KPMG Past Questions And Answers


66)

In the figure below at the right, each side of square ABCD is divided into three equal parts. If a point is chosen at random inside the square, what is the probability it will be in shaded region?


Since the answer doesn’t depend on the value of x(the probability will be the same no matter what x is), let x = 1. Then the area of the whole square is 3² = 9. The area of each shaded triangle or of all the white sector can be calculated, but there’s an easier way: notice that if you slide the four shaded triangles together, They form a square of side 1. Therefore the total shaded side is, and so the shaded area is 1/9 of the total area and the probability that the chosen point is in the shaded area is  1/9 (A). The idea of subtracting a part from the whole works with line segments as well as areas.

67)

In the figure below, ABCD is a rectangle, and arc BE and arc CF are arcs of circles centered at A and D. What is the area of the shaded region?


Solution
The entire region is a 2 × 5 rectangle whose area is 10. Since each white region is a quarter-circle of radius 2, the combined area of these region is that of a semicircle of radius 2: π (2) = 2π. Therefore, the area of the shaded region is
10 -2π = 2(5 – π) (B).

68)

From 1990 to 2000, Michael’s weight increase by 25%. If his weight was W kilograms in 2000, what was it in 1990?
 


Solution
Since Michael’s weight increase, his weight in 1990 was less than W. Eliminate
A, B, and C and guess. The answer is D
The Weight in 1990 is W/1.25 = 0.80W

69)

From 2002 to 2003 the sale s of a book decreased by 80%. If the sales in
2004 were the same in 2002, by what percent did they increase from 2003 to
2004?
 


Use tactic A7 and assume that 100 copies were sold in 2002 (and 2004).
Sales dropped by 80 (80% of 100) to 20 in 2003 and then increase by 80, from
20 back to 100, in 2004. The percent increase was  actual increase/orignal amount× 100% = 80/20×
100% = 400% (D).

70)

From 2003 to 2004 the number of boys in the school chess club decreased by 20%, and the number of girls increase by 20%. The ratio of girls to boys in the club in 2004 was how many times the ratio of girls to boys in the club in 2003?