Mensa Numerical Reasoning 4 — Questions and Answers
Question 1: A sequence is defined as: each term equals the average of the two preceding terms. If the first two terms are 4 and 16, what is the 4th term?
- 11
- 12
- 13 (Correct answer)
- 14
Correct answer: 13
t3 = (4+16)/2 = 10; t4 = (16+10)/2 = 13.
Question 2: In a set of 9 numbers the mean is 15. If the largest number is removed, the new mean of the remaining 8 numbers becomes 14. What is the largest number?
- 21
- 22
- 23 (Correct answer)
- 24
Correct answer: 23
Original sum = 9×15 = 135; new sum = 8×14 = 112; largest number = 135 − 112 = 23.
Question 3: A train travels from City A to City B at 90 mph and returns at 60 mph. What is the average speed for the entire round trip?
- 72 mph (Correct answer)
- 75 mph
- 78 mph
- 80 mph
Correct answer: 72 mph
Average speed = 2×(90×60)/(90+60) = 10800/150 = 72 mph using the harmonic mean for equal distances.
Question 4: What is the next number in the series: 3, 7, 13, 21, 31, 43, ?
- 55
- 57 (Correct answer)
- 59
- 61
Correct answer: 57
The differences are 4, 6, 8, 10, 12, 14 (increasing by 2 each step), so 43 + 14 = 57.
Question 5: If 40% of a number equals 60% of another number and their sum is 200, what is the larger of the two numbers?
- 100
- 110
- 120 (Correct answer)
- 130
Correct answer: 120
0.4x = 0.6y gives x = 1.5y; substituting into x + y = 200 yields 2.5y = 200, so y = 80 and x = 120.
Question 6: A square garden has its side length increased by 20%. By what percentage does its area increase?
- 20%
- 36%
- 40%
- 44% (Correct answer)
Correct answer: 44%
New area = (1.2s)² = 1.44s², representing a 44% increase over the original area.
Question 7: Three workers complete a job in 12 days. After working together for 4 days, one worker leaves. How many additional days do the two remaining workers need to finish?
- 10
- 12 (Correct answer)
- 14
- 16
Correct answer: 12
In 4 days, 3 workers finish 4/12 = 1/3 of the job; 2/3 remains; two workers work at 2/36 = 1/18 of the job per day, so they need (2/3)÷(1/18) = 12 more days.
Mensa Numerical Reasoning 4
A sequence is defined as: each term equals the average of the two preceding terms.
If the first two terms are 4 and 16, what is the 4th term?