SSC CGL 2025 Tier-I · 18 September 2025, Shift 1 · Quantitative Aptitude · Question 25 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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Simplify: ((0.5)³ + (0.05)³ + (0.005)³) ÷ ((0.1)³ + (0.01)³ + (0.001)³)

(a)5
(b)25
(c)125
(d)625

Answer

Why

Correct — C. Pair the terms across the brackets: 0.5 = 5 × 0.1, 0.05 = 5 × 0.01, 0.005 = 5 × 0.001.

First bracket = (5 × 0.1)³ + (5 × 0.01)³ + (5 × 0.001)³
= 5³ × (0.1³ + 0.01³ + 0.001³)
= 125 × second bracket
Value = 125 → option (c)

Direct check: 0.125125125 ÷ 0.001001001 = 125.

Why the others are wrong

(a)
5 — 5 is the base ratio 0.5 ⁄ 0.1, uncubed. Every term is a cube, so the factor 5 comes out as 5³.
(b)
25 — 25 = 5², the factor for a sum of squares. These are cubes, so the factor is 5³ = 125.
(d)
625 — 625 = 5⁴, one power too many. The exponent comes from the cube on each term, so the factor is 5³ = 125 however many terms the brackets hold.

Concept

When each term of one bracket is k times the matching term of the other, the power comes out whole: (ka)³ + (kb)³ + (kc)³ = k³(a³ + b³ + c³).

The number of terms does not matter. The ratio is k³ when the larger bases are in the dividend, and 1 ⁄ k³ when they are in the divisor.

Here k = 5, read from any one pair, and 5³ = 125.

Inside each bracket the bases also shrink by 10: 0.5, 0.05, 0.005. That pattern is a distraction. The factor that matters runs between the brackets, 0.5 ⁄ 0.1 = 5.

Key facts

(ka)³ + (kb)³ + (kc)³ = k³(a³ + b³ + c³).
5³ = 125, and 1 ⁄ 125 = 0.008.
Cubing a decimal triples its decimal places: 0.05³ = 0.000125.

Study next

Scaled sums of squares, where the factor is k²a³ + b³ + c³ − 3abc = (a + b + c)(a² + b² + c² − ab − bc − ca)Cubing decimals by counting decimal places

Common traps

Stopping at the base ratio 5 and forgetting to cube it.
Pairing terms within one bracket (0.5 with 0.05) instead of across the brackets (0.5 with 0.1).

The factor runs the other way at 18 Sep 2025, 12:30, Quant Q.25: (0.04³ + 0.02³) ÷ (0.2³ + 0.1³) has the larger bases in the divisor, factor 5, so the value is 1⁄125 = 0.008.

At 17 Sep 2025, 12:30, Quant Q.24 the factor is 10: (0.02³ + 0.004³) ÷ (0.2³ + 0.04³) = 1⁄1000 = 0.001.

Related PYQs

No directly related past PYQ was found.

Topic: Basic algebraic identities of School Algebra & Elementary surds — all 182 SSC CGL questions on it, every solved shift.