參考答案:

　　1.Correct Answer: 21

　　Explanation:

　　Let each side = 110, so area = 110 x 110 = 12,100

　　If each side is ten per cent too long then each side should be reduced to 100.

　　So the correct area is 100 x 100 = 10,000.

　　The area is 2100 units too large. 2100 as a percentage of the correct area = (2100 /10,000)

　　100 = 21

　　2.Correct Answer: 6

　　Explanation:

　　A > 2M

　　M > S + 4 (where A, M and S are Andy�s, Mark�s, and Sean�s ages today)

　　We can select numbers less than 16 for Andy�s age and check the equations.

　　If A = 15, then M could be 7

　　(S is not needed here, but cannot be less than 1, which means that M cannot be less than 6)

　　3.Correct Answer: 7/9

　　Explanation:

　　The octagon is not a �regular� octagon.

　　But the sides of the square are divided into three equal parts.

　　If we let one of these parts = 1, the area of the square = 9

　　The octagon is the square minus four equal 45-45-90 triangles. The area of one such triangle = ½ x 1 x 1 = ½. Four triangles = 2

　　The octagon area = 9 - 2 = 7

　　The fraction = 7/9

　　4.Correct Answer: 2.4

　　Explanation:

　　This is another �special triangle� problem. The hypotenuse = 5, one leg = 3, so the other leg (AB) = 4

　　Now we can calculate the area = ½ x 4 x 3 = 6

　　The line segment DB is also the height of the triangle if we take AC as the base.

　　Area = ½ x AC x DB; 6 = ½ x 5 x DB; DB = 6/2.5 = 2.4

　　5.Correct Answer: 25

　　Explanation:

　　Let the total number of games to be played = n

　　Number lost = 5; number won = n-5

　　n-5 = 80/100 x n; n - 5 = 0.8n; 0.2n = 5; n = 25

　　6.Correct Answer: 4

　　Explanation:

　　We can find f(y²) by plugging in to get f(y²) = y² -1 Now we take 1/3 of this value as equal to 5; (y² � 1)/3 = 5; thus y² = 16 and y = 4

　　7.Correct Answer: 2.5

　　Explanation:

　　For inverse proportions remember the formula x1y1 = x2y2

　　Here initial painters x days = final painters x days; 3 x 5 = 2 x days

　　Total days taken will be 15/2 = 7.5, but there is a catch: you were asked how much longer it would take. Initial time was 5 days so it will take 2.5 days longer.

　　8.Correct Answer: 6

　　Explanation:

　　The description tells us that l and m are parallel lines with the circle lying between and touching both. Area of the circle = πr² = 9 π. Radius = 3 and diameter = 6.

　　9.Correct Answer: 154

　　Explanation:

　　The total number of chocolates to start with is 22. The first student has a chance of 5/22 of taking a soft center. The second student has a only 21 sweets left of which 4 could be soft: his chance is therefore 4/21. Similarly the third student has a chance of 3/20

　　Total probability is obtained by multiplying all these chances together: (5/22)(4/21)(3/20) = 1/154 [It is best to cancel the terms down rather than using a calculator because we want a fraction not a decimal]

　　10.Correct Answer: 21

　　Explanation:

　　A ratio of 5: 2 means 5x: 2x. Total shots = 7x. The last three shots added one unit to the ratio, and so x = 3. 7x = 21