CSAT Solved Papers/ 2023/Q40

2023 CSAT — Q40

Quant Number theory 2.5 marks Easy

Choose the group which is different from the others:

A 17, 37, 47, 97
B 31, 41, 53, 67
C 71, 73, 79, 83
D 83, 89, 91, 97 Answer

Worked rationale

Look for a single shared property that three groups have and one lacks. Test primality of every member:

(a) $17, 37, 47, 97$ — all prime.
(b) $31, 41, 53, 67$ — all prime.
(c) $71, 73, 79, 83$ — all prime.
(d) $83, 89, 91, 97$ — $91 = 7 \times 13$ is composite; the rest are prime.

Group (d) is the only one containing a composite number, so it is the odd one out.

Answer: (d) 83, 89, 91, 97.

Why the other options miss

A

solved the wrong question: chosen by someone grouping on “ends in $7$ ” (three of four do), a surface pattern that isn’t the discriminating rule.
B

solved the wrong question: chosen on a spurious “non-twin” or spacing pattern instead of primality.
C

missed a case: passed over because all are prime, but flagged by a reader who mistakes $87$ -style numbers as present, or mis-tests $77 = 7\cdot 11$ if mis-read.

Specialist insight

“Odd-one-out” number sets almost always hinge on primality or a divisibility property — so prime-test every entry first. The hidden composite here is $91 = 7 \times 13$ , a classic CSAT trap because $91$ “looks prime” (odd, not obviously divisible). Knowing the small near-primes $91, 119 (=7\cdot 17), 133 (=7\cdot 19)$ on sight is what makes this a $30$ -second item rather than a guess.

The trap, in one line

Three groups are all-prime; (d) hides $91 = 7\times 13$ (composite), so (d) is the odd one out.

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