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Question

Quantitative Aptitude Question on Number Systems

If (3x-13x\frac{1}{3x})=4, , then what is the value of (27x3-127x3\frac{1}{27x^3}) ?

A

52

B

64

C

48

D

76

Answer

76

Explanation

Solution

The correct option is (D): 76.
We know, (a – b)3 = a3 - b3 - 3ab(a –b)
Now, (3x−13x)3=(27x3−127x3)−3(3x)(13x)(3x−13x)(3x-\frac{1}{3x})^3=(27x^3-\frac{1}{27x^3})-3(3x)(\frac{1}{3x})(3x-\frac{1}{3x})
43=(27x3−127x3)−3∗44^3=(27x^3-\frac{1}{27x^3})-3*4
(27x3−127x3)(27x^3-\frac{1}{27x^3})=76