If triangle represents Men, rectangle represents Businessman and circle represents Millionaire, then which number represents Men that are both Businessman and Millionaire ?
[FIGURE: A three-shape over

Question

If triangle represents Men, rectangle represents Businessman and circle represents Millionaire, then which number represents Men that are both Businessman and Millionaire ?
[FIGURE: A three-shape overlap diagram. A large horizontal RECTANGLE (Businessman) occupies the lower-left of the figure. A CIRCLE (Millionaire) sits above and to the right of the rectangle's centre, so that the rectangle's top edge cuts the circle horizontally — the upper part of the circle lies outside the rectangle, the lower part inside it. A TRIANGLE (Men) with its apex at the top right leans left: its left side runs down-left as a diagonal that slices through the circle from the circle's upper-right through to a bottom-left vertex sitting below-left of the circle; its base then runs from that bottom-left vertex rightwards and slightly downwards to the triangle's bottom-right vertex, which lies outside the rectangle's right edge. The triangle's right side crosses the rectangle's right edge, so part of the triangle lies outside the rectangle. Numbers by region: 7 — inside the circle only, in the circle's upper-left part above the rectangle's top edge and left of the triangle's diagonal side (Millionaire only). 3 — inside the circle and inside the triangle but above the rectangle's top edge, in the circle's upper-right lens right of the triangle's diagonal side (Millionaire + Men, not Businessman). 8 — inside the circle and inside the rectangle but left of the triangle's diagonal side, in the circle's lower-left part just below the rectangle's top edge (Millionaire + Businessman, not Men). 10 — inside all three: in the circle's lower-right part, below the rectangle's top edge and right of the triangle's diagonal side and above the triangle's base (Millionaire + Businessman + Men). 12 — inside the rectangle and inside the triangle but outside the circle, below the circle and just above the triangle's base, left of the rectangle's right edge (Businessman + Men, not Millionaire). 13 — inside the triangle only, to the right of the rectangle's right edge and outside the circle (Men only).]

UnlockIAS · Accepted Answer

Correct — A, 10. Translate the sentence before looking at the figure. 'Men that are both Businessman and Millionaire' imposes three conditions at once — the person must be a Man, a Businessman and a Millionaire — so the number wanted must lie inside the triangle, inside the rectangle and inside the circle simultaneously. There is exactly one such region on the page, and 10 is printed in it. Now read the figure region by region, which is the only reliable way to do these and takes about twenty seconds. Six numbers are printed and each sits in a different region. 7 lies in the upper-left of the circle, above the rectangle's top edge and to the left of the triangle's slanting side: circle only, so Millionaire and nothing else. 3 lies in the circle's upper-right lens, still above the rectangle's top edge but now to the right of the triangle's side: circle and triangle, so Millionaire and Man, but not a Businessman. 8 lies in the circle's lower-left, below the rectangle's top edge but still left of the triangle: circle and rectangle, so Millionaire and Businessman, but not a Man. 10 lies in the circle's lower-right, below the rectangle's edge and right of the triangle's side and above the triangle's base — inside all three. 12 lies inside the rectangle and inside the triangle but below the circle, so Businessman and Man without being a Millionaire. 13 lies to the right of the rectangle's edge and outside the circle, inside the triangle alone: a Man only. Written as a table of ticks, only 10 carries three ticks, and it is option (a). Notice how the option set is built: each of the three wrong numbers satisfies exactly two of the three conditions and fails one — 3 is not a Businessman, 12 is not a Millionaire, 13 is neither. That is the standard construction for this question type, and it means a candidate who misjudges a single boundary of the figure will land on a wrong option that feels entirely reasonable.

Why the other options are wrong — (b) Sits in the circle and inside the triangle, so a Millionaire and a Man — but it lies above the rectangle's top edge, outside the Businessman shape. It answers the question 'Men who are Millionaires', dropping the businessman condition. It is the trap for a reader who spots the circle–triangle overlap first and stops there.  (c) Lies inside the triangle alone, to the right of the rectangle's edge and clear of the circle — a Man who is neither a Businessman nor a Millionaire. It is offered because the sentence begins with the word 'Men', and a candidate reading the grammatical subject rather than the whole condition will take the Men-only region.  (d) Inside the rectangle and inside the triangle but below the circle, so a Man who is a Businessman and not a Millionaire. Two conditions out of three, and the missing one is the hardest to see, because 12 sits close under the circle's lower edge — this is the option a hurried eye picks.

Concept: A figure like this is a Venn diagram drawn with different outlines instead of three circles, and nothing about the reasoning changes because the shapes differ. Each closed shape is a set; a point either lies inside it or does not; and every region of the picture is defined by which shapes contain it. With three overlapping sets there can be at most seven bounded regions inside the union — three regions belonging to one set alone, three to each pair, and one to all three — plus the outside. This figure prints six of them: the three-way region, two of the three pair regions, and one single-set region. The vocabulary that maps sentences onto regions is small and fixed. 'And', 'both' and 'who are also' mean intersection, so add a shape. 'But not' and 'only' mean exclusion, so remove a shape. 'Or' means union. The number of shapes named in the phrase is the number of ticks the region must carry, which is the single fastest check available.

State PCS 2025 Q139 — Science & Technology PYQ with Answer

State PCS 2025 Q139 — Science & Technology PYQ with Answer