Mensa Numerical Reasoning 4

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?

Accepted Answer

13

Answer

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?

Accepted Answer

23

Answer

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?

Accepted Answer

72 mph

Answer

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, ?

Accepted Answer

57

Answer

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?

Accepted Answer

120

Answer

0.4x = 0.6y gives x = 1.5y; substituting into x + y = 200 yields 2.5y = 200, so y = 80 and x = 120.

Mensa Practice Test

Mensa Practice Test

Mensa Numerical Reasoning 4