SSC CGL 2024 Tier-I · 26 September 2024, Shift 3 · Quantitative Aptitude · Question 22 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.

Simplify (4x² − 49y²) ⁄ (2x + 7y) + 7y − 2x

Answer

Why

Correct — A. The stem is printed as an image: Simplify (4x² − 49y²) ⁄ (2x + 7y) + 7y − 2x.

The numerator is a difference of two squares, since 4x² = (2x)² and 49y² = (7y)².
4x² − 49y² = (2x + 7y)(2x − 7y)

Cancel the factor 2x + 7y against the denominator:
(4x² − 49y²) ⁄ (2x + 7y) = 2x − 7y

Add what is left: (2x − 7y) + 7y − 2x = 0.

Option (a) is the choice printed as 0.

Why the others are wrong

(b)
Option (b) reads 4x. It comes from adding the last term instead of subtracting it: (2x − 7y) + 7y + 2x = 4x. The stem writes − 2x.
(c)
Option (c) reads 7y. It follows from cancelling the fraction down to just 2x and losing the − 7y half of the quotient, after which 2x + 7y − 2x leaves 7y.
(d)
Option (d) reads 4x − 14y, which is 2 × (2x − 7y) — the quotient counted twice. That happens when the trailing + 7y − 2x has both of its signs flipped before it is added.

Concept

One identity carries the whole item: a² − b² = (a + b)(a − b).

With a = 2x and b = 7y the numerator factorises as (2x + 7y)(2x − 7y), and the denominator is one of those two factors, so the fraction reduces to 2x − 7y in a single step.

What remains, 7y − 2x, is the exact negative of that quotient, so the two cancel and the expression is 0. Spotting the difference of squares is the method — dividing long-hand costs the minute SSC is measuring.

The cancellation assumes 2x + 7y is not zero, which the question takes for granted by writing the fraction at all.

The answer does not depend on x or y, and a constant result is itself a signal: substitute x = 1 and y = 1 and you get −45 ⁄ 9 + 7 − 2 = 0, which confirms the simplification in a few seconds.

Key facts

a² − b² = (a + b)(a − b), so 4x² − 49y² = (2x + 7y)(2x − 7y).
A fraction whose numerator factorises to include the denominator reduces to the remaining factor.
Substituting x = 1 and y = 1 gives −45 ⁄ 9 + 7 − 2 = 0, a fast check on the simplification.

Study next

Difference of squares where a and b carry coefficients rather than being single lettersReducing an algebraic fraction by factorising before dividingChecking an algebraic identity by substituting convenient values for the variables

Common traps

Cancelling term by term inside the fraction instead of factorising the numerator first.
Writing the quotient as 2x + 7y, which is the factor that was cancelled away.
Dropping the minus sign on − 2x when the quotient is added to the trailing terms.

Here the stem and all four choices are printed as images — the options read 0, 4x, 7y and 4x − 14y — so the method has to be recognised from the shape of the expression, with only the word Simplify as instruction.

Related PYQs

No directly related past PYQ was found.