5-QUESTION
CHALLENGE 25
Name
cartons
1.����������The
bar graph shows the number of
cartons of milk sold per day last week
at Jones Junior High. What is the
positive difference between the mean
and median number of cartons of milk
sold per day over the five-day period? Cartons Of Milk Sold Per Day
40
Number Sold
Calculators may be used.
30
20
10
0
Mon Tues Wed Thurs
Fri
Day
rectgls How many rectangles are in this figure? Each angle is a right
2. ���������
angle. % If B is 30% greater than A, and C is 80% greater than A, by what percent
3.����������
is C greater than B? Express your answer as a decimal to the nearest
tenth. 4.���������� The sum of 40 consecutive integers is 100. What is the largest of these
integers?
boys
5.����������
Currently, 41 of the members of a local club
are boys, and there are 80 members. If no
one withdraws from the club, what is the
minimum number of boys that would need to
1
join to make the club 3 boys? Copyright MATHCOUNTS Inc. 2013. All rights reserved. The National Math Club: 5 Question Challenges
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5-QUESTION
CHALLENGE 25
So
Calculators may be used.
Name
Cartons Of Milk Sold Per Day
Number Sold
1 cartons
1.����������The
bar graph shows the number of cartons of
milk sold per day last week at Jones Junior High.
What is the positive difference between the mean
and median number of cartons of milk sold per
day over the five-day period? 40
30
20
10
0
Mon Tues Wed Thurs
Fri
Day
The mean number of cartons sold per day is (15 + 20 + 25 + 30 + 30) ÷ 5 = 24, and the
median number of cartons sold per day is 25. The positive difference is 25 − 24 = 1.
19 rectgls How many rectangles are in this figure? Each angle is a right
2.����������
angle. We need a systematic way to keep track of the rectangles. There are 7 rectangles made
of a single region (which happen to be unit squares). There are 8 rectangles that consist
of two adjacent unit squares or “doubles” (4 horizontal and 4 vertical). There are only 2
“triples” (one horizontal and one vertical) and only 2 “quadruples” (the 2 by 2 squares).
That’s 7 + 8 + 2 + 2 = 19 rectangles in all.
38.5 % If B is 30% greater than A, and C is 80% greater than A, by what percent
3.����������
is C greater than B? Express your answer as a decimal to the nearest
tenth. The statement that B is 30% greater than A implies that B = 1.3 A. Similarly, we have C
= 1.8 A. Comparing C to B by division, we get (1.8A)/(1.3A) = (1.8)/(1.3) ≈ 1.3846, which
means that C is 38.5% greater than B, to the nearest tenth. Note, too, that we could start
by letting A = 100, then figuring that B = 130 and C = 180 and determining that C is 50
more than B in this case, which is 50/130 ≈ 0.3846 or 38.5% greater.
Copyright MATHCOUNTS Inc. 2013. All rights reserved. The National Math Club: 5 Question Challenges
22
4.����������
The sum of 40 consecutive integers is 100. What is the largest of these
integers?
The sum of the first 40 positive integers is (1 + 2 + ... + 39 + 40) = (41)(20) since we could
make 20 pairs of numbers each with a sum of 41. This is equal to 820 and is way too
large. We must start in the negative integers. If the list started at −19, it would have to
end at 20, and the sum would be 20. If we slide up one integer, and take the sum of the
integers −18 through 21, we get a sum of 60. Sliding up one integer more, we get the list
of integers −17 through 22, which has a sum of 100.
10 boys
5.����������
Currently, 41 of the members of a local club
are boys, and there are 80 members. If no
one withdraws from the club, what is the
minimum number of boys that would need to
1
join to make the club 3 boys? There must be 1/4 × 80 = 20 boys and 80 − 20 = 60 girls in the club now. If we add enough
boys to make them 1/3 of the club, then the 60 girls now in the club would be the other
2/3 of the members. If 60 is 2/3, then 30 is 1/3, so 10 more boys would need to join.
Copyright MATHCOUNTS Inc. 2013. All rights reserved. The National Math Club: 5 Question Challenges