CMAT Exam 2023 Shift 2 Solved Paper

Question : 15 of 100

Marks: +1, -0

The number of all integers

{\n}

for which

n^2+96

is a perfect square, is

Solution:

Let

n^2+96=k^2

k^2-n^2=96

\;(k+n)(k-n)=96

\;(k+n)(k-n)=2 × 48,4 × 24,6 × 16,8 × 12,12 × 8,16 × 6,24 × 4,48 × 2

{\n}

can take 8 values, i.e.

-23,-10,-5,-2,2,5,10

and 23 .
The answer is option C.

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