SSC CGL 2025 Tier-I · 16 September 2025, Shift 1 · Quantitative Aptitude · Question 19 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 13 September 2026.

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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.

In a triangle ABC, medians AD and BE intersect at G. If the length of median AD is 12 cm, what is the length of the segment AG?

(a)4 cm
(b)6 cm
(c)8 cm
(d)9 cm

Answer

Why

Correct — C. The medians meet at the centroid G, which divides each median 2 : 1 from the vertex.

AD = 12 cm = 3 equal parts of 4 cm
AG = 2 parts = 2 × 4 = 8 cm
GD = 1 part = 4 cm (check: 8 + 4 = 12)

AG = 8 cm → option (c)

Why the others are wrong

(a)
4 cm — 4 cm is GD, the short piece from G to the midpoint D. The 2 : 1 split puts the longer two-thirds, 8 cm, on the vertex side A.
(b)
6 cm — 6 cm is half the median, which treats G as the midpoint of AD. The centroid sits two-thirds of the way from A, at 8 cm.
(d)
9 cm — 9 cm is three-quarters of AD (12 × 3⁄4), a 3 : 1 split. The centroid ratio is 2 : 1, so AG = 12 × 2⁄3 = 8 cm.

Concept

The three medians of a triangle meet at one point, the centroid, and it cuts each median in the ratio 2 : 1 measured from the vertex.

So AG = 2⁄3 × AD and GD = 1⁄3 × AD in every triangle. The second median BE just locates G; its length is not needed.

Why the split is 2 : 1. D and E are midpoints of BC and CA, so DE is parallel to AB and half its length (midpoint theorem).

Triangles GDE and GAB are then similar with DE : AB = 1 : 2, so GD : GA = 1 : 2.

Key facts

The centroid divides each median in the ratio 2 : 1, the longer part next to the vertex.
AG = 2⁄3 × AD and GD = 1⁄3 × AD, whatever the shape of the triangle.
Joining G to the vertices makes triangles GAB, GBC and GCA, each one-third of the area of triangle ABC.

Study next

Medians meeting at right angles: finding a side from AG and BGLength of a median from the three sides (Apollonius's theorem)Areas of the six small triangles made by the three medians

Common traps

Treating G as the midpoint of the median and answering 6 cm.
Measuring the 2 : 1 from the wrong end and giving GD = 4 cm as AG.

The same 12 cm median decides 11 Sep 2024, 16:00, Quant Q.8: medians AD = 12 and BE = 9 meet at right angles, so AG = 8, BG = 6 and AB = √(8² + 6²) = 10 cm.

15 Sep 2025, 09:00, Quant Q.19 asks the area form: triangle GAB is 1 : 3 of triangle ABC.

Related PYQs

No directly related past PYQ was found.

Topic: Triangle, Quadrilaterals, Regular Polygons, Circle — all 97 SSC CGL questions on it, every solved shift.