Download 10-question challenge 3

10-QUESTION
CHALLENGE 3
Name
Calculators may be used on this challenge.
students The scores on the Monthly Challenge #1 and Monthly Challenge
1.����������
#2 for the 15 students in Mrs. Baldrate’s math club are shown in
the graph. How many students improved their score from Monthly
Challenge #1 to Monthly Challenge #2?
Score on
Challenge
Mrs. Baldrate’s Math Club Challenge Scores
MC #1
MC #2
5
4
3
2
1
1 2 3 4 5
6 7 8 9 10 11 12 13 14 15
Students (Numbered 1 – 15)
2.���������� What is the largest two-digit integer that occurs in both of the
following arithmetic sequences?
Sequence A: 4, 8, 12, 16, ..., 104 Sequence B: 6, 12, 18, 24, ..., 114?
games At two local billiards clubs patrons can pay to use the billiards
3.����������
tables. At Buckley’s Billiard, customers are charged $3.25, plus
$1.00 per game. At The Pool Place, customers are charged $5.00,
plus $0.75 per game. For what number of games at
Buckley Billiards is the cost the same at The Pool Place?
°F When the temperature is 75°F outside, Aaron plays outside for
4.����������
90 minutes. When the temperature drops to 35°F outside, Aaron
plays outside for 30 minutes. Assumming the relationship between
the outside temperature and the time Aaron plays outside is linear,
at what temperature would Aaron’s time playing outside exactly
equal 24 minutes?
Copyright MATHCOUNTS Inc. 2013. All rights reserved. The National Math Club: 10 Question Challenges
sq units What is the area of the triangle with vertices
5.����������
located at A(2, –1), B(4, 5) and C(6, –1)?
students
6.����������
There are 25 students in Ben’s class. Four of the
students have last names that start with “S,” and
14 of the students have brown hair. What is the
greatest possible number of students who could
have neither a last name that starts with “S” nor
brown hair?
7.���������� If 2x + y = 12 and x + 2y = 9, what is the value of x?
sq cm The perimeter of square LMNO is 16 cm. Point
8.����������
M on square LMNO is also the center of circle M.
If circle M and square LMNO are coplanar and
circle M intersects segment LM at its midpoint,
what is the area of circle M? Express your
answer in terms of �.
L
M
O
N
9.���������� Michael has a bag containing six ping pong balls that he has
numbered 1 through 6, inclusive. If Michael selects two ping pong
balls at random and without replacement, what is the probability
that the product of the numbers on the two balls is a multiple of 4?
Express your answer as a common fraction.
comb.
10.���������
In the game of basketball, a shot that goes in
the basket is worth 1 point, 2 points or 3 points.
How many different combinations of 1, 2, or 3 points will result in a total score of 6 points?
Note: the scoring sequences 1, 1, 1, 2, 1 and
2, 1, 1, 1, 1 are considered to be the same
combination of points.
Copyright MATHCOUNTS Inc. 2013. All rights reserved. The National Math Club: 10 Question Challenges
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10-QUESTION
CHALLENGE 3
s
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A
Name
Calculators may be used on this challenge.
6 students The scores on the Monthly Challenge #1 and Monthly Challenge
1.����������
#2 for the 15 students in Mrs. Baldrate’s math club are shown in
the graph. How many students improved their score from Monthly
Challenge #1 to Monthly Challenge #2?
96
2.����������
What is the largest two-digit integer that occurs in both of the
following arithmetic sequences?
Sequence A: 4, 8, 12, 16, ..., 104 Sequence B: 6, 12, 18, 24, ..., 114?
7 games At two local billiards clubs, patrons can pay to use the billiards
3.����������
tables. At Buckley’s Billiards, customers are charged $3.25, plus
$1.00 per game. At The Pool Place, customers are charged $5.00,
plus $0.75 per game. For what number of games at
Buckley’s Billiards is the cost the same at The Pool Place?
31 °F When the temperature is 75°F outside, Aaron plays outside for 90
4.����������
minutes. When the temperature drops to 35°F outside, Aaron plays
outside for 30 minutes. Assumming the relationship between the
outside temperature and the time Aaron plays outside is linear, at
what temperature would Aaron’s time playing outside exactly equal
24 minutes?
Copyright MATHCOUNTS Inc. 2013. All rights reserved. The National Math Club: 10 Question Challenges
12 sq units What is the area of the triangle with vertices
5.����������
located at A(2, –1), B(4, 5) and C(6, –1)?
11 students
6.����������
There are 25 students in Ben’s class. Four of the
students have last names that start with “S,” and
14 of the students have brown hair. What is the
greatest possible number of students who could
have neither a last name that starts with “S” nor
brown hair?
5
7.����������
If 2x + y = 12 and x + 2y = 9, what is the value of x?
4� sq cm The perimeter of square LMNO is 16 cm. Point
8.����������
M on square LMNO is also the center of circle M.
If circle M and square LMNO are coplanar and
circle M intersects segment LM at its midpoint,
what is the area of circle M? Express your
answer in terms of �.
L
M
O
N
2
5
9.����������
Michael has a bag containing six ping pong balls that he has
numbered 1 through 6, inclusive. If Michael selects two ping pong
balls at random and without replacement, what is the probability
that the product of the numbers on the two balls is a multiple of 4?
Express your answer as a common fraction.
7 comb.
10.���������
In the game of basketball, a shot that goes in
the basket is worth 1 point, 2 points or 3 points.
How many different combinations of 1, 2 or 3 points will result in a total score of 6 points?
Note: the scoring sequences 1, 1, 1, 2, 1 and
2, 1, 1, 1, 1 are considered to be the same
combination of points.
Copyright MATHCOUNTS Inc. 2013. All rights reserved. The National Math Club: 10 Question Challenges