 146

PROBLEM 25 :

In the figure shown, $\overline{U S}$ and $\overline{U T}$ are line segments each of length 2 , and $m \angle T U S=60^{\circ}$. Arcs $\overparen{\mathrm{TR}}$ and $\overparen{\mathrm{SR}}$ are each one-sixth of a circle with radius 2 . What is the area of the region shown?

ANSWER : (B)