SSC CGL 2024 Tier-I · 26 September 2024, Shift 3 · General Intelligence and Reasoning · Question 20 of 100

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 number-pairs are alike in some manner and hence form a group. Which number-pair does not belong to that group? (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/subtracting/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)8 – 100
(b)6 – 64
(c)12 – 225
(d)9 – 121

Answer

Why

Correct — C. Every second number here is a perfect square, so take roots and compare them with the first numbers.

Rule: second number = (first number + 2)².

8 → 10² = 100, and 10 is 8 + 2
6 → 8² = 64, and 8 is 6 + 2
9 → 11² = 121, and 11 is 9 + 2

12 → the pair prints 225, which is 15², and 15 is 12 + 3, not 12 + 2. The rule would demand 14² = 196.

So 12 – 225 is the pair that breaks the shared pattern — option (c).

Why the others are wrong

(a)
8 – 100 — 100 is 10² and 10 is 8 + 2, so this pair obeys the rule exactly. A pair that fits the pattern cannot be the odd one out.
(b)
6 – 64 — 64 is 8² and 8 is 6 + 2. It is built the same way as the other two conforming pairs, so it belongs inside the group.
(d)
9 – 121 — 121 is 11² and 11 is 9 + 2, so this pair fits. Note that the group mixes odd and even first numbers, so parity is not the pattern being tested.

Concept

Odd-one-out items on number pairs are settled by finding the rule that fits three of them, never by finding something odd-looking about one.

All four second numbers here are perfect squares — 100, 64, 225 and 121 — so being a square is not the discriminator.

The move that works is: take the square root and compare it with the first number. The roots are 10, 8, 15 and 11 against first numbers 8, 6, 12 and 9.

The gaps are 2, 2, 3 and 2, and the pair with a gap of 3 is the outsider.

All four second numbers being squares is the cover story. Stopping at 'they are all squares' finds the similarity and never reaches the difference, which is what the item is asking for.

Key facts

100 = 10², 64 = 8², 121 = 11² and 225 = 15².
The roots exceed their first numbers by 2, 2, 3 and 2 respectively.
For 12 – 225 to follow the shared rule the second number would have to be 196.

Study next

Number-pair rules built on a cube, or a cube with a constant addedOdd-one-out on pairs where the operation is multiplication by a fixed factorRecognising every square up to 30² on sight

Common traps

Stopping at 'all four are squares' and then guessing.
Breaking 12 into 1 and 2, which the stem's bracketed note forbids.
Testing the rule on one conforming pair and assuming the others agree.

This stem carries a bracketed warning against splitting digits.

10 Sep 2024, 12:30, Reasoning Q.7 asks it of 15 – 240, 18 – 306, 22 – 462 and 21 – 420, and 23 Sep 2024, 16:00, Reasoning Q.15 asks it of 12 – 156, 21 – 462, 14 – 196 and 17 – 306. The underlying rule changes but the method does not.

Related PYQs

No directly related past PYQ was found.