NRP Math challenge club May 2nd, 2017

Team Challenge

Question 1 You have 2017 five-cent coins in your treasure box. What is the value of your treasure in dollars, correct to 2 decimal places?

Question 1 You have 2017 five-cent coins in your treasure box. What is the value of your treasure in dollars, correct to 2 decimal places? Answer: $100.85

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Question 2 Of all the two-digit primes, what is the largest that consists of 2 consecutive digits?

Question 2 Of all the two-digit primes, what is the largest that consists of 2 consecutive digits? Answer : 89

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Question 3 Simplify: (2+0+1+7)(2-0+1-7)

Question 3 Simplify: (2+0+1+7)(2-0+1-7) Answer : -40

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Question 4 The area of square B is 300% larger than the area of the square A. How much larger is the perimeter of square B (in percent) than the perimeter of square A?

Question 4 The area of square B is 300% larger than the area of the square A. How much larger is the perimeter of square B (in percent) than the perimeter of square A? Answer : 100%

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Question 5 You write all the letters of the alphabet, in order, over and over again. What is the 2017-th letter that you write?

Question 5 You write all the letters of the alphabet, in order, over and over again. What is the 2017-th letter that you write? Answer : Letter O

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Question 6 If a train travels at a speed of 105 km per hour for 1 hour and 20 minutes, how many km does it travel?

Question 6 If a train travels at a speed of 105 km per hour for 1 hour and 20 minutes, how many km does it travel? Answer : 140 km

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Question 7 What is the probability of getting 5 heads in a row when tossing a fair coin? Express your answer as a common fraction.

Question 7 What is the probability of getting 5 heads in a row when tossing a fair coin? Express your answer as a common fraction. Answer : 𝟏 𝟑𝟐

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Question 8 One cm2 on a map represents an area of 0.36 km2. How many meters are represented by one cm?

Question 8 One cm2 on a map represents an area of 0.36 km2. How many meters are represented by one cm? Answer : 600m

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Question 9 What is the value of the 2015-th term of the arithmetic sequence whose first 3 terms are -3998, -3996, and -3994?

Question 9 What is the value of the 2015-th term of the arithmetic sequence whose first 3 terms are -3998, -3996, and -3994? Answer : 30

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Question 10 How many diagonals go through the center of a regular 9-sided polygon?

Question 10 How many diagonals go through the center of a regular 9-sided polygon? Answer : zero

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Question 11 You write the first 30 whole numbers. How many times did you write the digit 1?

Question 11 You write the first 30 whole numbers. How many times did you write the digit 1? Answer : 13 times

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Question 12 A regular polygon with 2017 sides is divided into 2 congruent polygons by drawing a line from a corner to the midpoint of its opposite side edge. How many sides does each of the two polygons have?

Question 12 A regular polygon with 2017 sides is divided into 2 congruent polygons by drawing a line from a corner to the midpoint of its opposite side edge. How many sides does each of the two polygons have? Answer : 1010 sides

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Question 13 At the Martian General Store, one Deku and one Sephora together costs 10 Freckles. Martha the Martian paid 22 Freckles for two Dekus and three Sephoras. How much does one Deku cost?

Question 13 At the Martian General Store, one Deku and one Sephora together costs 10 Freckles. Martha the Martian paid 22 Freckles for two Dekus and three Sephoras. How much does one Deku cost? Answer : 8 Freckles

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Question 14 Find the volume of a cube whose surface area is 96.

Question 14 Find the volume of a cube whose surface area is 96. Answer : 64

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Question 15 The numbers M and N are both prime. Each is smaller than 40. It is known that M<N and M + N = 66. What is the value of M?

Question 15 The numbers M and N are both prime. Each is smaller than 40. It is known that M<N and M + N = 66. What is the value of M? Answer : 29

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Question 16 There are 5 flavors of ice cream available. In how many ways can Ashley choose 2 scoops of ice cream? Note that chocolate and vanilla is the same choice as vanilla and chocolate.

Question 16 There are 5 flavors of ice cream available. In how many ways can Ashley choose 2 scoops of ice cream? Note that chocolate and vanilla is the same choice as vanilla and chocolate. Answer : 10 ways

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Question 17 The first two terms of the sequence are 1 and 3, and after that any term of the sequence is the sum of the previous two terms. What is the 5th term of the sequence?

Question 17 The first two terms of the sequence are 1 and 3, and after that any term of the sequence is the sum of the previous two terms. What is the 5th term of the sequence? Answer : 11

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Question 18 Nathan has a total of $1.95 in standard Canadian coins (no pennies). What is the smallest number of coins that Nathan could have?

Question 18 Nathan has a total of $1.95 in standard Canadian coins (no pennies). What is the smallest number of coins that Nathan could have? Answer : 6 coins

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Question 19 You write all the numbers from 1 to 11. What is the sum of all the individual digits that you wrote?

Question 19 You write all the numbers from 1 to 11. What is the sum of all the individual digits that you wrote? Answer : 48

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Question 20 How many different sums can you get when you roll 3 dice?

Question 20 How many different sums can you get when you roll 3 dice? Answer : 16 sums

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Question 21 The sum of two different primes is another prime. What is the value of the smaller of these two primes?

