216 : 42 :: 512 : ?

64Correct answerYour answer72Correct answerYour answer80Correct answerYour answer81Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

216 is $6^3$ . The second number, 42, is $6 \times 7$ : take the cube root n and find $n \times (n + 1)$ .
$512 = 8^3$ , so the answer is $8 \times 9 = 72$ .

Worth noting

64 is $8^2$ and 80 is $8 \times 10$ . 'Cube root times 7' also fits 216 : 42 but gives 56, which is not offered, so the rule must be $n(n + 1)$ .

Ten questions from Analogies and Classification, at your own pace.

Ten questions from Analogies and Classification, at your own pace.

Explanation