CAT 2022 Question Paper | Quant Slot 3

CAT 2022 Quant was dominated by Arithmetic followed by Algebra. 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 22 : The lengths of all four sides of a quadrilateral are integer valued. If three of its sides are of length 1 cm, 2 cm and 4 cm, then the total number of possible lengths of the fourth side is

Video Explanation

Explanatory Answer

In any polygon, the largest side length should be less than the sum of the lengths of the other sides.
Let the fourth side be ‘x’.
Case i) x is the largest side.
x < 1 + 2 + 6
x < 7
x can take the following values, 4, 5, 6
Case ii)
4 is the largest side and x is less than 4.
4 < x + 1 +2
x > 1
x can take the values 2 or 3
So, x can take the values 2, 3, 4, 5, 6.
x can take 5 values.

The question is " The lengths of all four sides of a quadrilateral are integer valued. If three of its sides are of length 1 cm, 2 cm and 4 cm, then the total number of possible lengths of the fourth side is "

Hence, the answer is '5'

Choice C is the correct answer.

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