SSC CGL 2024 Tier-I · 11 September 2024, Shift 1 · Quantitative Aptitude · Question 12 of 95

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.

A rectangular courtyard is 4m 95cm long and 16m 65cm broad. It is to be paved with the square tiles of the same size. Find the least number of such square tiles required to pave the rectangular courtyard.

(a)407
(b)388
(c)877
(d)944

Answer

Why

Correct — A. Convert to centimetres first, then find the largest square that fits both sides a whole number of times.

Length = 4 m 95 cm = 495 cm
Breadth = 16 m 65 cm = 1665 cm

The fewest tiles means the biggest tile, so take the HCF of 495 and 1665.

1665 = 3 × 495 + 180
495 = 2 × 180 + 135
180 = 1 × 135 + 45
135 = 3 × 45 + 0 → HCF = 45 cm

Tiles along the length = 495 ⁄ 45 = 11
Tiles along the breadth = 1665 ⁄ 45 = 37
Total = 11 × 37 = 407 tiles → option (a)

Why the others are wrong

(b)
388 — Fewer than 407 tiles needs a tile larger than 45 cm, but 45 cm is the HCF — no bigger square divides both 495 and 1665 exactly.
(c)
877 — The floor is 495 × 1665 = 824,175 cm², and 824,175 is not divisible by 877, so 877 identical squares cannot cover it whatever their size.
(d)
944 — 824,175 does not divide by 944 either. Step down to the next usable tile, 15 cm, and the count jumps to 33 × 111 = 3,663 — it does not drift up to 944.

Concept

'Same size square tiles, least number' is an HCF question in carpentry dress.

A square of side s paves the floor without cutting only if s divides both 495 and 1665. The count is (495 ⁄ s) × (1665 ⁄ s), which falls as s grows, so the fewest tiles come from the largest common divisor.

The arithmetic is short; the marks are lost on the units. 4 m 95 cm and 16 m 65 cm have to become 495 and 1665 before the HCF is taken.

The paper writes the courtyard as 4 m 95 cm long and 16 m 65 cm broad — the 'long' side is the shorter number. It makes no difference to the count, since both sides are divided by the same tile.

Key facts

Least number of identical square tiles = (length ⁄ HCF) × (breadth ⁄ HCF), in a single unit.
HCF(495, 1665) = 45, since 495 = 3² × 5 × 11 and 1665 = 3² × 5 × 37.
The tile is 45 × 45 = 2,025 cm² and the floor 824,175 cm², and 824,175 ⁄ 2,025 = 407.
The only usable tile sides are the divisors of 45: 45, 15, 9, 5, 3 and 1 cm.

Study next

HCF by Euclid's division algorithm on three-digit and four-digit numbersHCF word problems: largest tile, longest measuring tape, greatest common vesselLCM word problems, and telling the two apart from the wording

Common traps

Reaching for the LCM, which answers the smallest common length, not the largest common tile.
Leaving one side in metres so the divisor is a hundred times out.
Answering 45, the tile's side, when the question asks how many tiles.

SSC dresses HCF as a physical fit. The same question in three dimensions is at 11 Sep 2024, 16:00, Quant Q.15, where a 50 × 150 × 175 cm cuboid is cut into identical largest cubes: the HCF is 25 cm, and 2 × 6 × 7 = 84 cubes.

This one states the sides in compound units, so make the conversion to centimetres your first written line.

Related PYQs

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