Choose the similar pair for the following: 9 : 1000 :: ______ : ______.

2019

Choose the similar pair for the following: 9 : 1000 :: ______ : ______.

  1. A.

    5 : 125

  2. B.

    6 : 49

  3. C.

    8 : 64

  4. D.

    2 : 27

Attempted by 17 students.

Show answer & explanation

Correct answer: D

Key idea: the relationship is number : (number + 1)^3.

Verify with the given pair:

  • For 9 : 1000, compute (9 + 1)^3 = 10^3 = 1000, so the pattern holds.

  • Check 5 : 125 — (5 + 1)^3 = 6^3 = 216, so 125 does not fit the pattern (125 = 5^3).

  • Check 6 : 49 — (6 + 1)^3 = 7^3 = 343, so 49 does not fit the pattern (49 = 7^2).

  • Check 8 : 64 — (8 + 1)^3 = 9^3 = 729, so 64 does not fit the pattern (64 = 8^2 or 4^3).

  • Check 2 : 27 — (2 + 1)^3 = 3^3 = 27, so this pair matches the pattern.

Conclusion: The similar pair is 2 : 27 because it follows the rule number : (number + 1)^3.

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