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SSC CGL 2021 PYQ — Question 71

SSC CGL - 13 Aug 2021 - Shift 1 • Quantitative Aptitude • Q71

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If x + y = 4 = 1x\frac{1}{x} + 1y\frac{1}{y} = 1615\frac{16}{15}, then what is the value of (x3 + y3)?

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Correct answer: C

Explanation

The correct answer is option 3 i.e. 19

⇒ 1x+1y=1615\frac{1}{x} + \frac{1}{y}=\frac{16}{15}

⇒ x+yxy=1615\frac{x+y}{xy}=\frac{16}{15}

⇒ 4xy=1615\frac{4}{xy}=\frac{16}{15}

⇒ xy = 15/4

⇒ (x + y)3 = x3 + y3 + 3xy(x + y)

⇒ 64 = x3 + y3 + 3(15/4)(4)

⇒ x3 + y3 = 64 - 45

⇒ 19