Logical Problems MCQs set 3 for LUMS LCAT intelligence — 20 solved questions.
Q1. A snail is at the bottom of a 20 feet well. Each day, it climbs up 3 feet, but at night, it slips back 2 feet. How many days will it take for the snail to reach the top?
Answer: 18 days
Explanation: The snail effectively climbs 1 foot per day. On the 18th day, it climbs 3 feet and reaches the top.
Q2. A bat and a ball together cost 110. The bat costs 100 more than the ball. How much does the ball cost?
Answer: 5
Explanation: Let the ball's cost be x. Then the bat's cost is x + 100. So, x + (x + 100) = 110, giving 2x = 10, hence x = 5.
Q3. A is 3 times as fast as B. If A takes 12 days to complete a task, how many days will B take?
Answer: 36 days
Explanation: If A is 3 times as fast as B, then B takes 3 times as long as A. So, B takes 3 * 12 = 36 days.
Q4. In a family of 6, there are 2 fathers, 2 sons, and 1 grandfather. How is this possible?
Answer: There are 3 generations
Explanation: The family consists of a grandfather, a father, and a son, making 3 generations, hence 2 fathers and 2 sons.
Q5. If 10 men can reap a field in 20 days, how many men are needed to reap the same field in 10 days?
Answer: 20 men
Explanation: The work done is constant, so men * days = constant. 10 men * 20 days = x men * 10 days, giving x = 20 men.
Q6. In a certain code, 'oka' means 'not', 'meta lisa' means 'good boy', and 'oka lisa' means 'not good boy'. What is the code for 'boy'?
Answer: lisa
Explanation: From 'meta lisa' and 'oka lisa', 'lisa' is common and corresponds to 'boy'. 'meta' corresponds to 'good'.
Q7. A is to B as C is to D. If A is 2 and B is 4, and C is 6, what is D?
Answer: 12
Explanation: The ratio of A to B is 1:2, so the ratio of C to D should be the same. Hence, D = 2 * 6 = 12.
Q8. What comes next in the series: 1, 2, 4, 7, 11?
Answer: 16
Explanation: The pattern is adding 1, 2, 3, 4, ... to the previous term. So, the next difference should be 5, making the next number 11 + 5 = 16.
Q9. If 1 / 2 of the workers are men and 1 / 3 of the men are married, what fraction of workers are married men?
Answer: 1 / 6
Explanation: To find the fraction of married men, we multiply the fraction of men by the fraction of married men: 1 / 2 * 1 / 3 = 1 / 6.
Q10. In a row of 40 students, Rohan is 15th from the left. What is his position from the right?
Answer: 26th
Explanation: To find Rohan's position from the right, we subtract his position from the left from the total number of students and add 1: 40 - 15 + 1 = 26.
Q11. If 5 machines take 5 minutes to make 5 widgets, how long will it take for 100 machines to make 100 widgets?
Answer: 5 minutes
Explanation: The rate of production per machine is 1 widget per 5 minutes. So, 100 machines will take 5 minutes to make 100 widgets.
Q12. A man is 4 times as old as his son. 4 years ago, he was 6 times as old as his son. What is the man's current age?
Answer: 40 years
Explanation: Let's denote the son's current age as x. The man's current age is 4x. 4 years ago, the man's age was 4x - 4 and the son's age was x - 4. So, 4x - 4 = 6(x - 4).
Q13. A, B, C, D, E are sitting in a row. B is between A and E. If A is at one end and there are 3 people between A and B, who is at the other end?
Answer: D
Explanation: Since A is at one end and there are 3 people between A and B, B is at the 5th position. E must be at the other end because B is between A and E.
Q14. If it takes 5 hours to travel from city A to city B at a speed of 60 km/h, how long will it take to travel the same distance at 75 km/h?
Answer: 4 hours
Explanation: First, we find the distance between the cities: distance = speed * time = 60 * 5 = 300 km. Then, we find the time taken at 75 km/h: time = distance / speed = 300 / 75 = 4 hours.
Q15. A is twice as good as B and together they finish a task in 14 days. How many days will A take to finish the task alone?
Answer: 21 days
Explanation: Let's denote B's rate as x. A's rate is 2x. Together, they work at a rate of 3x. Since they finish the task in 14 days, their combined rate is 1 / 14 of the task per day.
Q16. If 15 men can reap a field in 35 days, how many men are required to reap the same field in 21 days?
Answer: 25 men
Explanation: The work done is the same in both cases. So, the product of the number of men and the days should be equal. 15 * 35 = 21 * x, x = (15 * 35) / 21 = 25.
Q17. In a certain code, 'TEACHER' is coded as 'VGCEGT'. How is 'STUDENT' coded in the same way?
Answer: UWVGFVP
Explanation: Each letter is shifted 2 places forward in the alphabet: T+2=U, E+2=G, A+2=C, C+2=E, H+2=J, E+2=G, R+2=T. Applying the same shift to 'STUDENT': S+2=U, T+2=V, U+2=W, D+2=F, E+2=G, N+2=P, T+2=V.
Q18. A train 100 meters long is running at a speed of 60 km/h. How long will it take to pass a pole?
Answer: 6 seconds
Explanation: First, we convert the speed to meters per second: 60 km/h = 60 * 1000 / 3600 = 16.67 m/s. Time = distance / speed = 100 / 16.67 = 6 seconds.
Q19. If a bakery sells 250 loaves of bread per day at 2 / loaf, and it operates 7 days a week, how much does it earn in a week?
Answer: 3500
Explanation: Daily earnings = 250 loaves * 2 / loaf = 500. Weekly earnings = 500 * 7 = 3500.
Q20. A and B can do a work in 10 and 15 days, respectively. If they work together, how many days will they take to complete it?
Answer: 6 days
Explanation: A's rate is 1 / 10, B's rate is 1 / 15. Together, their rate is 1 / 10 + 1 / 15 = (3 + 2) / 30 = 5 / 30 = 1 / 6. So, they will take 6 days.