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10 Question 1
10 Question 1 (2)
5 Question 1
10 Question 2
10 Question 2 (2)
100
The following histogram shows the number of runners who finished the marathon in particular periods of time. How many runners finished the marathon in less than 5 hours?
744 Runners
100
The area of squareABCD is 36 square inches. The area of rectangle WXYZ is 20 square inches. If the two shapes have equal perimeters, what is the longer side length of rectangle WXYZ?
10 inches
100
Patrick is able to determine Sam’s secret integer, using the answers to the questions below. Is it a factor of 30? Yes Is it a prime number? No Is it a multiple of 3? No Is it less than 3? No What is Sam’s secret integer?
10
100
Julia likes to eat Skittles® in a specific color pattern: green, yellow, orange, red, purple, green, yellow, orange, red, purple,… If Julia continues this pattern, assuming she has an infinite supply of Skittles®, what will be the color of her 63rd Skittle?
Orange
100
Shanel is buying notepads and pencils for school. She buys a total of 15 items and spends $10.50, before tax. If pencils cost $0.50 each and notepads cost $1.00 each, how many pencils did Shanel buy?
9 pencils
200
An arithmetic sequence is a sequence of terms in which the difference between consecutive terms remains the same. This means the terms in an arithmetic sequence will all increase by the same amount, all decrease by the same amount or all remain the same. The figure shows two different arithmetic sequences with some of the terms left out. The first sequence is written horizontally, and the second sequence is written vertically. What value should be written in the shaded square?
6
200
When the puzzle shown is filled in correctly, each circle contains a prime number. The number in each square is the product of the prime numbers to which it is directly connected. What number should replace the “?” in the bottom square?
35
200
Ten students will stand on a circle. No two students standing next to each other can both have blonde hair. What is the greatest number of students that could have blonde hair?
5 Students
200
A rectangle that measures 12 inches by 24 inches is cut in half to make two squares with side length 12 inches. How many more inches is the combined perimeter of the two squares than the perimeter of the original rectangle?
24 inches
200
Every week Mr. Magoo's MATHCOUNTS students take a 10-point practice test. Last week, his three 6th graders scored an average of exactly 8 points at their practice test. This week a new 6th grader joined the club. If the original three 6th graders scored the same as they did last week. what is the highest possible average the four 6th graders could earn this week? Express your answer as a decimal to the nearest tenth.
8.5 points
300
If only circles may be used, how many circles must be placed on the right side of the third scale so that all three scales are balanced? (The distance of the objects from the centers of these scales is not relevant.)
3 Circles
300
At each successive stage, an equilateral triangle is added to each side of the largest, outer equilateral triangle of the previous stage to form a new equilateral triangle. If the area of the equilateral triangle in Stage 1 is 2 square units, what is the total area of the figure formed at Stage 4?
128 sq. units
300
Each circle at a vertex in the diagram below is colored red (R), yellow (Y) or blue (B). No two vertices of a drawn triangle have the same color. One triangle has been completed. What is the color of the vertex marked by the question mark?
Y or Yellow
300
What is the sum of the values of a and b in the following arithmetic sequence? -5, 3, 11, a, 27, b........
54
300
Alternating between row 1 and row 2, congruent segments are used to form a new regular hexagon in the sequence, as shown below. If Figure 4 is made up of 19 congruent segments, how many congruent segments must be used to make Figure 20?
83 segments
400
Kena made chocolate chip cookies using a bag of 200 chocolate chips. Every chocolate chip went into a cookie. Every cookie had exactly 8 or 10 chocolate chips, and Kena made exactly 24 cookies. How many of her cookies had 10 chocolate chips?
4 Cookies
400
In Mathville, 5 yoodles are equivalent to 4 doodles, and 3 doodles are equivalent to 2 toodles. How many toodles are equivalent to Janet’s 15 yoodles?
8 toodles
400
At what time is the sum of the digits which represent the hours and minutes on a 12-hour digital clock the greatest? For example, the time 7:17 has a sum of 7 + 1 + 7 = 15.
9:59
400
Suppose that a☺b = 2a – b + ab for all integers a and b. What is the value of 2☺3?
7
400
On last weeks test, Alice got 15% of the questions wrong and Jennifer got 5% of the questions wrong. If Jennifer got 6 more questions correct than Alice, how many questions were on the test?
60 questions
500
Here are three different views of the same cube. What number is on the face opposite the face with “5”?
3
500
Connor will stack four cubes to make a column that is four cubes tall. He has one blue cube, one red cube, one yellow cube and one green cube. How many color arrangements are possible from top to bottom if we know Connor will put either the blue cube or the green cube as the bottom cube of his column?
12 arr
500
Marcia has 65 game pieces with a total value of 89 points. Each game piece is worth one or two points. How many two-point game pieces does she have?
24 two-point game pieces
500
Jamie plans to divide her jellybeans evenly amongst herself and her 3 friends. When Jamie’s little sister walks in, Jamie decides to include her in the group and share with her, too. If each person could get an equal number of whole jellybeans without any left over in both situations, what is the smallest number of jellybeans Jamie could have had originally?
20 jellybeans
500
Howard selects two numbers without replacement from the set {3,4,5,6,7,8,9}. What is the probability that the absolute value of the difference between the two selected numbers is greater than 4? Express your answer as a common fraction
1/7