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SSC CPO 2019 PYQ — Question 144

SSC CPO Tier I - 11th December 2019 - Shift 1 • Quantitative Aptitude • Q144

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If (2x – 5y)3 – (2x + 5y)3 = y [Ax2 + By2], then what is the value of (2A – B)?

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Correct answer: D

Explanation

The correct answer is option 4 i.e. 10

Understanding

Use the formula:

a3 – b3 = (a – b) (a2 + b2 + ab)

Application

Now,

(2x – 5y)3 – (2x + 5y)3 = y[Ax2 + By2]

⇒ [(2x – 5y) – (2x + 5y)] [(2x – 5y)2 + (2x + 5y)2 + (2x – 5y)(2x + 5y)] = y[Ax2 + By2]

⇒ [2x – 5y – 2x – 5y][4x2 + 25y2 – 20xy + 4x2 + 25y2 + 20xy + 4x2 – 25y2] = y[Ax2 + By2]

⇒ [– 10y] [12x2 + 25y2] = y[Ax2 + By2]

⇒ y[– 120x2 – 250y2] = y[Ax2 + By3]

Comparing the coefficients:

A = -120 and B = -250

Hence,

(2A – B) = -240 + 250 = 10