Question 21 The sum of two different primes is another prime. What is the value of the smaller of these two primes? Answer : 2

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Question 22 How many positive non-prime numbers are there smaller than 20?

Question 22 How many positive non-prime numbers are there smaller than 20? Answer : 11 non-prime numbers

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Question 23 The sum of two angles of a triangle is 125 degrees. What is the value of the third angle?

Question 23 The sum of two angles of a triangle is 125 degrees. What is the value of the third angle? Answer : 55 degrees

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Question 24 There are 4 jelly beans in a tray, 2 blue and 2 yellow. Amir eats 2 of the jelly beans, chosen at random. What is the probability that these 2 jelly beans are of different colours? Express your answer as a common fraction.

Question 24 There are 4 jelly beans in a tray, 2 blue and 2 yellow. Amir eats 2 of the jelly beans, chosen at random. What is the probability that these 2 jelly beans are of different colours? Express your answer as a common fraction. Answer : 𝟐 𝟑

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Question 25 The sum of the ages of the 20 people in the class is 302 years. What will the sum of their ages be 2 years from now?

Question 25 The sum of the ages of the 20 people in the class is 302 years. What will the sum of their ages be 2 years from now? Answer : 𝟑𝟒𝟐 𝐲𝐞𝐚𝐫𝐬

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Question 26 What is the smallest positive integer n such that 1 + 2 + 3 +⋯+(n-1) + n is a multiple of 10?

Question 26 What is the smallest positive integer n such that 1 + 2 + 3 +⋯+(n-1) + n is a multiple of 10? Answer : 𝟒

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Question 27 What is the smallest prime number which is larger than 89?

Question 27 What is the smallest prime number which is larger than 89? Answer : 𝟗𝟕

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Question 28 Richie has $200, and Erik has $10. How many dollars should Richie give to Erik so that Richie will have 4 times as many dollars as Erik?

Question 28 Richie has $200, and Erik has $10. How many dollars should Richie give to Erik so that Richie will have 4 times as many dollars as Erik? Answer : $32

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Question 29 Simplify: (1+ 1 4 )(1+ 1 5 )(1+ 1 6 )(1+ 1 7 )

Question 29 Simplify: (1+ 1 4 )(1+ 1 5 )(1+ 1 6 )(1+ 1 7 ) Answer : 2

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Question 30 What is the smallest positive integer N such that 20N is a perfect square?

Question 30 What is the smallest positive integer N such that 20N is a perfect square? Answer : 𝟓

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Question 31 How many seconds are there in 2.5 hours?

Question 31 How many seconds are there in 2.5 hours? Answer : 9,000 seconds

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Question 32 The average of 4 numbers is 20. You add a 5th number, the average increase by 15. What is the value of the 5th number?

Question 32 The average of 4 numbers is 20. You add a 5th number, the average increase by 15. What is the value of the 5th number? Answer : 95

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Question 33 What is the number of sides of a regular polygon which has 77 diagonals?

Question 33 What is the number of sides of a regular polygon which has 77 diagonals? Answer : 14 sides

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Question 34 The sum of the five consecutive integers is 2015. What is the value of the largest of these integers?

Question 34 The sum of the five consecutive integers is 2015. What is the value of the largest of these integers? Answer : 405

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Question 35 The average speed of a bus travelling the 123 km from Vancouver to Whistler was 90 km/hr. How long, in minutes, was the trip?

Question 35 The average speed of a bus travelling the 123 km from Vancouver to Whistler was 90 km/hr. How long, in minutes, was the trip? Answer : 82 minutes

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Question 36 What is the value of the largest two-digit number that is the product of exactly 2 different primes?

Question 36 What is the value of the largest two-digit number that is the product of exactly 2 different primes? Answer : 95

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Question 37 You have 4 hats and 8 scarves. You must select one of the scarves, and one hat or no hats. In how many different ways can you do the choosing?

Question 37 You have 4 hats and 8 scarves. You must select one of the scarves, and one hat or no hats. In how many different ways can you do the choosing? Answer : 40 ways

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Question 38 Suppose N is 150% of 160% of 15. What is the value of N?

Question 38 Suppose N is 150% of 160% of 15. What is the value of N? Answer : 36

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Question 39 You have two 5 cent coins, two 10 cent coins, and two 25 cent coins. How many different sums can you make if you use exactly 2 coins?

Question 39 You have two 5 cent coins, two 10 cent coins, and two 25 cent coins. How many different sums can you make if you use exactly 2 coins? Answer : 6 sums

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Question 40 13 students sit in a circle and after getting to know each other, each student becomes friends with the two students beside them. If the students are divided into teams with no two friends on the same team, what is the minimum number of teams possible?

Question 40 13 students sit in a circle and after getting to know each other, each student becomes friends with the two students beside them. If the students are divided into teams with no two friends on the same team, what is the minimum number of teams possible? Answer : 3 teams

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Question 41 Is it possible to draw a regular hexagon and all of its diagonals without lifting up your pencil or drawing over a line you’ve already drawn? Why not?

Question 41 Is it possible to draw a regular hexagon and all of its diagonals without lifting up your pencil or drawing over a line you’ve already drawn? Why not? Answer : No