Mensa Numerical Reasoning 5

Question 1

A number leaves a remainder of 3 when divided by 5 and a remainder of 4 when divided by 7. What is the smallest such positive integer?

Accepted Answer

18

Answer

18 ÷ 5 = 3 remainder 3 ✓ and 18 ÷ 7 = 2 remainder 4 ✓, making 18 the smallest such integer.

Question 2

In a geometric progression, the 3rd term is 18 and the 6th term is 486. What is the common ratio?

Accepted Answer

3

Answer

The 6th term divided by the 3rd term equals r³ = 486/18 = 27, so r = ∛27 = 3.

Question 3

A shop sells items at a 25% profit on cost. If the cost price rises by 20% but the selling price stays the same, what is the new profit percentage?

Accepted Answer

4.17%

Answer

With original cost = 100, selling price = 125; new cost = 120; new profit = 5; profit % = 5/120 × 100 ≈ 4.17%.

Question 4

What value of x satisfies the equation 2^(x+3) = 4^(x−1)?

Accepted Answer

5

Answer

Rewriting 4^(x−1) as 2^(2x−2) gives x+3 = 2x−2, so x = 5.

Question 5

The ratio of boys to girls in a class is 3:4. If 6 more boys join and 2 girls leave, the ratio becomes 1:1. How many students were in the class originally?

Accepted Answer

56

Answer

Let boys = 3k and girls = 4k; setting 3k+6 = 4k−2 gives k = 8, so original total = 7k = 56.

Mensa Practice Test

Mensa Practice Test

Mensa Numerical Reasoning 5