SSC CGL 2024 Tier-I · 24 September 2024, Shift 3 · General Intelligence and Reasoning · Question 20 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.

Study the given diagram carefully and answer the question that follows. The numbers in different sections indicate the number of persons who can drive different vehicles. What is the difference between the number of persons who can drive all the three vehicles and that of persons who can drive any two of these vehicles?

(a)15
(b)12
(c)27
(d)21

Answer

Why

Correct — D. Name the regions of the diagram, then do one subtraction.

All three vehicles is the centre region: 6.

Any two of these is the three overlap regions that are not the centre:
cycle and car 8, cycle and bike 7, car and bike 12
8 + 7 + 12 = 27

Difference = 27 − 6 = 21 → option (d)

Why the others are wrong

(a)
15 — 15 = 27 − 6 − 6. The centre 6 has been taken off a second time, once inside the overlap total and once again at the end.
(b)
12 — 12 is the car-and-bike overlap on its own. Any two of these covers all three overlap regions, so the 8 and the 7 are still owed.
(c)
27 — 27 is the exactly-two total itself, 8 + 7 + 12. The question asks for its difference from the 6 at the centre, so one subtraction remains.

Concept

Three overlapping circles cut the diagram into seven regions, and the number written in a region counts only the people who belong to that region and no other.

The centre 6 drive all three vehicles. The three lens-shaped regions around it — 8, 7 and 12 — drive exactly two. The outer parts, 45 for cycle, 75 for car and 52 for bike, drive one only, and no part of this question uses them.

Label the seven regions before reading the sentence and the arithmetic is trivial afterwards.

The key reads any two of these as exactly two, which is the standard reading and excludes the centre. Read as at least two it would take in the 6 as well, giving 33 and a difference of 27 — the value printed as option (c).

Key facts

The centre region holds 6 people, who drive all three vehicles.
The exactly-two regions hold 8 (cycle and car), 7 (cycle and bike) and 12 (car and bike).
8 + 7 + 12 = 27, and 27 − 6 = 21.
The single-vehicle regions are 45 for cycle, 75 for car and 52 for bike.

Study next

Reading exactly-two against at-least-two regions on a three-set diagramFinding the total for one set by adding every region that touches its circleTwo-set questions where only-A is what remains after the overlap is removed

Common traps

Adding the centre 6 into the exactly-two total and answering 27
Taking a single overlap region as the answer because it is the largest of the three

The picture stays much the same while the sentence changes, so the mark is won by reading the sentence slowly, not the diagram. Diagram items also run at 09 Sep 2024, 16:00, Reasoning Q.9 and at 25 Sep 2024, 16:00, Reasoning Q.20.

Related PYQs

No directly related past PYQ was found.