MATHCOUNTS 1993-1994 State Competition Countdown Round

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MATHCOUNTS1993-1994State CompetitionCountdown
Round
2
A man digs a hole 6 inches deep for a post to
hold his mailbox. If the square base of the post
is 4 in. x 4 in., how many cubic inches of dirt
will be displaced by the post?
3
96 (cubic inches)
4
If 2x 8 what is 3x?
5
27
6
At a certain intersection, 30 of the cars turn
left, 40 turn right, and 30 go straight. What
is the probability that the next car turns left
and the following one turns right?
7
3 25
8
Express in simplest form
9
16
10
What is the sum of the two values that will make
the following expression undefined? x 2
x2 6x 8
11
6
12
Find the largest integer less than or equal to
2-3 33.
13
3
14
Seven equal 10-inch-long pieces are cut from an
eight-foot-long piece of lumber. If the waste
per cut is 1/8 inch, how many inches long is the
piece that is left over? Express your answer as
a mixed number.
15
25 1/8 (inches)
16
If 5 technicians can produce 64 surfboards in 4
days, how many surfboards can 8 technicians
produce in 10 days?
17
256 (surfboards)
18
What digit is used only once in the decimal
representation of(1,111,111)2
19
7
20
The school population has increased from 3,200 to
3,600 this year. If this percent rate of
increase remains constant, what will be the
school population be at the end of next year?
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4,050 (students)
22
In an arithmetic sequence the 113th term is 786
and the 125th term is 870. Find the 150th term
23
1,045
24
A rectangle has length 15 inches and width 10
inches. If these dimensions are both increased
by 20, by how many square inches will the area
of the rectangle be increased?
25
66 (square inches)
26
If f(x) 2x 3 and g(x) 3x 2, find
f(g(f(2))) g(f(g(2)))Express your answer in the
form a .b
27
41 31
28
What is the sum of the distinct prime factors of
3, 780
29
17
30
Two interior angles A and B of pentagon ABCDE
are 60º and 85º. Two remaining angles, C and D,
are equal and the fifth angle is 15º more than
twice C. Find the measure of the largest angle.
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205 (degrees)
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Simplify the following and express the result
without using negative exponents.(3a-2b3c-1)2
(v2ab-1c2)2 3
33
3v2b5 2a3
34
Evaluate 1312 2(131)(31) 312
35
10,000
36
Segment AC has three semi-circles with radii 4cm,
6cm, and 10 cm. In terms of p, how many square
centimeters are in the shaded area? A
C
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24p (sq. cm.)
38
Find
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120
40
Find the volume, in cubic inches, of a cube whose
surface area is 96 square inches.
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64 (cubic inches)
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Given that a?b (a2 - b2),
abexpress 6?2 as a common fraction.
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8 3
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A candy bar weighs 4.48 oz. If a person eats
half the remaining candy bar with each bite, how
many bites have been taken when there is exactly
0.07 oz remaining?
45
6 (bites)
46
Evaluate (35)(23) (24)(34)
47
648
48
If the sides of a right triangle are 14cm, 48 cm,
and 50 cm, how many square centimeters are in its
area?
49
336 (sq. cm.)
50
Central angles a, b, and c separate the circle
into regions which are 1/3, 1/4, and 1/6 of the
area. How many degrees are there in central
angle d? a b c d
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90 (degrees)
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What is the value of (81)0.04 (81) 0.21 ?
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3
54
Find the sum of all possible values for C which
will make 49C345 divisible by 15.
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15
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If X gt 3 find Y such that Y X - 3 X
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3
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How many positive integers less than 575 are
divisible by 2, 3, and 5?
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19 (integers)
60
One bus company has a bus arrive at the Parkview
bus stop every 16 minutes, while another bus
company has a bus arrive at the same stop every
20 minutes. If a bus from each company arrives
at Parkview bus stop simultaneously at 300 PM,
what is the next time they will arrive there
simultaneously?
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420 (PM) or 1620
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Find the value of (n 1)! when n 100
(n 1)!
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10,100
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Find the value of x in the triangle shown.
Express your answer in simplest radical
form. 45
16 x x
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8v2 (sq. cm.)
66
Express 0.003 X 0.00033 in scientific notation.
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9.9 X 10-7
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A girls basketball team has 4 players of heights
61, 59, 58, and 511. If the average
height of the 5-girl team is 510, then the
fifth player must be 5a tall. Find a.
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9
70
The sum of two numbers is 19 and their difference
is 5. What is their product?
71
84
72
Express as a common fraction.
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- 3 2
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What is the greatest common factor of (a2 9)
and (3a2 3a 36)?
75
( a 3)
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What is the value of x in the diagram?
x 2 60 45
77
v6 (units)
78
Find the area of the shaded cross section of the
magnet, where OE 2, OF 4, OP 4, and both
arcs shown are semicircles. Leave your answer in
terms of p. E 2 F 2
o 4 2 P 2
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16 6p (sq. units)
80
Find the product of (1/4)-3(8)-2
81
1
82
What is the value of 6! (6 4)!4!
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15
84
If a light bulb has an expected life of 1,000
hours, for how many complete days of continuous
use can it be expected to work?
85
41 (days)
86
Laws in certain states require a 60 approval
rate from voters before an issue is passed. If
1,140 people voted in favor of the law, and this
represents 57 of the total number of voters, how
many voters were there in this election?
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2,000 (voters)
88
If a 25cm X 12cm X 7cm full box of paper towels
contains 175 individual towels, what is the
volume of each towel in cm3?
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12 (cm.3)
90
Given the square of an integer x is 1,521. What
is the value of (x 1)(x 1)
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1,520
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A step pyramid is formed by stacking successively
smaller steps as illustrated in the drawing.
If the edges of each square step have lengths
9,7,5,3, and 1, and each step is 1 unit high,
find the number of cubic units in the volume of
the pyramid. 1 3
3 5 5 7
7 9 9
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165 (units3)
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What is the value of (3/5)2 2(3/5)(2/5)
(2/5)2?
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1
96
The configuration below is built from 27
segments. How many paths are there from A to B
using exactly five of these segments?
B A
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6 (paths)
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Suppose the estimated 45 billion cost of sending
a person to Mars is shared equally by the 250
million people of the United States. What is
each persons share?
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180 (dollars)
100
If (x 1)1/2 21/3 find the value of (x 1)2
in simplest radical form.
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2 3v2
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How many numbers can be written as the sum of two
or more distinct members of the set 0, 1, 2, 3,
4, 5
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15 (numbers)
104
How many positive integers less than 100 can be
expressed as a power of 3?
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5 (integers)
106
How many ways can 5 distinct paperback books and
1 hardcover book be arranged on a shelf if the
hardcover book must be the rightmost book on the
shelf?
107
120 (ways)
108
Find the negative root(s) of the equation (x
1)2 2(x 1)
109
- 1
110
Given x varies directly as y2 and x 3 when y
5, find x when y 6. Express your answer as a
common fraction.
111
108 25
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17 (yards)
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v2
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54 (diagonals)
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2
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29 ¼
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51
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24 (sq. cm.)
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18
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1 38
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1
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34 27
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7
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