SSC CGL 2025 Tier-I · 16 September 2025, Shift 2 · General Intelligence and Reasoning · Question 18 of 100

We transcribed this text from the pictures on a candidate's response sheet for this shift; the answer is the key SSC colour-marked on that sheet. Solution last reviewed 13 September 2026.

Where this paper and its answers come from

SSC does not publish CGL question papers or a public answer key. From 2025 the candidate response sheet prints every question and option as a picture, so the text here is transcribed from those pictures for this shift and checked against them independently; where the layout carries meaning, the picture is shown as well. Each answer is the key SSC colour-marked on that sheet. SSC released a tentative key for challenge and later its final one, both only to candidates behind a login, and the sheet does not say which of the two it carries. The solutions are written by UnlockIAS.

Comprehension:
In a certain number system there are only two notations to represent numbers: Δ and β.
0 is represented by Δ and 1 by β. The subsequent numbers are represented in the following manner:
2 is represented as βΔ,
3 is represented as ββ,
4 is represented as βΔΔ,
5 is represented as βΔβ and so on.

How will you represent 81 in the given number system?

(a)βΔΔβΔβΔ
(b)βΔβΔβΔβ
(c)βΔβΔΔββ
(d)βΔβΔΔΔβ

Answer

Why

Correct — D.
Rule: Δ = 0 and β = 1, so the system is binary (2 = βΔ = 10, 4 = βΔΔ = 100).

81 = 64 + 16 + 1
Places 64, 32, 16, 8, 4, 2, 1 → 1, 0, 1, 0, 0, 0, 1
1 → β, 0 → Δ: βΔβΔΔΔβ → option (d).

Why the others are wrong

(a)
βΔΔβΔβΔ — βΔΔβΔβΔ is 1001010 = 64 + 8 + 2 = 74. It ends in Δ, a 0, so it is even, and 81 is odd.
(b)
βΔβΔβΔβ — βΔβΔβΔβ is 1010101 = 64 + 16 + 4 + 1 = 85. It carries a 4 that 81 does not contain.
(c)
βΔβΔΔββ — βΔβΔΔββ is 1010011 = 64 + 16 + 2 + 1 = 83, which is 2 above 81.

Concept

This is binary, base 2, written with new symbols. Each place is worth double the place to its right: 1, 2, 4, 8, 16, 32, 64.

To convert, take the largest power of 2 that fits and subtract, then repeat: 81 − 64 = 17, 17 − 16 = 1, 1 − 1 = 0.

The places used (64, 16, 1) get β and the rest get Δ.

Key facts

Powers of 2: 1, 2, 4, 8, 16, 32, 64, 128.
81 in binary is 1010001.
A binary number ending in 0 is even, and one ending in 1 is odd.

Study next

Decimal to binary by repeated division by 2Binary to decimal by adding place valuesOther bases, such as base 3, written in coded symbols

Common traps

Leaving the units place as Δ after 64 + 16 = 80, one short of 81
Taking β as 0, which the given 2 = βΔ and 4 = βΔΔ rule out

The system is taught through a short list (0 to 5 in symbols), and the item asks for a number far beyond it. Spot the base from the list, then convert.

Related PYQs

No directly related past PYQ was found.

Topic: Coding & de-coding — all 138 SSC CGL questions on it, every solved shift.