SSC CGL 2024 Tier-I · 26 September 2024, Shift 3 · Quantitative Aptitude · Question 10 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 the unknowns: x + 1.5y + 2z = 5.5 x + 5y + 7z = 15 3x + 11y + 13z = 25

(a)x = 4,y = -3,z = 2
(b)x = -3,y = 2,z = 4
(c)x = 2,y = -3,z = 4
(d)x = 2,y = 4,z = -3

Answer

Why

Correct — C. Eliminate x first — its coefficient is 1 in both of the first two equations.

(2) − (1): 3.5y + 5z = 9.5, doubled → 7y + 10z = 19
(3) − 3×(1): 6.5y + 7z = 8.5, doubled → 13y + 14z = 17

Clear y: 13×(first) − 7×(second) → 130z − 98z = 247 − 119
32z = 128 → z = 4

Back-substitute: 7y + 40 = 19 → y = −3
x = 5.5 − 1.5(−3) − 2(4) = 2 → option (c).

Why the others are wrong

(a)
x = 4,y = -3,z = 2 — Put it in equation (1): 4 + 1.5(−3) + 2(2) = 3.5, not 5.5. The x and z values have been swapped, and the first equation already rejects it.
(b)
x = -3,y = 2,z = 4 — The right numbers sit in the wrong slots: −3 + 1.5(2) + 2(4) = 8, not 5.5. A triple has to satisfy all three equations, not merely use the correct digits.
(d)
x = 2,y = 4,z = -3 — Here y and z are interchanged: 2 + 1.5(4) + 2(−3) = 2, not 5.5. Equation (1) rules this out before you touch the other two.

Concept

Three linear equations in three unknowns are solved by elimination: remove one variable twice to reach two equations in two unknowns, then one equation in one.

Here x carries coefficient 1 in both of the first two equations, so a single subtraction removes it; scaling equation (1) by 3 removes it from the third as well.

The decimals are cosmetic. Doubling 3.5y + 5z = 9.5 gives whole numbers, and slips drop sharply once nothing has a fractional coefficient.

SSC hands you the four answers, so the fastest route in the hall is substitution — drop each option into the simplest equation and stop at the one that fits.

Equation (1) alone separates all four here: the options give 3.5, 8, 5.5 and 2.

Key facts

Three independent linear equations in three unknowns have exactly one solution.
Subtracting two equations that carry the same coefficient of a variable removes that variable in one step.
Multiplying an equation through by a constant leaves its solution unchanged, which is how decimals are cleared.

Study next

Elimination versus substitution in three-variable linear systemsConsistency of a linear system — unique, no, or infinitely many solutionsVerifying a candidate solution against every equation, not just one

Common traps

Scaling equation (1) by 3 but leaving its right-hand side at 5.5 instead of 16.5.
Stopping at the first equation an option satisfies, when two options can pass the same equation.
Losing the decimal point when equation (1) is scaled by 3 — 1.5y becomes 4.5y, not 15y.

SSC keeps three-variable systems small — integer answers you can confirm by substitution rather than by a full solve. Treat the options as part of the method, not as something to check at the end.

Related PYQs

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