SSC CGL 2025 Tier-I · 19 September 2025, Shift 3 · 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 11 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.

What is the value of (0.2³ + 0.02³) ÷ (0.4³ + 0.04³)?

(a)0.055
(b)0.051
(c)0.125
(d)0.052

Answer

Why

Correct — C. Each number on top is exactly half the matching number below.

Halve: 0.2 = 0.4 × 1⁄2 and 0.02 = 0.04 × 1⁄2
Cube: 0.2³ = 0.4³ × 1⁄8 and 0.02³ = 0.04³ × 1⁄8
Factor: numerator = 1⁄8 × (0.4³ + 0.04³)

Check: 0.008 + 0.000008 = 0.008008
0.064 + 0.000064 = 0.064064
0.008008 ÷ 0.064064 = 0.125 ✓

Ratio = 1⁄8 = 0.125 → option (c)

Why the others are wrong

(a)
0.055 — 0.055 is less than half of 1⁄8. Multiply back: 0.055 × 0.064064 ≈ 0.0035, not the numerator 0.008008.
(b)
0.051 — 0.051 × 0.064064 ≈ 0.0033, well short of the numerator 0.008008. Halving every term divides each cube by 8, so the ratio is 0.125.
(d)
0.052 — 0.052 × 0.064064 ≈ 0.0033, again far from 0.008008. The exact ratio is (1⁄2)³ = 0.125.

Concept

When every term of one sum is the same multiple k of the matching term in another, the sums of cubes are in the ratio k³: (ka)³ + (kb)³ = k³(a³ + b³).

Here k = 1⁄2, so the numerator is 1⁄8 of the denominator. No decimal cube has to be worked out.

Key facts

(ka)³ + (kb)³ = k³(a³ + b³) for any k.
(1⁄2)³ = 1⁄8 = 0.125.
Cubing a decimal triples its decimal places: 0.2³ = 0.008 and 0.02³ = 0.000008.

Study next

a³ + b³ = (a + b)(a² − ab + b²)a³ + b³ + c³ − 3abc, and the case a + b + c = 0Ratios of sums of squares when every term scales by the same factor

Common traps

Stopping at the base ratio 1⁄2 and forgetting to cube it
Cubing 0.02 as 0.0008 instead of 0.000008

Also asked 18 Sep 2025, 12:30, Quant Q.25: (0.04³ + 0.02³) ÷ (0.2³ + 0.1³), where each top term is 1⁄5 of the one below, so the ratio is (1⁄5)³ = 0.008, keyed (a).

Related PYQs

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