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1. A typist can type 45 words per minute. He increases his speed by 20 per cent. How many words can he now type per hour ?

2. If 2y - x = 8 , and 3x - y = 1, what is the value of x ?

3. The sum of four consecutive integers is 410. What is the value of the least of these integers?

4. On a map showing only four countries, A, B, C and D, A shares a border with B and C. Country D shares a border with B and C. But countries B and C and countries A and D do not share borders. If the map requires different colours for countries with common borders, what is the minimum number of colours required to complete the map?

5. A square has sides s and diagonal d. If 2s² + d² = 100, what is the value of s?

6. Different four-letter passwords can be constructed using the letters A, B, C and D only once. How many such passwords exist if either C or B must be in second position?

7. A book distributor sends out standardized packages weighing 1, 1.5 or 2 kilograms. If during one week 40 per cent of the packages weigh 1 kg, 50 per cent weigh 1.5 kg and 10 per cent weigh 2 kg, what is the average weight in kilograms of the parcels that week?

student-produced response questions参考答案

1.Correct Answer: 3240

Explanation:

A 20 per cent increase on 45 words per minute = 1.2 x 45 = 54 words per minute.

To get words per hour, multiply by 60 = 3240

2.Correct Answer: 2

Explanation:

This is a pair of simultaneous equations. Rearrange :

2y - x = 8; -y +3x = 1; multiply the second by 2

-2y + 6x = 2; then add to the first to give

5x = 10; x = 2

3.Correct Answer: 101

Explanation:

Four consecutive integers can be written n + (n + 1) + (n + 2) + (n + 3)

Their sum = 4n + 6 = 410

4n = 404; n = 101

4.Correct Answer: 2

Explanation:

Draw a diagram.

A and D can be the same color because they do not share a border. Also B and C can be one color, but B and C must differ from A and D. So two colors are needed.

5.Correct Answer: 5

Explanation:

The diagonal and two sides form an isosceles right triangle.

Using Pythagoras s² + s² = d²; 2s² = d²

Since these terms are equal we can replace d² in the given equation

Hence 2s² + 2s² = 100; 4s² = 100; s² = 25; s = 5

6.Correct Answer: 12

Explanation:

First imagine C in second position. This gives a choice of 1 out of three for first place, and one out of two for third place. This is equivalent to 6 possible combinations.

Now putting B in second place and using the same logic there are 6 more combinations.

Total = 12

7.Correct Answer: 1.35

Explanation:

This is a weighted average problem.

The average weight = (40 x 1 + 50 x 1.5 + 10 x 2) 100

(40 + 75 + 20)/100 = 1.35