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.

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