5-QUESTION
CHALLENGE 30
Name
Calculators may not be used.
minutes
1.����������
Erik can set up and burn a single CD on his computer in
3.5 minutes. At this rate, how long will it take Erik to set up
and burn 20 of this same CD? units The square shown is divided into 4 congruent rectangles.
2. ���������
If the perimeter of the square is 144 units, what is the
perimeter of one of the four congruent rectangles? students Two-hundred students at Hypatia Middle School were surveyed about
3.����������
their after-school activities.
57 participated in basketball
113 participated in MATHCOUNTS
46 participated in neither activity
How many students participated in both activities? N
4.����������
65
34
9
In this Number Wall, you add the numbers next to each
other and write the sum in the block directly above the
two numbers. What number will be in the block labeled
N?
15
7
5.����������If ♦(a, b, c) = abc, what is the value of ♦(1, 2, 3) + ♦(3, 2, 1) + ♦(3, 1, 2)?
Copyright MATHCOUNTS Inc. 2013. All rights reserved. The National Math Club: 5 Question Challenges
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5-QUESTION
CHALLENGE 30
So
Name
Calculators may not be used.
70 minutes
1.����������
Erik can set up and burn a single CD on his computer in
3.5 minutes. At this rate, how long will it take Erik to set up
and burn 20 of this same CD? It will take Erik 20 × 3.5 = 70 minutes to burn 20 CDs.
2. ���������
90 units The square shown is divided into 4 congruent rectangles.
If the perimeter of the square is 144 units, what is the
perimeter of one of the four congruent rectangles? If the perimeter of the square is 144 units, each side of the square is 144 ÷ 4 = 36 units.
One side of the square is equal to the length of each rectangle. One side of the square
also is equal to four rectangle widths, so 36 = 4w → w = 9. The perimeter of one of the
congruent rectangles is then 36 + 9 + 36 + 9 = 90 units.
16 students Two-hundred students at Hypatia Middle School were surveyed about
3.����������
their after-school activities.
57 participated in basketball
113 participated in MATHCOUNTS
46 participated in neither activity
How many students participated in both activities? Since 46 students participated in neither
activity, 200 − 46 = 154 students participated in
at least one activity. Knowing 113 of these 154 students did MATHCOUNTS, means there
are 154 − 113 = 41 students not doing MATHCOUNTS who must have played basketball.
However, there are 57 − 41 = 16 remaining basketball players who must be students who
also do MATHCOUNTS.
Copyright MATHCOUNTS Inc. 2013. All rights reserved. The National Math Club: 5 Question Challenges
132
4.����������In
this Number Wall, you add the numbers next to each other and write
the sum in the block directly above the two numbers. What number will
be in the block labeled N?
N
65
34
15
9
7
Working from the bottom row, we can determine the number between the 9 and 7 is 8,
since 15 − 7 = 8. The number to the left of 15 is 17 since 9 + 8 = 17. The number above 17
and 15 is 17 + 15 = 32. The number to the left of 32 is 65 − 32 = 33. The number above 34
and 33 is 34 + 33 = 67. The number, N, above 67 and 65 is 67 + 65 = 132.
17
5.����������If
♦(a, b, c) = abc, what is the value of ♦(1, 2, 3) + ♦(3, 2, 1) + ♦(3, 1, 2)?
Our expression has three addends, and we can determine the value of each of them:
♦(1, 2, 3) = 1 × 23 = 8; ♦(3, 2, 1) = 3 × 21 = 6; and ♦(3, 1, 2) = 3 × 12 = 3. Now we have
8 + 6 + 3 = 17.
Copyright MATHCOUNTS Inc. 2013. All rights reserved. The National Math Club: 5 Question Challenges