TITA type questions can often leave you second guessing whether your answer is correct or not as you don't have the option of cross verifying it with the given answer options. The best way to get comfortable around questions of this type is to practice questions from CAT previous year paper and understand what kind of questions you can expect in the CAT exam. Ace your CAT online preparation with these set of questions taken from CAT 2019 Question Paper Slot 2. Start with one from Number Systems right here! Make sure you do not look at the answers before giving it a go on your own.
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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] "
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