CAT 2021 Question Paper | Quant Slot 2

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 + 2^{n + 2} ≤ 202, the number of integer values of 3 + 3^{n + 1} is

Video Explanation

Explanatory Answer

2.25 ≤ 2 + 2^{n + 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 + 2^{n + 2} ≤ 202, the number of integer values of 3 + 3^{n + 1} is "

Hence, the answer is '7'