CAT 2023 Slot 3 QA Q6 Number Systems

Question 6 of the Quantitative Ability (QA) section, CAT 2023 Slot 3, with CAT's official answer and a worked solution.

The sum of the first two natural numbers, each having 15 factors (including 1 and the number itself), is

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

Answer: 468 Number Systems TITA

Solution

  1. 15 factors means \(N=p^{14}\) or \(N=p^4q^2\) (since \(15 = 15\times1 = 5\times3\)).
  2. Candidates: \(2^4\cdot3^2=144\), \(3^4\cdot2^2=324\), \(2^4\cdot5^2=400\), \(2^{14}=16384\).
  3. Two smallest: 144 and 324, sum \(= 468\).

Same concept in other years

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

More Number Systems questions from CAT

All 40 Number Systems questions asked since 2017.