SSC CGL 2024 Tier-I · 19 September 2024, Shift 1 · Quantitative Aptitude · Question 10 of 100

Text as printed on a candidate's response sheet for this shift; answer per SSC's tentative key as marked on that sheet. Solution last reviewed 10 September 2026.

Where this paper and its answers come from

SSC does not publish CGL question papers or a public answer key. The questions and options here are reproduced as printed on a candidate's own response sheet for this shift — the Commission's text, unchanged. Each answer is SSC's tentative key as marked on that sheet; SSC allowed challenges to it and never publishes a final key. The solutions are written by UnlockIAS.

WXYZ is a quadrilateral in which XQ and ZP are perpendicular to WY such that XQ = ZP. Diagonals ZX and WY intersect each other at point O. If OX = 12 cm, then find the value of ZX (in cm).

(a)18
(b)24
(c)36
(d)12

Answer

Why

Correct — B. XQ and ZP are perpendiculars dropped onto the same line WY, and they are equal. That forces the two triangles at O to be congruent.

In ΔXQO and ΔZPO:
∠XQO = ∠ZPO = 90° (both perpendicular to WY)
∠XOQ = ∠ZOP (vertically opposite at O)
XQ = ZP (given)

So ΔXQO ≅ ΔZPO by AAS, which gives OX = OZ.

OX = 12, so OZ = 12
ZX = OX + OZ = 12 + 12 = 24 cm → option (b)

Why the others are wrong

(a)
18 — 18 would need OZ = 6 while OX = 12, so the diagonal would be cut unequally. The equal perpendiculars force OX = OZ, and no split other than 12 and 12 survives that.
(c)
36 — 36 treats OX as one-third of ZX. The congruence produces two equal parts, not three, so 12 doubles to 24 rather than tripling.
(d)
12 — 12 is OX itself, the length already given. The question asks for the whole diagonal ZX, which is OX plus the equal OZ.

Concept

XQ and ZP are the perpendicular distances of X and of Z from the line WY. Making them equal says X and Z stand off WY by the same amount, on opposite sides of it.

Once that holds, the two triangles cut off at the crossing point share a right angle, a pair of vertically opposite angles and one equal side, so they are congruent by AAS.

Congruence hands you OX = OZ: the diagonal ZX is bisected by WY. Nothing else about WXYZ is used, so it need not be a parallelogram.

No diagram is printed with this question. Draw WY horizontal, put X above it and Z below, and drop the two perpendiculars — because ZX and WY are stated to intersect at O, X and Z must lie on opposite sides, which is what places O between X and Z.

Key facts

A right angle, a pair of vertically opposite angles and one equal side give congruence by AAS.
Equal perpendiculars from X and Z onto WY make O the midpoint of ZX.
With OX = 12 cm and OX = OZ, the full diagonal ZX = 24 cm.

Study next

AAS, ASA and RHS congruence, and which one a given set of facts supportsProving that the diagonals of a parallelogram bisect each otherEqual perpendicular distances as a statement about equal triangle areas on a common base

Common traps

Answering 12, the value the question already gave you as OX.
Assuming WXYZ must be a parallelogram and looking for a property that was never stated.
Reading XQ and ZP as segments of a diagonal rather than as perpendicular distances to WY.

SSC states the perpendicular condition in words and supplies no figure, so the sketch is half the work. The same lever — two equal perpendiculars forcing a congruence — settles 17 Sep 2024, 16:00, Quant Q.16, where DL = DM makes triangle ABC isosceles.

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