CAT 2023 Slot 2 QA Q6 Number Systems

Question 6 of the Quantitative Ability (QA) section, CAT 2023 Slot 2, with CAT's official answer and a worked solution.

The number of positive integers less than 50, having exactly two distinct factors other than 1 and itself, is

TITA: type in the answer. There are no options and no negative marking.

Answer: 15 Number Systems TITA

Solution

  1. Exactly two factors besides 1 and itself means exactly 4 divisors: the number is \(p^3\) or \(pq\) (distinct primes).
  2. Cubes below 50: \(8, 27\), so 2 numbers.
  3. \(2q\): \(6,10,14,22,26,34,38,46\) (8). \(3q\) with \(q>3\): \(15,21,33,39\) (4). \(5\times7 = 35\) (1). That gives 13.
  4. Total \(= 2 + 13 = 15\).

Same concept in other years

See every question on Count divisors of a special form using prime-factor exponents.

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All 40 Number Systems questions asked since 2017.