Q. A double convex lens has a focal length of 10 cm. If it is made of a material with a refractive index of 1.5, what is the radius of curvature of each surface assuming they are equal?
A.
15 cm
B.
20 cm
C.
25 cm
D.
30 cm
Solution
Using the lens maker's formula, R = 2f(n-1) = 2*10*(1.5-1) = 20 cm.
Q. A factory produces two types of widgets. The first type is produced every 12 days and the second every 15 days. How often will both types be produced on the same day? (2023)
A.
30 days
B.
60 days
C.
45 days
D.
75 days
Solution
The LCM of 12 and 15 is 60, so both types will be produced on the same day every 60 days.
Q. A family has 2 children. What is the probability that both children are boys if it is known that at least one is a boy?
A.
1/2
B.
1/3
C.
1/4
D.
1/5
Solution
The possible combinations of children are BB, BG, GB, GG. Given that at least one is a boy, we can eliminate GG, leaving us with BB, BG, GB. Out of these 3 combinations, only 1 is BB. Therefore, the probability is 1/3.
Q. A family has 3 children. What is the probability that at least one child is a girl given that at least one child is a boy?
A.
1/2
B.
2/3
C.
3/4
D.
1/4
Solution
The only combinations with at least one boy are: BBB, BBG, BGB, GBB, BGG, GBG, GGB. Out of these, all combinations except BBB have at least one girl. Thus, P(At least one girl | At least one boy) = 6/7.
Q. A family has an average income of $50,000. If the father earns $60,000 and the mother earns $40,000, what is the average income of their two children if the total family income is $200,000?
A.
$40,000
B.
$50,000
C.
$60,000
D.
$70,000
Solution
Total income of children = $200,000 - ($60,000 + $40,000) = $100,000. Average income of children = $100,000 / 2 = $50,000.
Q. A family has three children with ages 10, 12, and 14. If they have another child, what age must the new child be for the average age of the family to be 12?
A.
8
B.
10
C.
12
D.
14
Solution
Let the age of the new child be x. Then, (10 + 12 + 14 + x) / 4 = 12. Solving gives x = 8.
Q. A family has three children with ages 5, 10, and 15. If a new child is born, what age must the new child be to maintain an average age of 10?
A.
5
B.
10
C.
15
D.
20
Solution
Current total age = 5 + 10 + 15 = 30. To maintain an average of 10 with 4 children, total age must be 40. Therefore, the new child's age must be 40 - 30 = 10.
Q. A family has three children with ages 5, 10, and 15. If they have another child, what age must the new child be to maintain an average age of 10? (2023)
A.
5
B.
10
C.
15
D.
20
Solution
Current total age = 5 + 10 + 15 = 30. To maintain an average of 10 with 4 children, total age must be 40. Therefore, the new child's age must be 40 - 30 = 10.
Q. A farmer has a rectangular field of dimensions 50 m by 30 m. If he wants to irrigate it with water from a river, how much water is needed to cover the field to a depth of 0.1 m? (2023)
A.
150 m³
B.
300 m³
C.
500 m³
D.
100 m³
Solution
Volume of water needed = Area × Depth = (50 m × 30 m) × 0.1 m = 150 m³.
