Download 10-question challenge 2

10-QUESTION
CHALLENGE 2
Name
Calculators may NOT be used on this challenge.
1.���������� 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? inches A rectangle that measures 12 inches by 24 inches is cut in half to
2.����������
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? 3.���������� What is the sum of the values of a and b in the following arithmetic
sequence? −5, 3, 11, a, 27, b, … 4.���������� Suppose that a☺b = 2a – b + ab for all integers a and b. What is the
value of 2☺3?
jellybeans Jamie plans to divide her jellybeans evenly amongst herself and her
5.����������
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? Copyright MATHCOUNTS Inc. 2013. All rights reserved. The National Math Club: 10 Question Challenges
pencils Shanel is buying notepads and pencils for school. She
6.����������
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?
points Every week Mr. Magoo’s MATHCOUNTS students take a 10-point
7.����������
practice test. Last week, his three 6th graders scored an average of
exactly 8 points on the 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.
segments Alternating between row 1 and row 2, congruent segments are used to
8.����������
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?
Figure 1
row 1
Figure 2
Figure 3
Figure 4
...
row 2
questions On last week’s test, Alice got 15% of the questions wrong and Jennifer
9.����������
got 5% of the questions wrong. If Jennifer got 6 more questions correct
than Alice, how many questions were on the test?
10.��������� 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.
Copyright MATHCOUNTS Inc. 2013. All rights reserved. The National Math Club: 10 Question Challenges
r
e
w
y
e
K
10-QUESTION
CHALLENGE 2
s
An
Name
Calculators may NOT be used on this challenge.
orange
1.����������
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? 24 inches A rectangle that measures 12 inches by 24 inches is cut in half to
2.����������
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? 54
3.����������
What is the sum of the values of a and b in the following arithmetic
sequence? −5, 3, 11, a, 27, b, … 7
4.����������
Suppose that a☺b = 2a – b + ab for integers a and b. What is the
value of 2☺3?
20 jellybeans Jamie plans to divide her jellybeans evenly amongst herself and her
5.����������
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? Copyright MATHCOUNTS Inc. 2013. All rights reserved. The National Math Club: 10 Question Challenges
9 pencils Shanel is buying notepads and pencils for school. She
6.����������
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?
8.5 points Every week Mr. Magoo’s MATHCOUNTS students take a 10-point
7.����������
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.
83 segments Alternating between row 1 and row 2, congruent segments are used to
8.����������
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?
Figure 1
Figure 2
Figure 3
Figure 4
...
row 1
row 2
60 questions On last week’s test, Alice got 15% of the questions wrong and Jennifer
9.����������
got 5% of the questions wrong. If Jennifer got 6 more questions correct
than Alice, how many questions were on the test?
1
10.���������
Howard selects two numbers without replacement from the set {3,
7
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.
Copyright MATHCOUNTS Inc. 2013. All rights reserved. The National Math Club: 10 Question Challenges