What is the value of (0.1×0.1×0.1+0.03×0.03×0.03)⁄(0.3×0.3×0.3+0.09×0.09×0.09).
- (a)0.027
- (b)0.009
- (c)0.729
- (d)0.037
Answer
Why
Correct — D. Match each denominator term with its numerator partner.
0.3 = 3 × 0.1 and 0.09 = 3 × 0.03
Cube both: 0.3³ = 27 × 0.1³ and 0.09³ = 27 × 0.03³
So the denominator = 27 × the numerator
Divide: value = 1⁄27
= 0.037037… ≈ 0.037 → option (d)
Check by cubing: 0.001027 ÷ 0.027729 = 0.037037…
Why the others are wrong
- (a)0.027 — 0.027 is 0.3³, which is 27⁄1000, not 1⁄27. The factor 27 sits in the denominator, so you divide by it: 1⁄27 ≈ 0.037.
- (b)0.009 — 0.009 = 9⁄1000, about 1⁄111. The denominator here is exactly 27 times the numerator, which gives 1⁄27 ≈ 0.037.
- (c)0.729 — 0.729 is 0.9³, almost three-quarters. Every denominator term is bigger than its partner (0.3 > 0.1, 0.09 > 0.03), so the value is small: 1⁄27.
Concept
If each denominator term is the same multiple k of its numerator partner, the whole denominator is k³ times the numerator: (ka)³ + (kb)³ = k³(a³ + b³).
So the fraction is 1⁄k³ without any cubing. Here 0.1 pairs with 0.3 and 0.03 with 0.09, both with k = 3, so the value is 1⁄27. The shortcut needs both pairs to share one k.
Option (d) is 1⁄27 written to three decimal places. The exact value, 0.037037…, recurs.
Key facts
- (a³ + b³)⁄((ka)³ + (kb)³) = 1⁄k³ for any positive a, b and k.
- 27 × 37 = 999, so 1⁄27 = 0.037037… and 1⁄37 = 0.027027….
- 0.3³ = 0.027 and 0.09³ = 0.000729.
Study next
Common traps
- Reading the factor 27 as 0.027: the value is 1⁄27, which is 0.037…, not 27⁄1000.
- Pairing 0.1 with 0.09: that pair has ratio 0.9 while 0.3 and 0.03 have ratio 10, so no single factor comes out.
The same scaling appears at 18 Sep 2025, 12:30, Quant Q.25, where 0.2 and 0.1 are each 5 times 0.04 and 0.02, so the value is 1⁄125 = 0.008.
Related PYQs
No directly related past PYQ was found.