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 15 : If \(c=\frac{16 x}{y}+\frac{49 y}{x}\) for some non-zero real numbers \(x\) and \(y\), then \(c\) cannot take the value

Video Explanation

Explanatory Answer

\( c = \frac { 16 x } { y } + \frac { 49 y } { x } \)
Let k = \( \frac { x } { y } \), Since x and y are real, k is also real.
c = 16 k + \( \frac { 49 } { k } \)
\( 16 k ^ { 2 } - c k + 49 = 0 \)
We know that k is real, for k to be real, it has to be rational first.
That means, \( c ^ { 2 } > 4.16 .49 \)
\( c ^ { 2 } > 56 ^ { 2 } \)
|c| > 56
C can’t take the value -50.

The question is " If \(c=\frac{16 x}{y}+\frac{49 y}{x}\) for some non-zero real numbers \(x\) and \(y\), then \(c\) cannot take the value "

Hence, the answer is '-50'

Choice C is the correct answer.

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