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 2 : The minimum possible value of \(\frac{x^2-6 x+10}{3-x}\), for \(x\lt3\), is

Video Explanation

Explanatory Answer

\( \frac { x ^ { 2 } - 6 x + 10 } { 3 - x } \)
\( \frac { x ^ { 2 } - 6 x + 9 + 1 } { 3 - x } \)
\( \frac { x ^ { 2 } - 6 x + 9 } { 3 - x } + \frac { 1 } { 3 - x } \)
\( \frac { ( x - 3 ) ^ { 2 } } { 3 - x } + \frac { 1 } { 3 - x } \)
\( ( x - 3 ) ^ { 2 } = ( 3 - x ) ^ { 2 } \)
\( \frac { ( 3 - x ) ^ { 2 } } { 3 - x } + \frac { 1 } { 3 - x } \)
\( 3 - x + \frac { 1 } { 3 - x } \)
Since \( x < 3 \), \( 3 - x \) is positive.
Let k = \( 3 - x \).
Since k is positive, the minimum value of \( k + \frac { 1 } { k } \) is 2.

The question is " The minimum possible value of \(\frac{x^2-6 x+10}{3-x}\), for \(x\lt3\), is "

Hence, the answer is '\(2\)'

Choice C is the correct answer.