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2000 UTAH STATEMATHEMATICSCONTEST
PRELIMINARY TEST
GRADES 7-9
Each correct answer is awarded 4 points. Each incorrect answer
is worth 1 point. Unanswered
questions are worth 0 points. Calculators are not to be
used.
1. How many liters of ten percent salt solution must be added to
ten liters of five percentsalt solution to obtain seven percent
salt solution?
(a)20
3(b) 7 (c) 6.5 (d) 35 (e) none of these
2. One 16-inch diameter pizza has area equal to that of how many
8-inch diameter pizzas?
(a) 2 (b) 2.5 (c) 4 (d) 3.75 (e) none of these
3. The greatest common divisor of 12 and 42 is
(a) 2 (b) 3 (c) 4 (d) 6 (e) none of these
4. Jim and Elaine are riding on bicycles, heading directly
towards each other, starting two
miles apart. Jim rides at fifteen miles per hour, and Elaine
rides at ten miles per hour.They have a dog, which runs back and
forth between them, starting at Elaine,
immediately turning around upon reaching either child and
traveling to the other,averaging speed of twenty five miles an hour
in each trip between the two children. Findthe total distance
traveled by the dog by the time the two children meet.
(a)7
3miles (b) 2 miles (c) infinite (d)
2
5mile (e) none of these
5. If 2n is even, which of the following is odd?
(a)3
n (b) n (c) 2
2n
(d)2
3n (e) none of these
6. 27 3/2 =
(a) 3 (b) 4 (c) 9 (d) 81 (e) none of these
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7. If a square has an area of 2 then its diagonal has length
(a) 2 (b)2
51+(c) 4 (d) 1 (e) none of these
8. The perimeter of a circle of diameter one equals
(a) 3 (b) 2.71 (c) 5 (d)7
22(e) none of these
9. The area of a circle of circumference c and radius
requals
(a) 7
22 2r(b) 9
2c
(c)r
c2
(d) 2
cr
(e) none of these
10. A bag contains three green marbles, two red marbles and four
blue marbles. A man
draws three marbles from the bag at random. What is the
probability of drawing out one
marble of each color?
(a)1
3(b)
2
7(c)
17
20(d)
17
24(e) none of these
11. Let 120! Denote (120)(119)(118) . . . (3)(2)(1). What is the
smallest prime factor of
120! + 91?
(a) 3 (b) 2 (c) 7 (d) 137 (e) none of these
12. Let Ebe the mid-point of the circular arc AECwith center at
corner B of square ABCD.IfAB = 1, then DE=
(a) 12
2
(b) 2
2
(c) 2
1
(d) 12
(e) none of these
13. 15% of what number is 3?
(a) 45 (b) 85 (c) 20 (d) 25 (e) none of these
