# CAT 2021 Question Paper | Quant Slot 2

###### CAT Previous Year Paper | CAT Quant Questions | Question 15

CAT 2021 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 15 : For all possible integers n satisfying 2.25 ≤ 2 + 2n + 2 ≤ 202, the number of integer values of 3 + 3n + 1 is

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2.25 ≤ 2 + 2n + 2 ≤ 202
So, 2 + 2 n+2 has to be either lesser than or equal to 202.
27 = 128 and so will satisfy the inequality, but 28 wont.
Hence, the value of n can be 5 at most.
Further, subtracting 2 from the first two parts of the inequality,
0.25 ≤ 2n+2
Or, 2-2 ≤ 2n+2
Hence, n ≥ -4
So from the inequality we can say that the integral value of n can be [-4, 5].
For 3 + 3n+1 to have integral values, n but be greater than or equal to -1 and go up till 5.

Hence the number of values of n can be -1, 0, 1, 2, 3, 4, 5.
7 values

The question is " For all possible integers n satisfying 2.25 ≤ 2 + 2n + 2 ≤ 202, the number of integer values of 3 + 3n + 1 is "

##### Hence, the answer is '7'

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