SSC CGL 2025 Tier-I · 18 September 2025, Shift 1 · Quantitative Aptitude · Question 24 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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What is the value of (0.12³ + 0.06³) ÷ (0.24³ + 0.12³)?

(a)0.125
(b)0.5
(c)0.25
(d)1

Answer

Why

Correct — A. Pair the bases in order: 0.24 = 2 × 0.12 and 0.12 = 2 × 0.06. Each base in the second bracket is 2 × its partner in the first.

Second bracket = (2 × 0.12)³ + (2 × 0.06)³
= 2³ × (0.12³ + 0.06³)
= 8 × first bracket
Value = 1 ⁄ 8 = 0.125 → option (a)

Direct check: 0.001944 ÷ 0.015552 = 0.125.

Why the others are wrong

(b)
0.5 — 0.5 is the base ratio 0.12 ⁄ 0.24 before cubing. Scaling every base by 2 scales a sum of cubes by 2³ = 8, not by 2.
(c)
0.25 — 0.25 = (1⁄2)², the square of the base ratio. These are cubes, so the factor is (1⁄2)³ = 1⁄8.
(d)
1 — 1 needs the two brackets equal. The 0.12³ in both does not cancel across a sum: the second bracket is 0.015552, 8 × the first, 0.001944.

Concept

If every term of one sum is k times the matching term of another, a cube lets the factor out whole: (ka)³ + (kb)³ = k³(a³ + b³).

So (a³ + b³) ÷ ((ka)³ + (kb)³) is simply 1 ⁄ k³, whatever a and b are.

The skill is spotting k by pairing terms in order: 0.24 with 0.12, and 0.12 with 0.06. Both ratios are 2.

0.12 sits in both brackets but in different places: first in the first bracket, second in the second. Matching terms by position, not by value, is what shows the factor 2.

Key facts

(ka)³ + (kb)³ = k³(a³ + b³).
2³ = 8, and 1 ⁄ 8 = 0.125.
0.12³ = 0.001728 and 0.06³ = 0.000216.

Study next

The same scaling for squares: (ka)² + (kb)² = k²(a² + b²)a³ + b³ = (a + b)(a² − ab + b²) when the pairs are not scaled copiesCubing decimals by counting decimal places

Common traps

Cancelling the 0.12³ that appears in both brackets, which is not allowed across a sum.
Using the base ratio 1⁄2, or its square 1⁄4, instead of its cube 1⁄8.

The same scaled-cubes ratio is asked at 19 Sep 2025, 16:00, Quant Q.25: (0.2³ + 0.02³) ÷ (0.4³ + 0.04³), factor 2 again and answer 0.125.

At 16 Sep 2025, 12:30, Quant Q.25 the factor is 5, so (0.05³ + 0.01³) ÷ (0.25³ + 0.05³) = 1⁄125 = 0.008.

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.