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SSC CGL 2022 PYQ — Question 66

SSC CGL - 11 April 2022 - Shift 2 • Quantitative Aptitude • Q66

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Simplify the following expression:

(a2−4b2)3+64(b2−4c2)3+(16c2−a2)3(a−2b)3+(2b−4c)3+(4c−a)3{{(a^2 - 4b^2)^3} + 64(b^2 - 4c^2)^3 + (16c^2 - a^2)^3}\over (a-2b)^3 + (2b - 4c)^3 + (4c - a)^3

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Correct answer: B

Explanation

The correct answer is option 2 i.e.90. 

We need a short trick to solve these types of questions otherwise it will take a lot of time to find the answer.

By putting a, b, and c equal to 1, we get 

{(12 - 4 × 12)3 + 64 × (12 - 4 × 12)3 + (16 × 12 - 12)3}/{(1 - 2 × 1)3 + (2 × 1 -  4 × 1)3 + (4  × 1 - 1)3}

⇒ {(1 - 4)3 + 64 × (1 - 4)3 + (16 - 1)3}/{(1 - 2)3 + (2 -  4)3 + (4 - 1)3}

⇒ {(-3)3 + 64 × (-3)3 + (15)3}/{(-1)3 + (-2)3 + (33)}

Solving the numerator, we get

⇒ -27 + 64 × (-27) + 3375 = -1755 + 3375 = 1620

Solving the numerator, we get

⇒ -1 - 8 + 27 = 18

Thus, the value of the given expression is 1620/18 = 90

By putting a, b, and c equal to 1 in the given Options, only Option 2 is 90.

Option 1 can be directly neglected as it will give a negative number.

Option 3 is equal to 180

Option 4 is equal to 45