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SSC CGL 2021 PYQ — Question 62

SSC CGL - 17 Aug 2021 - Shift 3 • Quantitative Aptitude • Q62

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If x2 + 9y2 + 4z2 = 12 (x - 2y - 2z) - 88, then the value of (x - 3y + z) is ) is:

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Correct answer: B

Explanation

 The correct answer is Option 2 i.e 13.

x2+9y2+4z2=12(x−2y+2z)−88⇒x2+9y2+4z2=12x−24y+24z−88⇒x2+9y2+4z2−12x+24y−24z+88=0⇒x2−12x+36+9y2+24y+16+4z2−24z+36=0⇒(x−6)2+(3y+4)2+(2z−6)2=0\begin{aligned} &x^{2}+9 y^{2}+4 z^{2}=12(x-2 y+2 z)-88 \\ &\Rightarrow x^{2}+9 y^{2}+4 z^{2}=12 x-24 y+24 z-88 \\ &\Rightarrow x^{2}+9 y^{2}+4 z^{2}-12 x+24 y-24 z+88=0 \\ &\Rightarrow x^{2}-12 x+36+9 y^{2}+24 y+16+4 z^{2}-24 z+36=0 \\ &\Rightarrow(x-6)^{2}+(3 y+4)^{2}+(2 z-6)^{2}=0 \end{aligned}

Now,  one can conclude that,

⇒ x - 6 = 0 then x = 6.

⇒ 3y + 4 = 0 then y = -4/3.

⇒ 2z - 6 = 0 then z = 3.

So, x - 3y + z = 6 - 3 × -(4/3) + 3 = 13.