SSC CGL 2025 Tier-I · 14 September 2025, Shift 3 · Quantitative Aptitude · Question 17 of 95

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.

Where this paper and its answers come from

SSC does not publish CGL question papers or a public answer key. From 2025 the candidate response sheet prints every question and option as a picture, so the text here is transcribed from those pictures for this shift and checked against them independently; where the layout carries meaning, the picture is shown as well. Each answer is the key SSC colour-marked on that sheet. SSC released a tentative key for challenge and later its final one, both only to candidates behind a login, and the sheet does not say which of the two it carries. The solutions are written by UnlockIAS.

Find the slope of the line perpendicular to y = 1⁄4x + 7

(a)−4
(b)4
(c)−1⁄4
(d)1⁄4

Answer

Why

Correct — A.
The printed stem is y = (1⁄4)x + 7, with 1⁄4 multiplying x.
In y = mx + c the slope is m, so the given slope is 1⁄4.

Perpendicular slopes multiply to −1:
m₂ = −1 ÷ (1⁄4) = −4 → option (a)

Why the others are wrong

(b)
4 — 4 is the reciprocal with the sign left unchanged. 1⁄4 × 4 = 1, not −1, so a line of slope 4 is not perpendicular.
(c)
−1⁄4 — −1⁄4 changes the sign but does not flip the fraction. 1⁄4 × (−1⁄4) = −1⁄16, not −1.
(d)
1⁄4 — 1⁄4 is the given line's own slope. A line with it is parallel, not perpendicular.

Concept

A line written as y = mx + c has slope m and y-intercept c.

Two non-vertical lines are perpendicular exactly when their slopes multiply to −1, so the new slope is the negative reciprocal: flip the fraction and change the sign.

The +7 only shifts the line up or down. It changes neither the slope nor the slope of any line perpendicular to it.

In the printed stem 1⁄4 is a stacked fraction written before x, so it is the coefficient of x, not 1 ÷ 4x.

Key facts

In y = mx + c, m is the slope and c the y-intercept.
Perpendicular slopes satisfy m₁ × m₂ = −1 when neither line is vertical.
Parallel lines have equal slopes.

Study next

Slope of a line written as ax + by = c: m = −a⁄bEquation of the perpendicular bisector of a segmentSlope through two points: (y₂ − y₁) ÷ (x₂ − x₁)

Common traps

Doing half of the negative reciprocal: flipping without changing sign gives 4, changing sign without flipping gives −1⁄4.
Reading the stem as 1⁄(4x) instead of (1⁄4)x.

15 Sep 2025, 16:00, Quant Q.23 asks the same thing of y = −3x + 7, where the negative reciprocal of −3 is 1⁄3, the option its key marks.

17 Sep 2025, 16:00, Quant Q.16 asks for a slope from two points: (7 − 3) ÷ (4 − 2) = 2.

Related PYQs

No directly related past PYQ was found.

Topic: Graphs of Linear Equations — all 27 SSC CGL questions on it, every solved shift.