Algebra PlayClass 8 Mathematics Assertion & Reason Questions

Assertion (A): In the 'Think of a Number' trick involving the steps: 1. Think of a number, 2. Double it, 3. Add 10, 4. Divide by 2, 5. Subtract the original number; the final result is always 5.

Reason (R): If the starting number is $x$, the algebraic expression for the sequence of operations is $\frac{2x+10}{2} - x$, which simplifies to 5, independent of the value of $x$.

Assertion (A): In the date trick where the final algebraic expression is $100M + 165 + D$, if a person's final answer is 494, the date they thought of was April 29th.

Reason (R): To find the original date, one must subtract 165 from the final answer. The resulting number, in the form $100M+D$, reveals the month $M$ and the day $D$.

Assertion (A): For a 3-row number pyramid, if the bottom row is represented by the variables $a, b, c$, the number at the top of the pyramid is given by the expression $a+2b+c$.

Reason (R): In a number pyramid, the rule is that each number is the sum of the two numbers positioned directly below it.