SSC CGL 2024 Tier-I · 10 September 2024, Shift 3 · Quantitative Aptitude · Question 18 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 6 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.

If x² + y² = 280 and xy = 120, then find the value of (x − y) ⁄ (x + y).

Answer

Why

Correct — D. Both brackets come straight out of the two numbers you are given, so you never need x or y separately.

(x − y)² = x² + y² − 2xy
= 280 − 240 = 40

(x + y)² = x² + y² + 2xy
= 280 + 240 = 520

(x − y)² ⁄ (x + y)² = 40⁄520 = 1⁄13

That is the ratio of the squares, so take the square root:
(x − y)/(x + y) = 1⁄√13 → option (d).

Why the others are wrong

(a)
15 never appears in this question. The only quantities the identities produce are 40, 520 and their ratio 1⁄13, so no square root of 15 can be built from x² + y² = 280 and xy = 120.
(b)
The ratio the wrong way up. (x + y)²⁄(x − y)² = 520⁄40 = 13, so √13 answers (x + y)/(x − y), not the fraction the stem asks for.
(c)
Right shape, wrong number: a reciprocal square root built on 15 instead of 13. Dividing 520 by 40 gives 13, and nothing in the working gives 15.

Concept

The engine is the pair of identities (x − y)² = x² + y² − 2xy and (x + y)² = x² + y² + 2xy.

The stem hands you exactly the two quantities they need — the sum of the squares and the product — so both brackets are computable in one line each.

The last move is the one that decides the option. You have computed a ratio of squares, 40⁄520, so the answer is its square root, not the ratio itself.

The stem does not fix which of x and y is larger. Swapping them flips the sign, so strictly (x − y)/(x + y) is ±1⁄√13.

SSC's four options carry only the positive value, so take the positive root.

Key facts

(x + y)² = x² + y² + 2xy and (x − y)² = x² + y² − 2xy.
With x² + y² = 280 and xy = 120: (x − y)² = 40 and (x + y)² = 520.
40⁄520 reduces to 1⁄13, so the required ratio is 1⁄√13.

Study next

Getting x³ + y³ and x³ − y³ from x² + y² and xyTurning x + 1⁄x = k into x² + 1⁄x² and x³ + 1⁄x³Componendo and dividendo on (x + y)/(x − y) style ratios

Common traps

Answering 1⁄13 and forgetting that what you computed was a ratio of squares.
Reading the fraction upside down and solving for (x + y)/(x − y).
Using 2xy = 120 instead of 2xy = 240.

SSC's algebra block leans on the three square identities rather than on solving for the variables — you are given symmetric information and asked for a symmetric expression.

The same shift runs a perfect square in reverse at Quant Q.21, where 16x² + 40x + 25 has to be recognised as (4x + 5)².

Related PYQs

No directly related past PYQ was found.