Basic Numeracy/Quantitative Aptitude

Detailed Solution

1. c: Total area of disk:
Ad = pi * r ²
Angle t in radians of central angle of red sector
t = (360-120)* pi / 180 = (4/3) pi
Area of red sector:
As = (1/2) t * r 2
Percentage of total area in red
P = [ (1/2) t * r 2 ] / [ pi * r 2 ]
= 4 / 6 = 66.7% (3 significant digits)

2. b: Amy can travel clockwise or anticlockwise on the diagram.
Clockwise, she has no choice of route from A to B, a choice of one out of two routes from B to C, and a choice of one out of two routes from C back to A. This gives four possible routes.
Similarly, anticlockwise she has four different routes.
Total routes = 8

3. d: If we take AE as the base of triangle AEC, then the height is CD.
The height of the triangle is therefore, 9 (given).
To find the base we need to see that triangles AEB and CDE are similar. The ratio AB: CD, is therefore equal to the ratio AE: ED. The given information shows that the ratio is 3:9, or 1:3.
Now dividing AD (4) in this ratio gives us AE as 1.
The area of AEC = ½ base x height
=1/2 x 9 = 4.5

4. b: The marked angle, ABC must be more than 90 degrees because it is the external angle of triangle BDC, and must be equal to the sum of angles BDC (90) and DCB.
Also ABC is not a straight line and must be less than 180.
Therefore 90 < 5x < 180
The only value of x which satisfies this relation is 20.

5.

6.

7.

8. c: The correct answer is 1/2.
There are six numbers on a die: 1, 2, 3, 4, 5, and 6. There are three even numbers on the die: 2, 4, and 6. 3 out of six numbers are even. 3/6 reduces to 1/2.

9. a: The correct answer is 3/4.
A quick way of going about this problem is determining the probability that one of your friend's outcomes will appear. The probability of multiple events happening is equal to the product of the probability of each single event. The probability of flipping heads is 1/2, so the probability of flipping three heads in a row would be (1/2 * 1/2 * 1/2), or 1/8. The same thing occurs in the tails. (1/2 * 1/2 * 1/2) is equal to 1/8. The probability of your friend winning is 2/8, or 1/4. Subtract 1/4 from 1 to get 3/4, the probability of you winning

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