Download 5-question challenge 28

5-QUESTION
CHALLENGE 28
Calculators may be used.
Name
Favorite Vowel
I
people
1.����������The
exact results of a survey of 1000 people are shown
A
in the pie chart. How many more people chose A as their U
20%
30%
favorite vowel than chose U as their favorite vowel? 2%
40% 8%
O
E
units What is the number of units in the length of segment PQ? Express
2. ���������
your answer as a mixed number. P
Q
5
3
4
1
2
6
ints How many positive integers have a value between
3.����������
8 and 72 ? 4.���������� What is the sum of the 10th number
in each of the columns A, B and C
in the array shown? Column Column Column
A
B
C
Row 1 1
200
1
Row 2 10
195
4
Row 3 19
190
9
Row 4 28
185
16
Row 5 37
180
25
·
·
·
·
·
·
·
·
·
5.����������Aaron will roll a standard 6-sided die twice. What is the probability that
he will roll different numbers on the two rolls? Express your answer as a
common fraction.
Copyright MATHCOUNTS Inc. 2013. All rights reserved. The National Math Club: 5 Question Challenges
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5-QUESTION
CHALLENGE 28
l
o
S
Calculators may be used.
Name
Favorite Vowel
I
A
U
20%
30%
2%
280 people
1.����������The
exact results of a survey of 1000 people are shown
in the pie chart. How many more people chose A as their
40%
favorite vowel than chose U as their favorite vowel? E
If 30% of the people chose A as their favorite vowel, that is (0.30)(1000) = 300 people. If
2% of the people chose U as their favorite vowel, that is (0.20)(1000) = 20 people. There
8%
O
were 300 − 20 = 280 more people who chose A as their favorite vowel.
1
2
2. ���������
What is the number of units in the length
3
P
Q
of segment PQ? Express your answer as a
5
3
4
1
2
mixed number. onthe ruler
is divided into 6 equal sections. Therefore, there are 26
Each unit labeled
units from P to the mark at 2, 3 units from the mark at 2 to the mark at 5, and
the mark at 5 to Q. This is a total distance of 26 + 3 + 61 = 3 63 = 3 21 units.
6
3.����������
How many positive integers have a value between
8 and
1
6
6
units from
72 ?
Only the square root of a perfect square will result in an integer. The smallest perfect
square greater than 8 is 9, and 9 = 3 . The largest perfect square less than 72 is 64, and
64 = 8 . The 6 positive integers within the range are 3, 4, 5, 6, 7 and 8.
337
4.����������
What is the sum of the 10th number in each of
the columns A, B and C in the array shown? Column Column Column
A
B
C
Row 1 1
200
1
Row 2 10
195
4
Row 3 19
190
9
Row 4 28
185
16
Row 5 37
180
25
·
·
·
·
·
·
·
·
·
Column A is an arithmetic sequence adding 9 each time. Starting with 1, the 10th number
will be 1 + 9(9) = 82. Column B is an arithmetic sequence subtracting 5 each time.
Starting with 200, the 10th number will be 200 − 9(5) = 155. Column C is the list of positive
perfect squares. The 10th number will be 102 = 100. The sum of these values is 82 + 155 + 100 = 337.
Copyright MATHCOUNTS Inc. 2013. All rights reserved. The National Math Club: 5 Question Challenges
5
6
5.����������Aaron
will roll a standard 6-sided die twice. What is the probability that
he will roll different numbers on the two rolls? Express your answer as a
common fraction.
No matter what number Aaron rolls the first time, exactly 5 of the 6 possible outcomes for
the second roll will be successful. Therefore, the probability is 56 .
Copyright MATHCOUNTS Inc. 2013. All rights reserved. The National Math Club: 5 Question Challenges