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CAT 2022 Slot 3 Paper

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Question : 45 of 66

Marks: +1, -0

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

$60$
$-50$
$-70$
$-60$

Solution:

Let

\frac{x}{y}

be

t

Therefore,

c= 16t + \frac{49}{t}

Applying

\text{AM} \ge \text{GM}

\frac{16t + \frac{49}{t}}{2} \ge \left(16t \times \frac{49}{t}\right)^{\frac{1}{2}}

16t + \frac{49}{t} \ge 56

When

t

is positive then

c

is greater than equal to

56

.

When

t

is negative then

c

is less than equal to

-56

.

Therefore

c \in (-\infty, -56] \cup [56, \infty)

As

-50

is not in the range of

c

so it is the answer

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