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

- \(\frac{1}{2}\)
- \(-\frac{1}{2}\)
- \(2\)
- \(-2\)

Try upto 40 hours for free

Learn from the best!

Limited Seats Available - Register Now!

\( \frac { x ^ { 2 } - 6 x + 10 } { 3 - x } \)

\( \frac { x ^ { 2 } - 6 x + 9 + 1 } { 3 - x } \)

\( \frac { x ^ { 2 } - 6 x + 9 } { 3 - x } + \frac { 1 } { 3 - x } \)

\( \frac { ( x - 3 ) ^ { 2 } } { 3 - x } + \frac { 1 } { 3 - x } \)

\( ( x - 3 ) ^ { 2 } = ( 3 - x ) ^ { 2 } \)

\( \frac { ( 3 - x ) ^ { 2 } } { 3 - x } + \frac { 1 } { 3 - x } \)

\( 3 - x + \frac { 1 } { 3 - x } \)

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 " **

Choice C is the correct answer.

Copyrights © All Rights Reserved by 2IIM.com - A Fermat Education Initiative.

Privacy Policy | Terms & Conditions

CAT^{®} (Common Admission Test) is a registered trademark of the Indian Institutes of Management. This website is not endorsed or approved by IIMs.

2IIM Online CAT Coaching

A Fermat Education Initiative,

58/16, Indira Gandhi Street,

Kaveri Rangan Nagar, Saligramam, Chennai 600 093

**Mobile:** (91) 99626 48484 / 94459 38484

**WhatsApp:** WhatsApp Now

**Email: **info@2iim.com