SSC CGL 2024 Tier-I · 24 September 2024, Shift 2 · Quantitative Aptitude · Question 9 of 100

Text as printed on a candidate's response sheet for this shift; answer per SSC's tentative key as marked on that sheet. Solution last reviewed 10 September 2026.

Where this paper and its answers come from

SSC does not publish CGL question papers or a public answer key. The questions and options here are reproduced as printed on a candidate's own response sheet for this shift — the Commission's text, unchanged. Each answer is SSC's tentative key as marked on that sheet; SSC allowed challenges to it and never publishes a final key. The solutions are written by UnlockIAS.

Find the value of (453 × 453 × 453 − 383 × 383 × 383)⁄(453 × 383 + 383 × 383 + 453 × 453).

(a)60
(b)80
(c)50
(d)70

Answer

Why

Correct — D. The stem is printed as an image and reads: find the value of (453 × 453 × 453 − 383 × 383 × 383) ⁄ (453 × 383 + 383 × 383 + 453 × 453).

Write a = 453 and b = 383.
Numerator = a³ − b³
Denominator = ab + b² + a², which is a² + ab + b²

Identity: a³ − b³ = (a − b)(a² + ab + b²)
The bracket is exactly the denominator, so it cancels and the fraction is a − b.

a − b = 453 − 383 = 70 → option (d).

Why the others are wrong

(a)
60 — 60 is 443 − 383. The identity work is right and the subtraction is not — the stem's first number is 453.
(b)
80 — 80 is 463 − 383. Once the fraction collapses, nothing is left to compute except this one subtraction, so a single misread digit costs the mark.
(c)
50 — 50 is 433 − 383. Reading the printed digits off the image carefully matters more here than any algebra.

Concept

Two identities handle every fraction of this shape:

a³ − b³ = (a − b)(a² + ab + b²)
a³ + b³ = (a + b)(a² − ab + b²)

The sign in front of ab in the denominator tells you which one is in play. Here it is +ab, the partner of the difference of cubes, so the whole fraction reduces to a − b.

Nothing is ever multiplied out: 453³ is never computed, and the answer is one subtraction.

This row carries no text of its own — the entire question lives in the printed image, and the numbers 453 and 383 are read from it. Note the denominator is written in the order ab + b² + a², not the textbook a² + ab + b².

Key facts

a³ − b³ = (a − b)(a² + ab + b²).
a³ + b³ = (a + b)(a² − ab + b²).
When the numerator is a difference of cubes and the denominator is a² + ab + b², the fraction equals a − b.

Study next

a³ + b³ + c³ − 3abc = (a + b + c)(a² + b² + c² − ab − bc − ca)Simplifying (a² − b²) ⁄ (a − b) and its higher-power relativesFinding a³ + b³ when only a + b and ab are supplied

Common traps

Reaching for the calculator and actually cubing 453
Choosing the sum-of-cubes identity because the denominator's middle term is positive
Misreading a digit in an image-only stem when the whole answer is one subtraction

The tell is the shape, not the size: two large, close numbers, cubes in the numerator and a² + ab + b² underneath. That pairing exists so the bracket cancels.

The three-variable cousin is set at 10 Sep 2024, 09:00, Quant Q.22 — the sum of three numbers is 18 and the sum of their squares is 36, and the question wants a³ + b³ + c³ − 3abc, which factors as (a + b + c)(a² + b² + c² − ab − bc − ca).

Whenever a fraction is built from cubes, read the denominator's middle sign first and match it to an identity before doing any arithmetic.

Related PYQs

No directly related past PYQ was found.