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Number puzzles

Q1:

A 70

B 71

C 72

D 73

ANS:C - 72

Structure of the Pattern:

  1. Sequence of Square Numbers:
    • The sequence starts with square numbers. The first six square numbers are 12,22,32,42,52,1^2, 2^2, 3^2, 4^2, 5^2,12,22,32,42,52, and 626^262.
  2. Multiply Each Square Number by 2:
    • Each square number in the sequence is then multiplied by 2.

Explanation of the Pattern:

  1. Identify Square Numbers:
    • List the first six square numbers: 12=11^2 = 112=1, 22=42^2 = 422=4, 32=93^2 = 932=9, 42=164^2 = 1642=16, 52=255^2 = 2552=25, and 62=366^2 = 3662=36.
  2. Multiply by 2:
    • Multiply each square number by 2 to get the final sequence.

Step-by-Step Process:

  1. Calculate Square Numbers:
    • Square numbers are: 1,4,9,16,25,361, 4, 9, 16, 25, 361,4,9,16,25,36
  2. Multiply Each by 2:
    • Multiply each number by 2: 1×2=21 \times 2 = 21×2=2 4×2=84 \times 2 = 84×2=8 9×2=189 \times 2 = 189×2=18 16×2=3216 \times 2 = 3216×2=32 25×2=5025 \times 2 = 5025×2=50 36×2=7236 \times 2 = 7236×2=72
  3. Result:
    • The final sequence after multiplying by 2 is: 2,8,18,32,50,722, 8, 18, 32, 50, 722,8,18,32,50,72

Conclusion:

The answer "72" is the result of the pattern where each of the first six square numbers is multiplied by 2. The final number in this sequence is 72, which is 62×26^2 \times 262×2.



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