Q. If a clock shows 12:45, what is the angle between the hour and minute hands?
A.
135 degrees
B.
150 degrees
C.
165 degrees
D.
180 degrees
Solution
At 12:45, the hour hand is at 337.5 degrees (12 * 30 + 45 * 0.5) and the minute hand is at 270 degrees (45 * 6). The angle between them is |337.5 - 270| = 67.5 degrees.
Q. If a clock shows 3:15, what is the angle between the hour and the minute hand?
A.
7.5 degrees
B.
22.5 degrees
C.
45 degrees
D.
52.5 degrees
Solution
At 3:15, the hour hand is at 97.5 degrees (3 hours * 30 + 15 minutes * 0.5) and the minute hand is at 90 degrees (15 minutes * 6). The angle between them is |97.5 - 90| = 7.5 degrees.
Q. If a clock shows 4:20, what is the angle between the hour and minute hands?
A.
120 degrees
B.
130 degrees
C.
140 degrees
D.
150 degrees
Solution
At 4:20, the hour hand is at 130 degrees (4*30 + 20*0.5) and the minute hand is at 120 degrees (20*6). The angle between them is |130 - 120| = 10 degrees.
Q. If a coin is flipped three times, what is the probability of getting exactly two heads?
A.
3/8
B.
1/2
C.
1/4
D.
1/8
Solution
The total outcomes are 2^3 = 8. The combinations for exactly 2 heads are HHT, HTH, THH, which gives us 3 favorable outcomes. So, the probability is 3/8.
Q. If A invests $15,000 and B invests $25,000 in a business, and they share the profit in the ratio of their investments, what will be B's share if the total profit is $20,000?
Q. If A invests $40,000 and B invests $60,000 in a business, and they share the profit in the ratio of their investments, what will be A's share if the total profit is $30,000?
Q. If A invests $4000 and B invests $6000 in a business, and they agree to share profits in the ratio of their investments, what is A's share of a profit of $5000?
Q. If a kite is flying at a height of 100 meters and the angle of elevation from a point on the ground is 60 degrees, how far is the point from the base of the kite?
Q. If a kite is flying at a height of 60 meters and the angle of elevation from a point on the ground to the kite is 60 degrees, how far is the point from the base of the kite's vertical line?
Q. If a man can complete a work in 10 days and another man can complete the same work in 15 days, how long will it take for both to complete the work together?
A.
6 days
B.
8 days
C.
10 days
D.
12 days
Solution
Work done by first man in one day = 1/10. Work done by second man in one day = 1/15. Together they do = 1/10 + 1/15 = 1/6. Therefore, they will complete the work in 6 days.
