CSAT Solved Papers/ 2025/Q66

2025 CSAT — Q66

Quant Logical & quantitative reasoning 2.5 marks Medium

In a certain code if $64$ is written as $343$ and $216$ is written as $729$ , then how is $512$ written in that code?

A 1000
B 1331 Answer
C 1728
D 2197

Worked rationale

Recognise the numbers as perfect cubes and read the rule on the cube roots:

64 = 4^3 \to 343 = 7^3,\qquad 216 = 6^3 \to 729 = 9^3.

The cube root increases by $3$ : $4 \to 7$ and $6 \to 9$ . So the code of $n^3$ is $(n+3)^3$ . For

512 = 8^3 \to (8+3)^3 = 11^3 = 1331.

Answer: (b) 1331.

Why the other options miss

A

reached for the wrong shift: takes $(n+2)^3 = 10^3$ , shifting the root by $2$ instead of $3$ .
C

off by one (and then some): uses $12^3$ , shifting the root by $4$ ( $8 \to 12$ ).
D

an arithmetic slip: jumps to $13^3$ , overshooting the root shift.

Specialist insight

The unlock is spotting that both numbers and both codes are perfect cubes, turning a coding puzzle into a one-line rule on the roots: $\sqrt[3]{\cdot}$ goes up by $3$ . The decoys are exactly the cubes of $10, 12, 13$ — i.e. wrong root-shifts — so the only thing being tested is reading the shift correctly ( $+3$ , confirmed by both given pairs). Always confirm the rule on the second pair ( $6 \to 9$ ) before extending; that guards against fixing on a coincidental relation from one example.

The trap, in one line

These are cubes with the root shifted $+3$ : $512 = 8^3 \to 11^3 = 1331$ .

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