The best questions to practice for CAT Exam are the actual CAT Question Papers. 2IIM offers you exactly that, in a student friendly format to take value from this. In CAT 2019 we saw some beautiful questions that laid emphasis on Learning ideas from basics and being able to comprehend more than remembering gazillion formulae and shortcuts. Original CAT Question paper is the best place to start off your CAT prep practice. This page provides exactly that. To check out about 1000 CAT Level questions with detailed video solutions for free, go here: CAT Question Bank
Question 6 : How many factors of 24 × 35 × 104 are perfect squares which are greater than 1? [TITA]
24 x 35 x 104
24 x 35 x 24 x 54
28 x 35 x 54
Now, for any number to be a perfect square, it must have an even number of factors.
So, if we consider 28, only powers of 0, 2, 4, 6, 8 can lead to perfect squares - 5 ways
If we consider 35, only powers of 0, 2, 4 can lead to perfect squares - 3 ways
If we consider 54, only powers of 0. 2, 4 can lead to perfect squares - 3 ways
So, total number of possibilities = 5 x 3 x 3 ways = 45 ways
Since we need to find the number of factors greater than 1,
Required number of ways = 45 -1 = 44 ways
The question is "How many factors of 24 × 35 × 104 are perfect squares which are greater than 1? [TITA] "
CAT® (Common Admission Test) is a registered trademark of the Indian Institutes of Management. This website is not endorsed or approved by IIMs.
2IIM Online CAT Coaching
A Fermat Education Initiative,
58/16, Indira Gandhi Street,
Kaveri Rangan Nagar, Saligramam, Chennai 600 093