Mensa IQ Numerical Reasoning and Arithmetic Flashcards

Find the missing value in the sequence: 100, 91, 83, 76, 70, [?]

Answer: 65

The differences are −9, −8, −7, −6, −5; the next difference is −5, so 70 − 5 = 65.

In a number grid, row values follow: Row 1: 1, 4, 9. Row 2: 4, 16, 36. Row 3: 9, 36, [?].

Answer: 81

Each cell = (row × column)²; cell (3,3) = (3×3)² = 81. Alternatively, each cell = row² × col².

A rectangle has a perimeter of 54 cm. Its length is twice its width. What is its area?

Answer: 162 cm²

Let width = w; length = 2w. Perimeter: 2(w+2w) = 6w = 54, so w = 9; length = 18. Area = 9×18 = 162 cm².

What replaces [?]: 2, 6, 18, 54, [?], 486?

Answer: 162

Each term is multiplied by 3; 54 × 3 = 162.

If 30% of a number is 45, what is 70% of that number?

Answer: 105

30% = 45, so the whole number = 150. 70% of 150 = 105.

A sequence uses two interleaved rules: odd-position terms triple the previous odd term; even-position terms equal the previous odd term minus 5. Sequence so far: 4, [?], 12, 7, 36, 31, [?].

Answer: −1 and 108

Odd positions: 4, 4×3=12, 12×3=36, 36×3=108. Even positions (odd−5): 4−5=−1, 12−5=7, 36−5=31, 108−5=103? The two blanks are position 2 (=4−5=−1) and position 7 (=36×3=108).

A car travels from city A to city B in 3 hours at 80 km/h. It returns on a route 30 km shorter. The return trip takes 2.5 hours. What is the return speed?

Answer: 84 km/h

Distance A→B = 80×3 = 240 km; return route = 240−30 = 210 km; speed = 210÷2.5 = 84 km/h.