Quantitative Reasoning

Linear Equation

Hard

Which of the following pair of linear equations is / are inconsistent?

(A) $x - y = 5$ ; $3x - 3y = 10$

(B) $2x + 3y = 4$ ; $4x + 6y = 8$

(C) $9x + 6y = 6$ ; $3x + 2y = 3$

(D) $2x + 5y = 2$ ; $6x - 15y = 4$

Choose the correct answer from the options given below:

(A), (B) and (D) only

(A), (B), (C) and (D)

(B) and (D) only

(A) and (C) only

✅ Correct Option: 4

A pair $a_1x+b_1y=c_1$ , $a_2x+b_2y=c_2$ is inconsistent when $\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne\frac{c_1}{c_2}$ .

(A): ratios $\frac{1}{3}=\frac{-1}{-3}\ne\frac{5}{10}$ → inconsistent. (B): all ratios equal $\frac{1}{2}$ → coincident (many solutions). (C): $\frac{9}{3}=\frac{6}{2}=3\ne\frac{6}{3}=2$ → inconsistent. (D): $\frac{2}{6}=\frac{1}{3}\ne\frac{5}{-15}=-\frac{1}{3}$ → consistent (unique solution).

So only (A) and (C) are inconsistent.

2026: 14 May Shift 1

The system of linear equations x + y + 1 = 0 and 2x + 2y + 7 = 0 has:

2026: 14 May Shift 2

Solve the linear equation for $x$ :

$3x - 7 = 2x + 5$

2026: 19 May Shift 2

Five years ago, Sanjana was thrice as old as Sanjay. Ten years later, Sanjana will be twice as old as Sanjay. The age of Sanjay and Sanjana are respectively

A. 20

B. 30

C. 40

D. 50

Choose the correct answer from the options given below:

2026: 12 May Shift 1

The system of linear equations 3x + y + 4 = 0 and 2x + y + 9 = 0 has:

2023: 5 June Shift 2

In a 2-digit number, the ten's digit is two times its unit's digit and the number is 12 less than two times the number obtained by interchanging its digits. Find the original number.

2025: 27 May Shift 2

The pair of linear equations mx + 2y + 3 = 0 and 3x + 6y + 2 = 0 intersect each other, if

Solution

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