Download 10-question challenge 5

10-QUESTION
CHALLENGE 5
Name
Calculators may be used on this challenge.
1.���������� The array shown contains the
positive integers in a pattern
with three columns. The sum of
the three numbers in Row 2 is
15. What is the sum of the three
numbers in Row 20? Column Column Column
A
B
C
Row 1 1
2
3
Row 2 4
5
6
Row 3 7
8
9
·
·
·
·
·
·
·
·
·
partici- At a math competition, 75% of the participants got the answer to the first
2. ����������
pants
question on the test correct. If 120 participants did not get the correct
answer, how many total participants were there? inches The length of Jay’s straw can be seen here. Sam’s straw is three times
3. ����������
the length of Jay’s straw. How long is Sam’s straw? Express your answer
as a mixed number. inches
1
2
3
4
5
6
4. ���������� The sum of four consecutive odd integers is 56. What is the least of the
four integers? combos Two darts thrown at this dartboard land in two different
5.����������
regions. If the order that the two darts are thrown does
not matter, how many combinations of two different
regions from the 10 possible regions would result in a
sum of exactly 40 points?
5
20
40 35
15
30
40
10
45
20
Copyright MATHCOUNTS Inc. 2013. All rights reserved. The National Math Club: 10 Question Challenges
members After giving each member of the math team the same
6. ����������
number of pencils, there were 4 pencils left over. The
left-over pencils are enough to give 2/5 of the math team
members one more pencil each. How many members
does the math team have?
7.���������� Integers p and q are both prime and p 2 + q 2 = 53. What is the value
of p + q ? 8.���������� Sequence A is an arithmetic sequence that begins 3, 7, 11, 15, ... . The
sum of the first eight terms of sequence A is 136. The terms of a second
arithmetic sequence (sequence B) are each 1 less than the terms of
sequence A. What is the sum of the first eight terms of sequence B? units The areas of triangle ABC and rectangle QRST are equal. What is the
9.����������
length of segment RS? A
Q
R
6
C
B
T
9
12
Preschool Class
Number of Students
years In a preschool class, there are 3-year-olds
10.���������
and 4-year-olds. The number of students of
each age is shown in the graph to the right.
What is the average age of the students in the
class? Express your answer as a decimal to
the nearest tenth. S
8
7
6
4
3
2
0
3-year-olds 4-year-olds
Copyright MATHCOUNTS Inc. 2013. All rights reserved. The National Math Club: 10 Question Challenges
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10-QUESTION
CHALLENGE 5
s
n
A
Name
Calculators may be used on this challenge.
177
1.����������
The array shown contains the
positive integers in a pattern
with three columns. The sum of
the three numbers in Row 2 is
15. What is the sum of the three
numbers in Row 20? Column Column Column
A
B
C
Row 1 1
2
3
Row 2 4
5
6
Row 3 7
8
9
·
·
·
·
·
·
·
·
·
partici- At a math competition, 75% of the participants got the answer to the first
2. �480
���������
pants
question on the test correct. If 120 participants did not get the correct
answer, how many total participants were there? 63
8
inches The length of Jay’s straw can be seen here. Sam’s straw is three times
3. ����������
the length of Jay’s straw. How long is Sam’s straw? Express your answer
as a mixed number. inches
1
2
3
4
5
6
11
4. ����������
The sum of four consecutive odd integers is 56. What is the least of the
four integers? 3 combos Two darts thrown at this dartboard land in two different
5.����������
regions. If the order that the two darts are thrown does
not matter, how many combinations of two different
regions from the 10 possible regions would result in a
sum of exactly 40 points?
5
20
40 35
15
30
40
10
45
20
Copyright MATHCOUNTS Inc. 2013. All rights reserved. The National Math Club: 10 Question Challenges
10 members After giving each member of the math team the same
6. ����������
number of pencils, there were 4 pencils left over. The
left-over pencils are enough to give 2/5 of the math team
members one more pencil each. How many members
does the math team have?
9
7.����������
Integers p and q are both prime and p 2 + q 2 = 53. What is the value
of p + q ? 128 Sequence A is an arithmetic sequence that begins 3, 7, 11, 15, ... . The
8.����������
sum of the first eight terms of sequence A is 136. The terms of a second
arithmetic sequence (sequence B) are each 1 less than the terms of
sequence A. What is the sum of the first eight terms of sequence B? 4 units The areas of triangle ABC and rectangle QRST are equal. What is the
9.����������
length of segment RS? A
Q
R
6
C
B
T
9
12
Preschool Class
Number of Students
3.7 years In a preschool class, there are 3-year-olds
10.���������
and 4-year-olds. The number of students of
each age is shown in the graph to the right.
What is the average age of the students in the
class? Express your answer as a decimal to
the nearest tenth. S
8
7
6
4
3
2
0
3-year-olds 4-year-olds
Copyright MATHCOUNTS Inc. 2013. All rights reserved. The National Math Club: 10 Question Challenges