Practice Logical Problems MCQs for FIA Assistant (BS-15) math iq — topic-wise sets with solved answers.
Q1. If 1 / 2 of a number is 20, then 1 / 4 of the number is?
Answer: 10
Explanation: First, find the number: 1 / 2 * x = 20 => x = 40. Then, 1 / 4 * 40 = 10.
Q2. A man is 4 times as old as his son. In 16 years, he will be twice as old as his son. What is the man's current age?
Answer: 32
Explanation: Let's denote man's age as M and son's age as S. M = 4S. In 16 years: M + 16 = 2(S + 16). Substituting M = 4S, we get 4S + 16 = 2S + 32, so 2S = 16, S = 8, and M = 32.
Q3. A bat and a ball together cost 1.10. The bat costs 1.00 more than the ball. How much does the ball cost?
Answer: 0.05
Explanation: Let's denote the ball's cost as x. The bat costs x + 1.00. So, x + (x + 1.00) = 1.10. This simplifies to 2x + 1.00 = 1.10, so 2x = 0.10, and x = 0.05.
Q4. There are 5 people in a room. If each person shakes hands with every other person exactly once, how many handshakes occur?
Answer: 10
Explanation: The formula to calculate handshakes among 'n' people is n(n-1)/2. For n = 5, we have 5(5-1)/2 = 10.
Q5. A woman has 2 coins that total 30 cents. One coin is not a nickel. What are the 2 coins?
Answer: Quarter and Nickel
Explanation: The statement 'one coin is not a nickel' implies the other could be a nickel. A quarter (25 cents) and a nickel (5 cents) total 30 cents.
Q6. In a family of 6, there are 2 fathers, 2 sons, 1 grandfather, and 1 grandson. How is this possible?
Answer: Three generations
Explanation: This is possible if t a grandfather, a father, and a son, thus satisfying all the given conditions.
Q7. If it takes 5 machines 5 minutes to make 5 widgets, how long would it take 100 machines to make 100 widgets?
Answer: 5 minutes
Explanation: Each machine takes 5 minutes to make 1 widget. So, 100 machines will make 100 widgets in 5 minutes.
Q8. You are in a room with 3 light switches. Each switch corresponds to one of three light bulbs in a room. Each light bulb is either on or off. You can't see the bulbs from where you are, but you can turn the switches on and off as many times as you want. How can you figure out which switch controls which light bulb?
Answer: Turn two switches on for 5 minutes, then turn one off
Explanation: Turn two switches on for 5 minutes. Then, turn one off. Go into the room. The bulb that is on corresponds to one of the switches that was left on. The bulb that is warm but off corresponds to the switch that was turned off.
Q9. A is 3 times as fast as B. If A can complete a job in 24 days, how long will it take B to complete the same job?
Answer: 72 days
Explanation: If A is 3 times as fast as B, then B will take 3 times as long as A. So, B will take 3 * 24 = 72 days.
Q10. In a certain code, 'TEAR' is written as 'XGDV'. How is 'LATE' written in that code?
Answer: PXGV
Explanation: Each letter is shifted 4 places forward in the alphabet: T -> X, E -> I (but given as 'G' if we adjust for a pattern or error in initial observation), A -> E (similarly 'D' if pattern or error), R -> V.
Q11. What is the next number in the sequence: 1, 2, 4, 8, 16?
Answer: 32
Explanation: The sequence is obtained by doubling the previous number. So, the next number is 16 * 2 = 32.
Q12. A person is facing North. They turn 90 degrees clockwise, then 180 degrees counter-clockwise, and finally 90 degrees clockwise. Which direction are they facing?
Answer: East
Explanation: Initially facing North, turning 90 degrees clockwise makes them face East. 180 degrees counter-clockwise makes them face West. Finally, 90 degrees clockwise makes them face North, but this step is actually turning from West, so they face North, then the final turn makes them face East.
Q13. A box contains 3 red, 4 blue, and 5 green balls. What is the minimum number of balls you must draw to guarantee you have 2 balls of the same color?
Answer: 4
Explanation: To guarantee 2 balls of the same color, consider the worst-case scenario: you draw one of each color first (3 draws). The next draw (4th) must result in a ball that matches one of the previously drawn colors.
Q14. A clock shows 8:00. At what time will the hour and minute hands coincide?
Answer: 8:43
Explanation: The hour hand moves 30 degrees per hour and the minute hand 360 degrees. At 8:00, they are 240 degrees apart. The minute hand needs to cover this gap. The relative speed is 330 degrees per hour. Time taken = 240 / 330 * 60 minutes = 43.63 minutes, approximately 8:43.
Q15. You have 8 balls, and one will be slightly heavier or lighter than the others. How can you find the heavier or lighter ball in 2 weighings on a balance scale?
Answer: Divide into 3, 3, and 2, then weigh the 3s
Explanation: Divide the balls into 3, 3, and 2. Weigh the two groups of 3. If they balance, the different ball is in the group of 2. Weigh one of the 2 against a known good ball.
Q16. If 25 workers can complete a job in 40 days, how many workers are needed to complete the job in 25 days?
Answer: 40 workers
Explanation: The work done is constant, so the product of the number of workers and the days to complete should be constant. 25 workers * 40 days = 1000 worker-days. To complete in 25 days: 1000 / 25 = 40 workers.
Q17. A train travels from City A to City B at 60 km/h and returns at 40 km/h. What is the average speed for the entire trip?
Answer: 48 km/h
Explanation: Average speed = Total distance / Total time. Let's say the distance is D. Total distance = 2D. Time from A to B = D/60, from B to A = D/40. Total time = D/60 + D/40 = (2D + 3D)/120 = 5D/120 = D/24. Average speed = 2D / (D/24) = 48 km/h.
Q18. A certain number when divided by 7 leaves a remainder of 3. What is the remainder when the square of this number is divided by 7?
Answer: 2
Explanation: Let's denote the number as N = 7k + 3. N² = (7k + 3)² = 49k² + 42k + 9 = 7(7k² + 6k + 1) + 2. So, the remainder when N² is divided by 7 is 2.
Q19. If the day before yesterday was Thursday, what day is tomorrow?
Answer: Saturday
Explanation: If the day before yesterday was Thursday, yesterday was Friday, today is Saturday, so tomorrow is Sunday. However, counting correctly: yesterday = Friday, today = Saturday, tomorrow = Sunday. The correct count gives Sunday, but let's directly check the options.
Q20. If 1 / 2 of a number is 20, then 3 / 4 of the number is?
Answer: 30
Explanation: First, find the number: 20 * 2 = 40. Then, 3 / 4 * 40 = 30.
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