Gauss Solutions Worksheet With Answers - Grade 7 - University Of Waterloo - 1998 Page 5
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10Solutions
1998 Gauss Contest - Grade 7
12. Steve plants ten trees every three minutes. If he continues planting at the same rate, how long will it
take him to plant 2500 trees?
1
1
(A) 1
h
(B) 3 h
(C) 5 h
(D) 10 h
(E) 12
h
4
2
Solution 1
3
Since Steve plants ten trees every three minutes, he plants one tree every
minute.
10
3
3
750
1
×
×
=
=
=
In order to plant 2500 trees, he will need
minutes or
hours.
2 500 750
2500 750
.
12
10
10
60
2
Solution 2
Since Steve plants ten trees every three minutes, he plants 200 trees per hour.
2500
1
=
In order to plant 2500 trees, he will need
12
hours.
ANSWER: (E)
200
2
13. The pattern of figures
is repeated in the sequence
,
,
,
,
,
,
,
,
,
... .
,
The 214th figure in the sequence is
(A)
(B)
(C)
(D)
(E)
Solution
Since the pattern repeats itself after every five figures, it begins again after 210 figures have been
completed.
The 214th figure would be the fourth element in the sequence or
.
ANSWER: (D)
3
14. A cube has a volume of 125
cm . What is the area of one face of the cube?
2
2
2
2
2
2
(A) 20
cm
(B) 25
cm
(C) 41
cm
(D) 5
cm
(E) 75
cm
3
Solution
3
If the volume of the cube is 125
cm , then the length, width and height are each 5 cm.
2
× or 25
The area of one face is 5 5
cm .
ANSWER: (B)
15. The diagram shows a magic square in which the sums of the
8
numbers in any row, column or diagonal are equal. What is
the value of n?
9
5
(A) 3
(B) 6
(C) 7
4
n
(D) 10
(E) 11
Solution
+ + =
The ‘magic’ sum is 8 9 4 21
, so the centre square is 7.
+ + =
If the centre square is 7, then the square on the lower right has 6 in it giving 4
n
6 21
.
Therefore n = 11.
ANSWER: (E)
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