SSC CGL 2025 Tier-I · 15 September 2025, Shift 1 · Quantitative Aptitude · Question 3 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:(1.5 + 3⁄8)³−(9⁄5 × 1.25)

(a)4.3418
(b)5.3418
(c)6.5526
(d)7.5526

Answer

Why

Correct — A. Turn the first bracket into one fraction before cubing it.

Convert: 1.5 + 3⁄8 = 12⁄8 + 3⁄8 = 15⁄8
Cube: 15³⁄8³ = 3375⁄512 ≈ 6.5918
Second bracket: 9⁄5 × 1.25 = 1.8 × 1.25 = 2.25

Subtract: 6.5918 − 2.25 = 4.3418 → option (a)

Why the others are wrong

(b)
5.3418 — 5.3418 is 6.5918 − 1.25: the 1.25 subtracted without first multiplying it by 9⁄5. The second bracket is 1.8 × 1.25 = 2.25, which is 1 more.
(c)
6.5526 — 6.5526 sits just below the cube, 6.5918, so the second bracket would have to be about 0.04. It is 1.8 × 1.25 = 2.25.
(d)
7.5526 — 7.5526 is larger than the cube, 6.5918, yet a positive 2.25 is being subtracted from that cube. No value of this expression can exceed 6.5918.

Concept

Convert before you cube. 1.5 + 3⁄8 mixes a decimal and a fraction. In eighths it is 15⁄8, and a fraction is cubed by cubing its numerator and its denominator: 3375⁄512.

As a decimal check, 3⁄8 = 0.375, so the bracket is 1.875. Then 1.875² = 3.515625, and 3.515625 × 1.875 = 6.591796875.

Estimate to confirm. 1.9 is a little more than 1.875, and 1.9³ = 6.859, so the true cube is below 6.859. The answer is therefore below 6.859 − 2.25 ≈ 4.61, and 4.3418 is the option under that bound.

Key facts

3⁄8 = 0.375, so 1.5 + 3⁄8 = 1.875 = 15⁄8.
15³ = 3375 and 8³ = 512.
9⁄5 = 1.8, and 1.8 × 1.25 = 2.25.

Study next

Cubes of 1 to 20 by sight, including 15³ = 3375Eighths as decimals: 1⁄8 = 0.125, 3⁄8 = 0.375, 5⁄8 = 0.625, 7⁄8 = 0.875Estimating a power by rounding the base, then allowing for the direction of the rounding

Common traps

Cubing the parts separately: 1.5³ + (3⁄8)³ ≈ 3.375 + 0.053, which is not (1.5 + 3⁄8)³.
Subtracting 1.25 instead of 9⁄5 × 1.25, which lands on 5.3418.

Cubing decimals also decides 18 Sep 2025, 12:30, Quant Q.25: 0.04³ + 0.02³ = 0.000072 and 0.2³ + 0.1³ = 0.009, a quotient of 0.008.

12 Sep 2025, 09:00, Quant Q.2 needs the same mixed conversion: 2 1⁄2 = 2.5, so (2.5 + 3.6) − 1.9 = 4.2.

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.