Question 1

Aunt Anna is years old. Caitlin is years younger than Brianna, and Brianna is half as old as Aunt Anna. How old is Caitlin?

Solution

---

Question 2

Which of these numbers is less than its reciprocal?

Solution

---

Question 3

How many whole numbers lie in the interval between and

Solution

---

Question 4

In only of the working adults in Carlin City worked at home. By the "at-home" work force increased to . In there were approximately working at home, and in there were . The graph that best illustrates this is

Solution

---

Question 5

Each principal of Lincoln High School serves exactly one -year term. What is the maximum number of principals this school could have during an -year period?

Solution

---

Question 6

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

Solution

---

Question 7

What is the minimum possible product of three different numbers of the set

?

Solution

---

Question 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

Solution

---

Question 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?

Solution

---

Question 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?

Solution

---

Question 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?

Solution

---

Question 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?

Solution

---

Question 13

In triangle , we have

and

. If bisects , then

Solution

---

Question 14

What is the units digit of ?

Solution

---

Question 15

Triangles , , and are all equilateral. Points and are midpoints of and , respectively. If , what is the perimeter of figure

?

Solution

---

Question 16

In order for Mateen to walk a kilometer (1000m) 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?

Solution

---

Question 17

The operation is defined for all nonzero numbers by . Determine

.

Solution

---

Question 18

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

Solution

---

Question 19

Three circular arcs of radius 5 units bound the region shown. Arcs and are quarter-circles, and arc is a semicircle. What is the area, in square units, of the region?

Solution

---

Question 20

You have nine coins: a collection of pennies, nickels, dimes, and quarters having a total value of $ , with at least one coin of each type. How many dimes must you have?

Solution

---

Question 21

Keiko tosses one penny and Ephraim tosses two pennies. The probability that Ephraim gets the same number of heads that Keiko gets is

Solution

---

Question 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

Solution

---

Question 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 , then the number common to both sets of four numbers is

Solution

---

Question 24

If and

, then

Solution

---

Question 25

The area of rectangle is 72. If point and the midpoints of and are joined to form a triangle, the area of that triangle is

Solution

Answer Keys

Question 1: B
Question 2: A
Question 3: D
Question 4: E
Question 5: C
Question 6: A
Question 7: B
Question 8: D
Question 9: D
Question 10: E
Question 11: C
Question 12: D
Question 13: C
Question 14: D
Question 15: C
Question 16: C
Question 17: A
Question 18: E
Question 19: C
Question 20: A
Question 21: B
Question 22: C
Question 23: B
Question 24: D
Question 25: B