Assertion Reasoning Quiz

Assertion (A): In a hypothetical base-5 positional number system using Hindu-Arabic digits, the decimal number \(25\) is written precisely as \(100_5\).

Reason (R): The landmark numbers representing the positional values in a base-5 system follow the sequence \(5^0, 5^1, 5^2\) (i.e., \(1, 5, 25\)).

Assertion (A): When multiplying the Roman landmark number \(V\) by \(L\), the result yields another single Roman landmark symbol, \(D\).

Reason (R): A major limitation of the Roman numeral system that makes arithmetic difficult is that the product of two landmark numbers often yields complex groupings rather than a single basic landmark symbol.

Assertion (A): When executing the addition algorithm for \(375\) and \(46\) in the modern Hindu number system, evaluating the units (\(5 + 6 = 11\)) forces the user to write \(1\) in the units place and mechanically carry over a \(1\) to the tens place.

Reason (R): Because the Hindu number system operates strictly on a base-10 positional architecture, any accumulation of \(10\) units in one positional slot must instantly be regrouped and shifted as a single unit into the next higher multiplier position.

Assertion (A): If the Chinese rod numeral for \(61\) was written strictly with vertical rods in both positions (6 vertical next to 1 vertical) without any horizontal alternation, it could easily be misread mathematically as the number \(7\).

Reason (R): The Chinese rod numeral system initially relied on a blank physical space, rather than a dedicated drawn symbol, to represent a zero in a skipped place value.

Assertion (A): When performing addition in the Gumulgal counting system, evaluating (ukasar-urapon) + (ukasar) results in (ukasar-ukasar-urapon).

Reason (R): The Gumulgal counting system forms numbers exclusively by grouping collections into sizes of 5.