SSC CGL 2025 Tier-I · 19 September 2025, Shift 2 · General Intelligence and Reasoning · Question 22 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.

We doubt SSC's key on this question.

On the stem as printed in both English and Hindi, 20 students each shaking hands with exactly 3 others make 20 × 3 ÷ 2 = 30 handshakes, option (b); the key's 20 is the count when each student shakes hands only with the 2 students seated beside them.

The answer below is still the option SSC's key marks, and we solve to that option.

A group of 20 students are sitting in a circle. Each shakes hands with exactly 3 neighbors. How many handshakes occur?

(a)20
(b)30
(c)40
(d)60

Answer

Why

Correct — A. This card solves to SSC's key, 20. The stem prints 3 neighbours, which does not reach 20, and the note flagged beside the answer sets out that disagreement.

Rule: handshakes = (people × handshakes each) ÷ 2, because each handshake is shared by two people.

A seat in a circle has two neighbours, one on each side.
Hand-counts: 20 × 2 = 40
Each handshake counted twice: 40 ÷ 2 = 20 → option (a).

Why the others are wrong

(b)
30 — 30 is 20 × 3 ÷ 2, the count on the stem as printed, three handshakes each. SSC's key marks 20, and the note on the key sets out the disagreement.
(c)
40 — 40 is 20 × 2 without the halving. It counts each neighbour handshake twice, once from each student's side.
(d)
60 — 60 is 20 × 3 without the halving. Every handshake has two participants, so a plain product counts each one twice.

Concept

Handshake counts rest on one fact: every handshake involves two people. Add up each person's handshakes and you have counted every handshake twice, so divide by 2.

In a circle each seat has two neighbours, one on each side. If everyone shakes hands with both, the handshakes are the adjacent pairs around the ring, and a ring of 20 seats has 20 such pairs.

The stem and the key disagree. The response sheet prints exactly 3 neighbours, in the English and the Hindi text alike. On that figure the count is 20 × 3 ÷ 2 = 30.

Three handshakes each is possible in a circle of 20: both seat-neighbours plus the student directly opposite, which again totals 30. The key's 20 is the two-neighbour count. The sheet does not say whether it carries SSC's tentative key or its final one.

Key facts

Total handshakes = (sum of each person's handshakes) ÷ 2.
A circle of n seats has n adjacent pairs, so n neighbour handshakes.
If each of n people shakes hands with everyone else, the count is n(n − 1) ÷ 2.

Study next

Handshakes when everyone meets everyone: n(n − 1) ÷ 2Diagonals of a polygon: n(n − 3) ÷ 2Matches in a round-robin tournament

Common traps

Forgetting to halve, which gives 40 for two neighbours each or 60 for three
Reading 'neighbours' as everyone in the circle, which gives 20 × 19 ÷ 2 = 190

21 Sep 2025, 09:00, Reasoning Q.24 uses the same halving with everyone shaking hands: 6 people give 6 × 5 ÷ 2 = 15 handshakes (keyed c).

Related PYQs

No directly related past PYQ was found.

Topic: Problem Solving — all 123 SSC CGL questions on it, every solved shift.