# CAT 2022 Question Paper | Quant Slot 3

###### CAT Previous Year Paper | CAT Quant Questions | Question 22

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

1. 6
2. 4
3. 5
4. 3

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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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