Select the figure which satisfies the same conditions of placement of the dots…

2025

Select the figure which satisfies the same conditions of placement of the dots as in Figure (X), from amongst the figures marked (1), (2), (3) and (4).

  1. A.

    1

  2. B.

    2

  3. C.

    3

  4. D.

    4

Attempted by 4 students.

Show answer & explanation

Correct answer: B

Concept: In a "Dot Situation" problem, each dot in Figure (X) sits inside a specific set of overlapping shapes. The matching alternative must reproduce every one of those overlaps as a genuine two-dimensional region, not merely as a single point where boundaries happen to cross, so that a dot could be placed there satisfying the same condition.

Application: Figure (X) has three dots, each defined by which shapes contain it:

  1. The first dot lies inside both the triangle and the circle, but outside the square.

  2. The second dot lies inside all three shapes: the triangle, the circle, and the square together.

  3. The third dot lies inside both the circle and the square, but outside the triangle.

Checking each option for these same three regions, only figure (2) provides all of them: part of its triangle projects outside both the circle and the square, part of the triangle's interior lies inside the circle while staying outside the square, and the triangle's other edge crosses into the square while still inside the circle, while the circle-square overlap also extends beyond the triangle on either side. So figure (2) can hold all three dot placements exactly as Figure (X) does.

Cross-check: Confirm the others cannot work:

  • In figure (1), the triangle's two lower edges converge to a single point exactly where the circle and square boundaries also meet, so the whole triangle sits on one side of the square's edge; there is no area where the triangle overlaps the circle without the square also being present.

  • In figure (3), the triangle's boundary and the circle's boundary pass close to each other near the square's corner but never actually cross, so the triangle and circle share no interior region at all.

  • In figure (4), the triangle's full width stays inside the square's boundary throughout, so it never extends past the square to meet the circle on its own.

Only figure (2) reproduces every region Figure (X) needs, so it is the correct match.

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