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1.  
4, 6, 12, 24, 44, 74, ?

Correct Answer: A [116]

Explanation:

Differences 2, 6, 12, 20, 30 → second differences 4, 6, 8, 10 → 12 → 42 → 74 + 42 = 116.

2.  
64, 32, 32, 48, 96, ?

Correct Answer: B [240]

Explanation:

× 0.5, × 1, × 1.5, × 2, × 2.5: 96 × 2.5 = 240.

3.  
Find the wrong number: 2, 5, 14, 41, 123, 365

Correct Answer: E [123]

Explanation:

× 3 − 1: 41 × 3 − 1 = 122, not 123; 122 × 3 − 1 = 365 ✓.

4.  
Find the wrong number: 3, 7, 16, 32, 56, 93, 142

Correct Answer: C [56]

Explanation:

Differences 2², 3², 4², …: 32 + 25 = 57, not 56; 57 + 36 = 93 ✓.

5.  
37, 41, 43, ?, 53, 59

Correct Answer: D [47]

Explanation:

Consecutive primes 37, 41, 43, 47, 53, 59.

6.  
Series: 1, 3, 7, 15, 31, … Which of the following is/are correct?
I. Each term is twice the previous term plus 1.
II. The nth term is 2ⁿ − 1.
III. The 7th term is 127.

Correct Answer: E [All of I, II and III]

Explanation:

All true: 2(2ⁿ − 1) + 1 = 2ⁿ⁺¹ − 1, and 2⁷ − 1 = 127.

7.  
Trick Spotter: what is the quickest way to continue 9, 28, 65, 126, 217, ?

Correct Answer: B [Compare each term with the nearest cube (n³ + 1)]

Explanation:

9 = 2³ + 1, 28 = 3³ + 1, … → 7³ + 1 = 344 in one look (Square-Cube Radar).

8.  
Spot My Mistake: "3, 6, 12, 21, 33, ? – each term doubles, so the answer is 66." Which statement is correct?

Correct Answer: B [Doubling fails at 12 → 21; differences 3, 6, 9, 12, 15 give 48]

Explanation:

12 × 2 = 24 ≠ 21, so doubling is wrong; differences +3, +6, +9, +12 → +15 → 48.

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