How many people like either only cars or only Volkswagen vehicles as per the given Venn diagram? black vehicles only 49 | black vehicles and Car 25 | Car only 47 | black vehicles, Car and volkswagon vehicles 17 | black vehicles and volkswagon vehicles 26 | Car and volkswagon vehicles 28 | volkswagon vehicles only 38

Correct — A. The stem is printed inside the image: how many people like either only cars or only Volkswagen vehicles.

'Only' means the part of a circle that overlaps nothing else — one number on the diagram, never a sum.

Only cars = 47, the area inside the Car circle alone.
Only Volkswagen vehicles = 38, the area inside the bottom circle alone.

The two areas share nobody, so they simply add: 47 + 38 = 85 → option (a).

Why the others are wrong

• (b)
  66 — 66 is 28 + 38 — the Volkswagen-only area plus the Car-and-Volkswagen overlap. Those 28 people like both, so they cannot sit in an 'only' total.
• (c)
  28 — 28 is the Car-and-Volkswagen overlap on its own, a group of people who like both — the opposite of what 'only' asks for.
• (d)
  75 — 75 is 47 + 28, the Car-only area plus the overlap it shares with Volkswagen. Adding an overlap to an 'only' region double-counts the wrong people.

A three-circle Venn splits a population into seven regions, and every question about one is really a question about which regions to add.

'Only X' is the region inside X and outside both other circles. 'X and Y' without the word only also takes in the centre, where all three circles meet.

This diagram reads 49, 47 and 38 for the three single-circle areas, 25, 26 and 28 for the pairwise overlaps, and 17 at the centre. Naming each region before computing prevents almost every error on this question type.

Key facts

• In this diagram the Car circle alone holds 47 people and the Volkswagen circle alone holds 38.
• The pairwise overlaps are 25 for black-and-Car, 26 for black-and-Volkswagen and 28 for Car-and-Volkswagen, with 17 at the centre.
• 'Only cars or only Volkswagen vehicles' adds two regions that share nobody: 47 + 38 = 85.

Common traps

• Folding an overlap into an 'only' region, which turns 47 into 75 or 38 into 66.
• Reading 'either ... or' as the union of the two whole circles rather than the sum of the two 'only' areas.

No directly related past PYQ was found.