SarkariPYQ

SSC CGL 2019 PYQ — Question 69

SSC CGL - 6th June 2019 - Shift 1 • Quantitative Aptitude • Q69

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If (8x3 - 27y3) ÷ (2x - 3y) = (Ax2 + Bxy + Cy2), then the value of (2A + B - C) is:

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Correct answer: A

Explanation

Correct Answer is option 1 i.e. 5

Concept

Application

Formula:

a3 - b3 = (a - b) (a2 + b2 + ab)

[8x3 – 27y3] ÷ (2x – 3y) = Ax2 + Bxy + Cy2

⇒ [(2x)3 – (3y)3] ÷ (2x – 3y) = Ax2 + Bxy + Cy2

Using the formula:

⇒ [2x – 3y] [(2x)2 + (3y)2 + (2x) × (3y)] ÷ (2x – 3y) = Ax2 + Bxy + Cy2

⇒ [4x2 + 6xy + 9y2] = Ax2 + Bxy + Cy2

Comparing the coefficients:

⇒ A = 4, C = 9 and B = 6

Hence,

2A + B – C = 8 + 6 – 9 = 5