Target Level 1 | 08/07/2010
(1)
If a : b = 4 : 5 and b : c = 7 : 8, then what is a : c ? Express your answer as
a common fraction.
(2)
A lamppost in a park can illuminate an area of radius 40 feet. What is the
minimum number of lampposts that must be installed in the park below so that the entire
region is illuminated?
√
200 2 ft
√
120 2 ft
(3)
(4)
(5)
3?
How many positive multiples of 7 that are less than 1000 end with the digit
Katie read that the average human heart rate is 70 beats per minute. At
this rate, determine the number of times Katie's heart beat during her rst thirteen years.
Three of Katie's rst thirteen years were leap years.
Find the sum of all positive integral values of n for which n+6
n is an integer.
(6)
The circle graph shows the results of a 2002 survey of 4050 people. How
many people chose Billy Crystal as the best Oscars host? Express your answer to the
nearest hundred.
Billy
Crystal
Others
52%
(7)
centimeters.
Find x , in centimeters, if the area of the rectangle shown is 36 square
x
4x
(8)
Mrs. Kiernan listed two positive numbers on the board and asked the
students in her math class to add the numbers. Tai subtracted the numbers by mistake and
gave his answer as 37. Eileen multiplied them and gave her answer as 69,090. What was
the correct sum?
(9)
The largest colony of black-tailed prairie dogs contains 400 million prairie
dogs on 24,000 square miles of land. Using these estimates, what is the average number of
prairie dogs for each square mile? Express your answer to the nearest whole number.
(10)
Michael tells the following riddle about his favorite number: "My number is
the sum of 126 plus one-fourth my number minus one-eighth my number." What is
Michael's favorite number?
(11)
The positive square root of 200 is what percent larger than the positive
square root of 121? Express your answer to the nearest whole number.
(12)
Francisco starts with the number 5, doubles it, adds 1, doubles the result,
adds 1, doubles the result, adds 1, and continues this pattern of two alternating
calculations. Phong, meanwhile, starts with 5, adds 1, doubles the result, adds 1, doubles
the result, adds 1, doubles the result, and continues this pattern of two alternating
calculations. They each do eight total calculations. What is the positive dierence of their
nal results?
(13)
What integer on the number line is closest to 169
9 ?
(14)
Motorstar spark plugs regularly sell for 94 cents each. Willi has one coupon
to buy his rst four spark plugs at 79 cents each. With the coupon, how many cents will
Willi pay for six spark plugs?
(15)
Interior numbers begin in the third row of Pascal's Triangle. The sum of the
interior numbers in the fourth row is 6. The sum of the interior numbers of the fth row is
14. What is the sum of the interior numbers of the seventh row?
(16)
Murtha has decided to start a pebble collection. She collects one pebble the
rst day and two pebbles on the second day. On each subsequent day she collects one
more pebble than the previous day. How many pebbles will she have collected at the end of
the twelfth day?
(17)
A cylindrical closed toxic waste container eighteen inches high with an outer
diameter of 12 inches is made of stainless steel with a uniform thickness of 41 inch.
Assuming the cylinder is full, to the nearest percent what is the volume of the liquid to the
volume of the entire cylinder?
(18)
The Petronas Tower in Kuala Lumpar is 1483 feet tall and has 88 stories.
The Sears Tower in Chicago is 1450 feet tall and has 110 stories. How many feet taller is
the average height of a story in the Petronas Tower? Express your answer as a decimal to
the nearest tenth.
(19)
What common fraction is exactly half-way between 23 and 45 ?
(20)
What is the greatest prime factor of 3105?
Copyright MATHCOUNTS Inc. All rights reserved
Answer Sheet
Number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Answer
7
10
15
14
478598400
12
2100 people
3 cm
527
16,667
144
29
15
19
504
62
78 pebbles
89 percent
3.7 feet
11/15
23
Problem ID
0D13
AB4B
4D13
55BA
2DBA
BB11
B3A02
A5BA
0423
14B41
231D2
D342
C213
1323
3BA51
A3B
153B
C2D4
B1312
B3D3
Copyright MATHCOUNTS Inc. All rights reserved
Solutions
ID: [0D13]
(1) 107
No solution is available at this time.
(2)
15
ID: [AB4B]
(3)
14
ID: [4D13]
(4)
478598400
(5)
12
(6)
2100 people
(7)
3 cm
No solution is available at this time.
Listing the rst 10 multiples of 7, which are 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, we see
that the only positive multiples of 7 that end in 3 are those that are the product of 7 and a
number that ends in 9. Therefore, the positive multiples of 7 that are less than 1000 and
end with the digit 3 are 7 9 = 63, 7 19 = 133, 7 29 = 203, . . . Notice that we can get
from each to the next by adding 7 10 = 70, so our multiples of 7 less than 1000 that end
with the digit 3 are 63, 133, 203, . . ., 903, 973. The last one is 910 more than the rst.
Since 910=70 = 13, we see that we have taken 13 steps of 70 to get from the rst number
in the list to the last. Therefore, there are 14 numbers in the list.
ID: [55BA]
No solution is available at this time.
ID: [2DBA]
n
6
6
The expression n+6
n can be simplied as n + n , or 1 + n . So in order for this expression to
have an integral value, 6 must be divisible by n. Therefore, the sum of all positive integral
values of n is just the sum of all the divisors of 6. Since the prime factorization of 6 is 2 3,
we know that 6 is only divisible by 1, 2, 3, 6, and the nal answer is 1 + 2 + 3 + 6 = 12 .
ID: [BB11]
No solution is available at this time.
ID: [B3A02]
No solution is available at this time.
(8)
527
(9)
16,667
ID: [A5BA]
No solution is available at this time.
ID: [0423]
No solution is available at this time.
(10)
144
(11)
29
ID: [231D2]
(12)
15
ID: [D342]
ID: [14B41]
No solution is available at this time.
p
The positive square root of 200 is 10 2, or about 14:142. The positive square root of 121
is 11. Dividing 14.142
p by 11, we get about 1.2856.pSubtracting the 1 and multiplying by
100, we see that 200 is about 29% larger than 121:
The arithmetic is simple enough that we can just write down the results of the calculations.
Francisco's calculations give 5, 10, 11, 22, 23, 46, 47, 94, 95 (nine numbers, but only eight
calculations since the 5 was given). Phong's give 5, 6, 12, 13, 26, 27, 54, 55, 110. The
positive dierence is 15 .
(13) 19
ID: [C213]
We compute 169
9 = 18:7, which is closest to
(14)
504
(15)
62
(16)
78 pebbles
19 .
ID: [1323]
No solution is available at this time.
ID: [3BA51]
No solution is available at this time.
ID: [A3B]
Because the number of pebbles increases each day, the total number of pebbles is equal to
1 + 2 + 3 + + 11 + 12 = (1 + 12) + (2 + 11) + + (6 + 7) = 6 13 = 78 .
(17)
89 percent
(18)
3.7 feet
(19)
11/15
(20)
23
ID: [153B]
No solution is available at this time.
ID: [C2D4]
No solution is available at this time.
ID: [B1312]
The average of two numbers is exactly half-way between them. Therefore,
1 2 + 4 = 11 is half-way between 2 and 4 .
2 3 5
3
5
15
ID: [B3D3]
Let's nd the prime factorization of 3105: 3105 = 33 115 = 33 5 23. The greatest prime
factor of 3105 is 23 .
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