Counting Math Worksheet - 2013 Page 11
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1339,800 ÷ 280,000 ≈ 14.2% Ans.
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31
37, 41, 43, 47, 53, 57, 61, 67, 71, 73
79, 83, 89, 97, 101, 103, 107, 109, 113
2. A square and a regular hexagon share a
Let’s make a list of pairs of primes that
common side. Find the sum of the
are 50 apart. We have {3, 53}, {11, 61},
degree measures of angles 1 and 2.
{17, 67}, {23, 73}, {29, 79}, {47, 97}, {53,
103}, {57, 107}. Some of these choices
have a sum greater than 125.
Eliminating those leaves us with {3, 53},
{11, 61}, {17, 67}, {23, 73}, (29, 79}.
Now let’s determine which of these two
Let x and y represent the measures of
primes will result in a third prime to
angles 1 and 2, respectively. Let z
make them all sum up to 125.
represent the measure of the third angle
3 + 53 = 56; 125 – 56 = 69; too large
of that triangle, so x + y = 180 – z. In a
and not a prime
regular hexagon, each interior angle is
11 + 61 = 72; 125 – 72 = 53 which is a
120°. Adjacent to the hexagon we have
prime
an angle of 90°. That means
17 + 67 = 84; 125 – 84 = 41 which is a
z = 360 − (120 + 90) = 360 – 210 = 150.
prime
So, x + y = 180 – 150 = 30 Ans.
23 + 73 = 96; 125 – 96 = 29 which is a
prime
3. A trip costs $9000 for the bus plus $125
29 + 79 = 108; 125 – 108 = 17 which is
per student. Each student pays $375.
less than 29
We must find how many students must
So we have choices of {11, 53, 61}, {17,
go on the trip so that the total amount
41, 67} and {23, 29, 73}
paid is equal to the total cost of the trip.
The median of the first set is 53. The
Let x represent the number of students
median of the second set is 41. The
who must go on the trip. Then
median of the third set is 29. The
9000 + 125x = 375x
greatest is 53 Ans.
250x = 9000
x = 36 Ans.
6. What is the probability that a randomly
selected integer from 1 to 81, inclusive
4. Triangle ABC has vertices at A(−3, 4),
is equal to the product of two one-digit
B(5, 0) and C(1, −4). What is the
numbers?
x-coordinate of the point where the
Any number less than or equal to 81 is
median from C intersects AB?
the product of two one-digit numbers
Since [5 – (−3)]/2 = 8/2 = 4, the
except two-digit primes. Let’s see how
x-coordinate is −3 + 4 = 1 Ans.
many primes there are from 10 to 81:
11, 13, 17, 19, 23, 29, 31, 37, 41, 43,
5. The sum of three primes is 125. The
47, 53, 59, 61, 67, 71, 73, 79
difference between the largest and
That’s a total of 18 primes.
smallest prime is 50. We must find the
Add to this any other numbers that are
largest possible median of these three
multiples of these primes:
prime numbers.
11: 22, 33, 44, 55, 66, 77 or 6 more
OK. Let’s list all the primes up to 125.
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