What is the result of (0.5³ + 0.1³ − 0.6³) ÷ (3×0.5×0.1×0.6)?
- (a)−1
- (b)0
- (c)1
- (d)2
Answer
Why
Correct — A.
Name the bases: a = 0.5, b = 0.1, c = −0.6
Add them: 0.5 + 0.1 − 0.6 = 0
So a³ + b³ + c³ = 3abc
Numerator: 3 × 0.5 × 0.1 × (−0.6) = −0.09
Denominator, printed with +0.6: 3 × 0.5 × 0.1 × 0.6 = 0.09
Divide: −0.09 ÷ 0.09 = −1 → option (a)
Why the others are wrong
- (b)0 — 0 is the sum of the bases, not of their cubes. With a + b + c = 0, the cubes add to 3abc = −0.09, which is not zero.
- (c)1 — 1 drops the minus sign. The numerator is 3abc with c = −0.6, so it is −0.09, while the printed denominator uses +0.6 and is +0.09.
- (d)2 — 2 has no route from these numbers. Cubing directly gives 0.125 + 0.001 − 0.216 = −0.090, and −0.090 ÷ 0.09 = −1.
Concept
The identity a³ + b³ + c³ − 3abc = (a + b + c)(a² + b² + c² − ab − bc − ca) has a zero-sum case: when a + b + c = 0, the right side vanishes and a³ + b³ + c³ = 3abc.
Here the bases cancel, since 0.5 + 0.1 = 0.6. Once you see that, the numerator is 3abc and the denominator is the same product with c taken positive, so the ratio is −1.
The denominator is printed with +0.6, not −0.6, and that sign is the whole question. With −0.6 in both places the ratio would be +1.
Key facts
- If a + b + c = 0, then a³ + b³ + c³ = 3abc.
- a³ + b³ + c³ − 3abc = (a + b + c)(a² + b² + c² − ab − bc − ca).
- Decimal cubes: 0.5³ = 0.125, 0.1³ = 0.001, 0.6³ = 0.216.
Study next
Common traps
- Treating the zero sum of the bases as a zero sum of the cubes, which gives 0
- Losing the sign of −0.6 in the numerator, which gives 1
17 Sep 2025, 16:00, Quant Q.21 uses the identity with whole numbers: 19 + 20 − 39 = 0, so 19³ + 20³ − 39³ = 3 × 19 × 20 × (−39) = −44460, and adding 118 gives the keyed −44342.
19 Sep 2025, 09:00, Quant Q.21 is the contrast: 27 + 10 − 29 = 8, so the identity does not apply and the cubes must be worked out.
Related PYQs
No directly related past PYQ was found.