Assertion Reasoning Quiz

Assertion (A): A company uses 3-digit product codes where the digits are always consecutive (e.g., 234, 678). A quality check that sums the digits will always find the sum is a multiple of 3 .
Reason (R): The sum of three consecutive integers can be expressed as \((x-1)+ x+(x+1)=3 x\), which is mathematically always a multiple of 3.

Assertion (A): It is a known property that all 2-digit numbers will eventually form a palindrome using the reverse-and-add method.
Reason (R): The process is guaranteed to converge because the number of digits in the sum can never exceed four.

Assertion (A): When creating a \(3 \times 3\) heat map with unique values from 1 to 9 , the cell with value 1 can never be a "hot spot" (supercell).
Reason (R): A hot spot must have a value strictly greater than all its neighbours, and 1 is the minimum possible value.

Assertion (A): In a simulation of particle decay that follows the Collatz rule, a particle with a starting mass that is a power of 2 (e.g., \(2^n\) ) will decay to 1 through a series of even-mass steps.
Reason (R): Dividing an even number by 2 results in an odd number only when the number is 2 itself.

Assertion (A): A company's annual revenue, a 5 -digit figure, when added to next year's 5 -digit revenue, will sometimes result in a 6 digit total.
Reason (R): The sum will exceed 5 digits and become a 6 -digit number if the combined revenue is ₹1,00,000 or more.