In the following figure, the small square represents persons who know English,…

2024

In the following figure, the small square represents persons who know English, the triangle represents those who know Marathi, the big square represents those who know Telugu, and the circle represents those who know Hindi. The different regions in the figure are numbered from 1 to 12.

How many persons can speak English and Hindi both the languages only?

  1. A.

    5

  2. B.

    8

  3. C.

    7

  4. D.

    18

Show answer & explanation

Correct answer: A

Concept

In a numerical Venn diagram built from several overlapping shapes, the word 'only' picks out the single region that lies inside exactly the named shapes and outside every other shape drawn in the figure. Each numbered region already carries the count of persons in that exact combination, so once a shape is matched to its category, the answer is read directly off the one region satisfying both 'inside' conditions and both 'outside' conditions - no further arithmetic is needed unless the question explicitly asks for a total across regions.

Application

Per the figure's own labelling: the small square = English, the triangle = Marathi, the big square = Telugu, and the circle = Hindi. The question needs the region that is inside the small square AND inside the circle, but outside both the triangle and the big square. Tracing the shapes, that region is numbered 5 - it sits where the small square and the circle overlap, above the big square's top edge and clear of the triangle. So 5 persons know English and Hindi only.

Cross-check - why the other options don't fit

  • 8 lies in the circle-and-big-square overlap - that is Hindi paired with Telugu, not with English, so it is the wrong pair of shapes entirely.

  • 7 is what you get if you add the isolated English-Hindi region to the neighbouring region where the big square also overlaps in - that neighbouring region's people additionally know Telugu, so including them breaks the 'only' condition.

  • 18 comes from summing across regions that go well beyond the small-square-circle overlap, effectively counting people who satisfy just one of the two conditions (or a different pair of languages) instead of both together and nothing else.

Independent check: region 5 sits strictly above the big square's boundary line and strictly to the right of the triangle's boundary, confirming it carries neither Telugu nor Marathi membership - only English and Hindi.

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