SSC CGL 2024 Tier-I · 13 September 2024, Shift 3 · General Intelligence and Reasoning · Question 12 of 98

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 6 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 four options are alike in a certain way and thus form a group. Which is the one that 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)82 – 8 – 2
(b)164 – 10 – 4
(c)63 – 6 – 3
(d)360 – 12 – 6

Answer

Why

Correct — A. Rule: the first number equals the square of the second plus the cube of the third.

164 - 10 - 4, since 10 squared is 100 and 4 cubed is 64, and 100 + 64 = 164
63 - 6 - 3, since 6 squared is 36 and 3 cubed is 27, and 36 + 27 = 63
360 - 12 - 6, since 12 squared is 144 and 6 cubed is 216, and 144 + 216 = 360

Three triples obey the rule. Now test the fourth:

82 - 8 - 2, since 8 squared is 64 and 2 cubed is 8, and 64 + 8 = 72, not 82.

82 - 8 - 2 breaks the rule, so it is the odd one out, option (a).

Why the others are wrong

(b)
164 – 10 – 4 — 10 squared plus 4 cubed is 100 + 64 = 164, exactly the first number, so this triple obeys the rule and belongs with the group.
(c)
63 – 6 – 3 — 6 squared plus 3 cubed is 36 + 27 = 63, matching the first number. This is the smallest triple and the easiest place to spot the rule.
(d)
360 – 12 – 6 — 12 squared plus 6 cubed is 144 + 216 = 360, the first number again, so the largest triple is still the rule-following kind.

Concept

Three-number odd-one-out items hide a two-step formula. Start on the smallest triple, here 63 - 6 - 3, because small numbers make the operation visible.

6 and 3 reach 63 as 36 + 27, a square plus a cube. Test that guess on 12 and 6: 144 + 216 = 360. Two confirmations are enough to fix the rule.

The bracketed NOTE bars digit-splitting, so 82 cannot be read as the digits 8 and 2 written side by side. The relation has to be arithmetic performed on the whole numbers.

Option (a) is designed to look right to anyone who reads 82 as 8 followed by 2, which is exactly the reading the NOTE forbids.

Key facts

The rule is first number equals second squared plus third cubed.
8 squared plus 2 cubed is 72, while the triple prints 82.
The NOTE forbids treating 82 as the digits 8 and 2.

Study next

Odd-one-out triples built on a product of the last two numbersTriples whose rule is a weighted sum such as twice the first plus three times the secondRecognising small squares and cubes on sight

Common traps

Reading 82 - 8 - 2 as digit concatenation, which the NOTE forbids
Testing the rule on a single triple before deciding
Confusing 2 cubed with 2 squared, which turns 72 into 68

The same stem and the same NOTE carry a multiplication rule at 10 Sep 2024, 09:00, Reasoning Q.10, where 2 - 2 - 4 works because 2 times 2 is 4, and a weighted-sum rule at 19 Sep 2024, 16:00, Reasoning Q.15, where 18 - 12 - 72 works because twice 18 plus three times 12 is 72.

Related PYQs

No directly related past PYQ was found.