Mat 540 Quiz 2
ANSWERS
1. Consider the trade-story as if it describes two separate trades, where: In the first trade, the man buys something for $60 and sells it again for $70, so he makes a profit of $10. In the second trade, the man buys something for $80 and sells it again for $90, so he makes again a profit of $10.
Conclusion: The man makes an overall profit of $10 + $10 = $20.
You can also look at the problem as follows:
The total expenses are $60 + $80 = $140 and the total earnings are $70 + $90 = $160. The overall profit is therefore $160 - $140 = $20.
2. 100 Km/hr because that is the top speed of the bus.
3. The man had to reply the number of characters in the word the Doorman was asking. He should have replied "Three" instead of "Five".
4. There are 5 women, 1 man and 14 children. …show more content…
5.
Here are the answers.
a. Cubes that have at least two sides painted in different colours are 24 + 8 = 32.
b. Cubes that have only one side painted are 24.
c. Cubes that have no side painted = 8.
d. Cubes that have exactly one side not painted = 0.
6. There are actually 204 squares on a chessboard. Surprised! Here is the explanation. There are 64 (1x1) squares. There are 49 (2x2) squares. There are 36 (3x3) squares. There are 25 (4x4) squares. There are 16 (5x5) squares. There are 9 (6x6) squares. Then there are 4 (7x7) squares and 1 big 8x8 square. So, there are a total of 204 squares on a normal chessboard.
7. One Apple
8. Man 1 will shout first. If Man1 will not shout then Man 2 surely shouts.
Reason: Man 1 can see the other two criminals? hats. If the hats are same color then he told his hat is opposite color of remaining two hats. So he shouts first. If Man 1 does not shout, it means that the hats of Man 2 and Man 3 are of different color. So Man 2 sees the color of Man 3 hat and he tells that the color of his hat is opposite to the color of Man 3
Hat.
9. With two people, there is one handshake. With three people, there are three handshakes. With four people, there are six handshakes. In general, with n+1 people, the number of handshakes is the sum of the first n consecutive numbers: 1+2+3+...+n. Since this sum is n(n+1)/2, we need to solve the equation n(n+1)/2 = 66. This is the quadratic equation n2+n-132 = 0. Solving for n, we obtain 11 as the answer and deduce that there were 12 people at the party.
10. Fill the 3-litre bottle and pour it into the empty 5-litre bottle. Fill the 3-litre bottle again, and pour enough to fill 5-litre bottle. This leaves exactly 1 litre in the 3-litre bottle. Empty the 5-litre bottle; pour the remaining 1 litre from the 3-litre bottle into the 5-litre bottle. Fill the 3-litre bottle and pour it into the 5-litre bottle. The 5-litre bottle now has exactly 4 litres.
1. Consider the trade-story as if it describes two separate trades, where: In the first trade, the man buys something for $60 and sells it again for $70, so he makes a profit of $10. In the second trade, the man buys something for $80 and sells it again for $90, so he makes again a profit of $10.
Conclusion: The man makes an overall profit of $10 + $10 = $20.
You can also look at the problem as follows:
The total expenses are $60 + $80 = $140 and the total earnings are $70 + $90 = $160. The overall profit is therefore $160 - $140 = $20.
2. 100 Km/hr because that is the top speed of the bus.
3. The man had to reply the number of characters in the word the Doorman was asking. He should have replied "Three" instead of "Five".
4. There are 5 women, 1 man and 14 children. …show more content…
5.
Here are the answers.
a. Cubes that have at least two sides painted in different colours are 24 + 8 = 32.
b. Cubes that have only one side painted are 24.
c. Cubes that have no side painted = 8.
d. Cubes that have exactly one side not painted = 0.
6. There are actually 204 squares on a chessboard. Surprised! Here is the explanation. There are 64 (1x1) squares. There are 49 (2x2) squares. There are 36 (3x3) squares. There are 25 (4x4) squares. There are 16 (5x5) squares. There are 9 (6x6) squares. Then there are 4 (7x7) squares and 1 big 8x8 square. So, there are a total of 204 squares on a normal chessboard.
7. One Apple
8. Man 1 will shout first. If Man1 will not shout then Man 2 surely shouts.
Reason: Man 1 can see the other two criminals? hats. If the hats are same color then he told his hat is opposite color of remaining two hats. So he shouts first. If Man 1 does not shout, it means that the hats of Man 2 and Man 3 are of different color. So Man 2 sees the color of Man 3 hat and he tells that the color of his hat is opposite to the color of Man 3
Hat.
9. With two people, there is one handshake. With three people, there are three handshakes. With four people, there are six handshakes. In general, with n+1 people, the number of handshakes is the sum of the first n consecutive numbers: 1+2+3+...+n. Since this sum is n(n+1)/2, we need to solve the equation n(n+1)/2 = 66. This is the quadratic equation n2+n-132 = 0. Solving for n, we obtain 11 as the answer and deduce that there were 12 people at the party.
10. Fill the 3-litre bottle and pour it into the empty 5-litre bottle. Fill the 3-litre bottle again, and pour enough to fill 5-litre bottle. This leaves exactly 1 litre in the 3-litre bottle. Empty the 5-litre bottle; pour the remaining 1 litre from the 3-litre bottle into the 5-litre bottle. Fill the 3-litre bottle and pour it into the 5-litre bottle. The 5-litre bottle now has exactly 4 litres.