5-QUESTION
CHALLENGE 13
Name
1.�������� The points on this graph show the end-ofyear sales amounts for each year. During
what year after 1994 did sales increase the
most number of dollars? End-of-Year Sales
(in millions of dollars)
Calculators may NOT be used.
Year
2.�������� Each of the five numbers 1, 5, 9, 13 and 17 is placed in one of the five
squares so that the sum of the three numbers in the horizontal row
equals the sum of the three numbers in the vertical column. What is the
largest possible sum of the three numbers in the horizontal row? 3.�������� What is the greatest possible value of the expression (8 � (–2)) � 5
in simplified form when an operation symbol (+, –, ×, ÷) is placed in each
rectangle? m Alexander used exactly 20 meters of fencing around
4.��������
three sides of a rectangular flowerbed beside his house.
He did not fence the fourth side, which is an eight-meter
section along the side of the house. What is the area of
this flowerbed? 2
5.�������� A cube with faces numbered 1 to 6 is rolled once and a dime is tossed
once. What is the probability of rolling a number less than 3 and tossing a tail? 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 13
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Name
1998 The points on this graph show the end-of1.��������
or ‘98 year sales amounts for each year. During
what year after 1994 did sales increase the
most number of dollars? End-of-Year Sales
(in millions of dollars)
Calculators may NOT be used.
Year
Since we are looking for the largest increase, we want to find the segment
that has the largest slope. By looking at the graph we find that between the
1997 point and the 1998 point there is the steepest slope. So was the largest
increase during 1997 or during 1998? Well, we know that the points on the
graph represent the end-of-year sales. Thus, the change occurred between
the
end of 1997 and the end of 1998, meaning that the largest increase
occurred during
1998.
31 Each of the five numbers 1, 5, 9, 13 and 17 is placed in one of the five
2.��������
squares so that the sum of the three numbers in the horizontal row
equals the sum of the three numbers in the vertical column. What is the
largest possible sum of the three numbers in the horizontal row? Given that the horizontal row and vertical column share the middle square,
the sum of the two other numbers in the horizontal row must equal the sum
of the two other numbers in the vertical column. We can see that 1 + 5 and 1 + 9 have no other two values whose sum equals 6 and 10, respectively. But 1 + 13 = 9 + 5 = 14. Also, we have 1 + 17 = 5 + 13 = 18. So we will check out
both of these possibilities. In the first case, the middle number must be 17 leading to 1 + 13 + 17 = 31. In the second case, the middle number must
be 9 leading to 1 + 17 + 9 = 27. 31 > 27. Thus, the largest possible sum is 31.
Copyright MATHCOUNTS Inc. 2013. All rights reserved. The National Math Club: 5 Question Challenges
50 What is the greatest possible value of the expression (8 � (–2)) � 5
3.��������
in simplified form when an operation symbol (+, –, ×, ÷) is placed in each
rectangle? The first thing we should notice is that the two is negative, so if we want
this to be as large as possible we want to “cancel out” that negative
by putting a subtraction symbol in the first rectangle. This will give us
(8 – (–2)) � 5 = 10 � 5. Now, in order to maximize this expression, we
should put a multiplication symbol in the last remaining rectangle. This
gives us a maximum value of 10 × 5 = 50.
48 m Alexander used exactly 20 meters of fencing around
4.��������
three sides of a rectangular flowerbed beside his house.
He did not fence the fourth side, which is an eight-meter
section along the side of the house. What is the area of
this flowerbed? 2
We are told that the flower bed is rectangular and that one eight-meter
side of the rectangle is along the side of the house. There must be another
8-meter side of the rectangle that uses 8 meters of the 20 meters of
fencing. That leaves 20 – 8 = 12 meters to divide equally between the other
two sides of the rectangle. The dimensions of the flower bed must be 6 meters by 8 meters, so the area is 6 × 8 = 48 square meters.
1
6
5.�������� A cube with faces numbered 1 to 6 is rolled once and a dime is tossed
once. What is the probability of rolling a number less than 3 and tossing a tail? Express your answer as a common
fraction. There are two numbers less than 3 on a standard die (namely, 1 and 2),
so there is a 2/6 chance of rolling one of those. There is also a 1/2 chance
of tossing a tail on the dime. The probability that these two things will
happen together is 2/6 × 1/2 = 1/6.
Copyright MATHCOUNTS Inc. 2013. All rights reserved. The National Math Club: 5 Question Challenges