CAT 2023 Question Paper | Quant Slot 2

CAT Previous Year Paper | CAT Quant Questions | Question 6

CAT 2023 Quant was dominated by Algebra followed by Arithmetic. In Arithmetic, the questions were dominated by topics like Speed-time-distance, Mixture and Alligations. This year, there was a surprise. The questions from Geometry were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.

Question 6 : The number of positive integers less than 50, having exactly two distinct factors other than 1 and itself, is


🎉Grab a Vijayadashami & Dussehra Discount of up to ₹ 12,000 on 2024 & 2025 CAT courses! Offer valid until 12th October.


Register Now

🎉 2IIM CAT Revision Course 2024: 100+ Hours of Intensive Prep and everything is covered—Join Now!!! 🎉


Register Now


Video Explanation


Best CAT Coaching in Chennai


CAT Coaching in Chennai - CAT 2022
Limited Seats Available - Register Now!


Explanatory Answer

A positive integer less than 50, having exactly two distinct factors other than 1 and itself, is either a perfect cube below 50 or an integer that is a product of exactly two distinct primes.
Case i)
Perfect cubes below 50 are 23 and 33. So, two numbers here
Case ii)
For the product of two primes to be below 50, the individual primes should be below 25.
(Because, the smallest prime is 2 and multiplying 2 with anything greater than or equal to 25 yields a number greater than or equal to 50.)
2, 3, 5, 7, 11, 13, 17, 19, 23 are prime numbers less than 25.

2, 3, 5, 7 are the primes less than \( \sqrt { 50 } \), any product of two numbers among them yields a product less than 50.
So, there are \( 4 C _ { 2 } = 6 \) pairs here.
11, 13, 17, 19, 23 are the primes greater than \( \sqrt { 50 } \), any product of two numbers among them yields a product greater than 50.
So, there are 0 pairs here.
Between the two lists 11 and 13 can pair with 2 and 3, while 17, 19, and 23 can only pair with 2.
So, there are 7 pairs here.
So, totally, there are 2 + 6 + 0 + 7 = 15 such numbers.


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

Hence, the answer is '15'

CAT Questions | CAT Quantitative Aptitude

CAT Questions | Verbal Ability for CAT


Where is 2IIM located?

2IIM Online CAT Coaching
A Fermat Education Initiative,
58/16, Indira Gandhi Street,
Kaveri Rangan Nagar, Saligramam, Chennai 600 093

How to reach 2IIM?

Mobile: (91) 99626 48484 / 94459 38484
WhatsApp: WhatsApp Now
Email: info@2iim.com