SSC CGL 2025 Tier-I · 19 September 2025, Shift 1 · Quantitative Aptitude · Question 18 of 100

We transcribed this text from the pictures on a candidate's response sheet for this shift; the answer is the key SSC colour-marked on that sheet. Solution last reviewed 11 September 2026.

Where this paper and its answers come from

SSC does not publish CGL question papers or a public answer key. From 2025 the candidate response sheet prints every question and option as a picture, so the text here is transcribed from those pictures for this shift and checked against them independently; where the layout carries meaning, the picture is shown as well. Each answer is the key SSC colour-marked on that sheet. SSC released a tentative key for challenge and later its final one, both only to candidates behind a login, and the sheet does not say which of the two it carries. The solutions are written by UnlockIAS.

A parallelogram is a quadrilateral in which:

(a)Only one pair of opposite sides is parallel.
(b)All four interior angles are 90°
(c)Opposite sides are parallel and of equal length.
(d)The diagonals are perpendicular.

Answer

Why

Correct — C.
Rule: a parallelogram is a quadrilateral with both pairs of opposite sides parallel.

Equal length follows: a diagonal splits it into two triangles that are congruent by ASA (alternate angles plus the shared diagonal), so opposite sides are equal.

Option (c) states both facts, and both hold for every parallelogram → option (c).

Why the others are wrong

(a)
Only one pair of opposite sides is parallel. — Only one pair of parallel sides describes a trapezium that is not a parallelogram. A parallelogram needs both pairs of opposite sides parallel.
(b)
All four interior angles are 90° — All angles 90° describes a rectangle, a special parallelogram. A general parallelogram can have angles of 60°, 120°, 60° and 120°, so right angles are not required.
(d)
The diagonals are perpendicular. — Perpendicular diagonals belong to a rhombus or a square. A general parallelogram's diagonals bisect each other but meet at 90° only when all four sides are equal.

Concept

A parallelogram is a quadrilateral whose two pairs of opposite sides are parallel. The rest follows from that: opposite sides are equal, opposite angles are equal, adjacent angles add to 180°, and the diagonals bisect each other.

Rectangles, rhombuses and squares are parallelograms with extra conditions. Right angles and perpendicular diagonals belong to those special cases, not to parallelograms in general.

The keyed statement mixes the definition (parallel) with a consequence (equal length). A property that holds for some parallelograms but not all, such as right angles, cannot define the shape.

Key facts

A parallelogram has both pairs of opposite sides parallel and equal.
Its opposite angles are equal and its adjacent angles add up to 180°.
Its diagonals bisect each other.
A parallelogram with perpendicular diagonals is a rhombus.

Study next

Area of a parallelogram as base × heightProperties that separate a rhombus, a rectangle and a square from a general parallelogramProving a quadrilateral is a parallelogram from one pair of sides that are equal and parallel

Common traps

Choosing a property of a special parallelogram, such as right angles or perpendicular diagonals, as if it held for all of them
Reading 'only one pair of opposite sides parallel' as a parallelogram, when it describes a trapezium

18 Sep 2024, 16:00, Quant Q.7 puts these properties to work: in parallelogram MNOP with MN produced to Q so that NQ = MN, NQ is equal and parallel to PO, so triangles RNQ and ROP are congruent and R cuts ON in the keyed ratio 1 : 1.

11 Sep 2024, 09:00, Quant Q.1 turns on the rhombus property: its diagonals are perpendicular bisectors, so a point with OA = OC lies on BD, ∠DOB = 180°, and five-ninths of that is the keyed 100°.

Related PYQs

No directly related past PYQ was found.

Topic: Triangle, Quadrilaterals, Regular Polygons, Circle — all 65 SSC CGL questions on it, every solved shift.