SSC CGL 2024 Tier-I · 24 September 2024, Shift 3 · General Intelligence and Reasoning · Question 24 of 99

Text as printed on a candidate's response sheet for this shift; answer per SSC's tentative key as marked on that sheet. Solution last reviewed 10 September 2026.

Where this paper and its answers come from

SSC does not publish CGL question papers or a public answer key. The questions and options here are reproduced as printed on a candidate's own response sheet for this shift — the Commission's text, unchanged. Each answer is SSC's tentative key as marked on that sheet; SSC allowed challenges to it and never publishes a final key. The solutions are written by UnlockIAS.

Three of the following numbers are alike in a certain way and one is different. Pick the odd one out. (NOTE : Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 – Operations on 13 such as adding /deleting /multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)

(a)829
(b)237
(c)643
(d)821

Answer

Why

Correct — B. Test each number as a whole number, which is what the bracketed note demands.

Rule: three of them are prime and one is composite.

829, 643 and 821 have no factor besides 1 and themselves — no prime up to 29 divides any of them.

237 gives itself away at once: 2 + 3 + 7 = 12, a multiple of 3, so 237 = 3 x 79 and it is the composite one → option (b).

Why the others are wrong

(a)
829 — 829 is prime. Nothing from 2 to 28 divides it, and 29 x 29 = 841 is already past it, so the test is finished. It belongs with the three that are alike.
(c)
643 — 643 is prime. Its digits add to 13, so 3 is out, and 7, 11, 13, 17, 19 and 23 each leave a remainder.
(d)
821 — 821 is prime. It ends in 1, so 2 and 5 are out, its digits add to 11, so 3 is out, and no larger prime up to 23 divides it either.

Concept

The bracketed note is the instruction that matters: work on the whole number and never on its digits. Without it, digit sums and digit products would be fair game and the item would have more than one defensible answer.

Three-digit numbers that sit close together with no arithmetic linking them are usually a primality question. Test that property before hunting for a relation.

To test whether n is prime, divide by the primes up to the square root of n. All four numbers here are below 841, which is 29 x 29, so 2, 3, 5, 7, 11, 13, 17, 19, 23 is the entire list to try — from 841 upwards, 29 has to be tried as well.

Three of the four numbers begin with 8 or 6 and end in an odd digit, so nothing on the surface separates them. The only way through is to factorise, and the digit-sum test for 3 does it in one step.

Key facts

237 = 3 x 79, so it is composite.
829, 643 and 821 are all prime numbers.
A number is divisible by 3 when its digits add to a multiple of 3, and 2 + 3 + 7 = 12.
To test n for primality it is enough to divide by the primes up to the square root of n.

Study next

Divisibility tests for 3, 7, 11 and 13Primes between 600 and 900, learnt as a blockOdd-one-out items built on a relation between paired or tripled numbers

Common traps

Splitting the numbers into digits, which the printed note forbids
Stopping the division test early and taking a three-digit number for prime

The note about whole numbers is printed on these items and tells you the property is arithmetic rather than digit play.

The same instruction runs at 12 Sep 2024, 12:30, Reasoning Q.12 and at 13 Sep 2024, 09:00, Reasoning Q.16, where the numbers come in triples and a relation between them, not primality, is what separates them.

Related PYQs

No directly related past PYQ was found.