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RAS question

8 : 27 :: 64 : ?

Correct answer: (B) 125.

In the analogy 8 : 27 :: 64 : ?, the missing term is 125 because the numbers follow consecutive cubes: 2 cubed, 3 cubed, 4 cubed and then 5 cubed.

  1. (A)

    100

  2. (B)

    125

  3. (C)

    216

  4. (D)

    81

Explanation

The relation is based on recognising a number sequence, not on ordinary addition or multiplication. NCERT’s table of number sequences lists cubes as 1, 8, 27, 64, 125, 216, and so on. In the given analogy, 8 is 2 cubed and 27 is 3 cubed, so the same consecutive-cube pattern should continue from 64. Since 64 is 4 cubed, the matching next term is 5 cubed, which is 125. This makes option B the only answer that preserves the rule across both pairs.

Why the other options are wrong

  • (A) 100 is not the cube immediately after 64 in the consecutive-cube sequence.
  • (C) 216 is a cube, but it is 6 cubed and skips the required next cube, 5 cubed.
  • (D) 81 does not continue the cube sequence after 64, so it breaks the analogy.

Concept

This tests number-pattern recognition within Reasoning & Mental Ability, specifically the ability to identify cubes in a sequence. Such items recur in RAS because they check whether the candidate can infer the governing rule quickly rather than compute mechanically.

Source

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