Assertion Reasoning Quiz

Assertion (A): For pairs of consecutive odd natural numbers both larger than 10 with a sum less than 40, the pair (19, 21) is a valid solution.
Reason (R): If \( x \) is the smaller odd number, \( x > 10 \) and \( x + (x+2) < 40 \Rightarrow 2x < 38 \Rightarrow x < 19 \). Thus, \( x \) can only be up to 17.

Assertion (A): The system of inequalities \( 3x - 7 < 5 + x \) and \( 11 - 5x \le 1 \) has no solution.
Reason (R): The first inequality yields \( x < 6 \) and the second yields \( x \ge 2 \). Their intersection is the interval \( [2, 6) \).

Assertion (A): When adding \( x \) litres of a 30% acid solution to 600 litres of a 12% acid solution to achieve a mixture between 15% and 18% acid, the allowed range is \( 120 < x < 300 \).
Reason (R): The concentration of the final mixture is determined solely by averaging 30% and 12%, independent of the total volume of the mixture.

Assertion (A): The graphical representation of \( 2x - 4 < 0 \) on a number line corresponds to the solution interval \( (-\infty, 2) \).
Reason (R): \( 2x - 4 < 0 \Rightarrow 2x < 4 \Rightarrow x < 2 \). Since it is a strict inequality, the boundary point 2 is excluded, and the solution covers all values strictly less than 2.

Assertion (A): If a student obtains 70 and 75 marks in the first two tests, the minimum marks needed in the third test to average at least 60 is 35.
Reason (R): The inequality formulation is \( \frac{70 + 75 + x}{3} \ge 60 \).