Gauss Solutions Worksheet With Answers - Grade 7 - University Of Waterloo

Gauss Solutions Worksheet With Answers - Grade 7 - University Of Waterloo - 1998 Page 7

Solutions

1998 Gauss Contest - Grade 7

18. The letters of the word ‘GAUSS’ and the digits in the number ‘1998’ are each cycled separately and

then numbered as shown.

1. AUSSG 9981

2. USSGA 9819

3. SSGAU 8199

etc.

If the pattern continues in this way, what number will appear in front of GAUSS 1998?

(A) 4

(B) 5

(D) 16

(E) 20

Solution

Because the word ‘GAUSS’ has five letters in it, the numbers 5, 10, 15, 20, ... will appear beside this

word. Similarly, the four digits of ‘1998’ will have the numbers 4, 8, 12, 16, 20, 24, ... beside this

number.

From this listing, we can see that the correct number is 20 which is the l.c.m. of 5 and 4.

ANSWER: (E)

19. Juan and Mary play a two-person game in which the winner gains 2 points and the loser loses 1 point.

If Juan won exactly 3 games and Mary had a final score of 5 points, how many games did they play?

(A) 7

(B) 8

(D) 5

(E) 11

Solution

If Juan won 3 games then Mary lost 3 points so that she must have had 8 points before losing in order

to have a final total of 5.

If Mary had 8 points before losing then she must have won 4 games.

If Mary won 4 games and Juan won 3 games there was a total of 7 games.

ANSWER: (A)

20. Each of the 12 edges of a cube is coloured either red or green. Every face of the cube has at least one

red edge. What is the smallest number of red edges?

(A) 2

(B) 3

(D) 5

(E) 6

Solution

If the heavy black lines represent the colour red, every face

will have exactly one red edge. So the smallest number of

red edges is 3.

ANSWER: (B)

Gauss Solutions Worksheet With Answers - Grade 7 - University Of Waterloo - 1998 Page 7