Category B: Grades 6 – 8
Round 3
Thursday, November 20, 2014
Question #1
Frank is 10 years old and is 51 inches tall. When he was 6, he was 44 inches tall. He has grown
at a constant rate from age 1 until now. From birth to age 1, he grew 1 foot.
How tall was he when he was born? Give your answer in inches.
(Remember: 1 foot = 12 inches.)
Question #2
A fast clock gains one minute per hour and a slow clock loses two minutes per hour. At a
certain time, both clocks are set to the correct time. Less than 24 hours later, the fast clock
registers 9 o’clock at the same moment that the slow clock registers 8 o’clock. What is the
correct time at that moment?
Question #3
A sum of money is to be divided among Alex, Bill and Carol. Alex receives
$1 plus one-third of what is left. Bill then receives $6 plus one-third of what
remains. Carol receives the rest, which amounts to $40.
How much did Bill receive?
Question #4
A circle is inscribed in trapezoid PQRS.
If PS = QR = 25 cm, PQ = 18 cm and SR = 32 cm,
what is the length of the diameter of the circle?
Question #5
If the sides of a triangle have lengths 30, 40 and 50, what is the length of the shortest altitude?
Question #6
A cube measures 10 cm x 10 cm x 10 cm. Three cuts are made parallel
to the faces of the cube as shown creating eight separate solids which
are then separated. What is the increase in the total surface area?
Question #7
The number 315 can be written as the product of two odd integers each greater than 1.
In how many ways can this be done?
Question #8
A regular pentagon has all sides and angles equal. If the shaded pentagon is
enclosed by squares and triangles, as shown, what is the size of angle x?
Question #9
Claire takes a square piece of paper and folds it in half four times without unfolding, making an
isosceles right triangle each time. After unfolding the paper to form a square again, what
would the creases on the paper look like?
Question #10
Compute the remainder when 230 is divided by 1000.
Question #11
Stephen had a 10:00 am appointment 60 km from his home. He averaged 80 km/h for the trip
and arrived 20 minutes late for the appointment. At what time did he leave his home?
Question #12
In the 4 x 4 square shown, each row, column and diagonal should contain
each of the numbers 1, 2, 3, and 4. Find the value of K + N.
Question #13
Find the area of the smallest possible square that contains the points (2, −1) and (4, 4).
Question #14
George and two of his friends go to a famous jiaozi restaurant, which serves only two kinds of
jiaozi: pork jiaozi, and vegetable jiaozi. Each person orders exactly 15 jiaozi. How many
different ways could the three of them order? Two ways of ordering are different if one
person orders a different number of pork jiaozi in both orders.
Question #15
Ben works quickly on his homework, but tires quickly. The first problem takes him 1 minute to
solve, and the second problem takes him 2 minutes to solve. It takes him N minutes to solve
problem N on his homework. If he works for an hour on his homework, compute the
maximum number of problems he can solve
Question #16
Boris is driving on a remote highway. His car’s odometer reads 24942 km, which Boris notices
is a palindromic number, meaning it is not changed when it is reversed. “Hmmm,” he thinks,
“it should be a long time before I see that again.” But it takes only 1 hour for the odometer to
once again show a palindromic number! How fast is Boris driving in km/h?
Question #17
Five boys weighed themselves in pairs in all possible combinations. The measured weights
were 90 kg, 92 kg, 93 kg, 94 kg, 95 kg, 96 kg, 97 kg, 98 kg, 100 kg, and 101 kg. What was the
total weight of the five boys?
Question #18
Consider the set of all four-digit numbers formed by the digits 1,2,3,4 without repetitions.
What is the sum of all numbers from this set?
Question #19
Three children ate 17 cookies altogether. Andrew ate more cookies than
any other child.
What is the smallest possible number of cookies that Andrew ate?
Question #20
The number of seconds in 6 weeks is n!. Find the value of n.