How many integer values of n satisfy \frac{5}{3}

CAT Exam Model Paper 8 with solutions for free online practice

Question : 3 of 60

Marks: +1, -0

How many integer values of n satisfy

{5}/{3}< {n}/{n+4}< {14}/{3}

Solution:

Let assume that n + 4 is positive i.e. n > - 4.
⇒ 5n + 20 < 3n and 3n < 14n + 56

⇒n < - 10

and

n > -56/11

so no solution is possible.
Now let us assume that n + 4 is negative i.e. n < - 4.
⇒ 5n + 20 > 3n and 3n > 14n + 56
⇒

n>-10

and

n<- {56}/{11}

So n can take 4 integral values - 6, - 7, - 8, - 9.

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