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SSC CGL 2019 PYQ — Question 54

SSC CGL - 4th June 2019 - Shift 2 • Quantitative Aptitude • Q54

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If 16x2 + 9y2 + 4z2 = 24(x - y + z) - 61, then the value of (xy + 2z) is:

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Correct answer: A

Explanation

Correct Answer is option 1 i.e. 5

Application

16x2 + 9y2 + 4z2 = 24(x – y + z) – 61

⇒ (4x)2 + (3y)2 + (2z)2 = 24x – 24y + 24z – 61 

⇒ (4x)2 – 24x + 9 + (3y)2 + 24y + 16 + (2z)2 – 24z + 36 = 0

⇒ (4x – 3)2 + (3y + 4)2 + (2z – 6)2 = 0

Hence, x = 3/4, y = -4/3 and z = 3

Now,

(xy + 2z) = 3/4 × -4/3 + 2 × 3 

⇒ -1 + 6 = 5