CAT 2019 Question Paper | Quants Slot 2

CAT Questions

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.
To know more about what kind of questions you can expect in the CAT Exam, visit 2IIM's CAT Blueprint .
To practice more questions like these, visit 2IIM's CAT Question Bank.

Question 6 : How many factors of 2⁴ × 3⁵ × 10⁴ are perfect squares which are greater than 1? [TITA]

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Video Explanation

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Explanatory Answer

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

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The question is "How many factors of 2⁴ × 3⁵ × 10⁴ are perfect squares which are greater than 1? [TITA] "

Hence, the answer is 44

 

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