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SSC CGL 2022 PYQ — Question 55

SSC CGL - 20 April 2022 - Shift 3 • Quantitative Aptitude • Q55

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if (4a - 3b) = 1, ab = 12\frac{1}{2}, where a > 0 and b > 0, what is the value of (64a3 + 27b3)?

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Correct answer: C

Explanation

The correct answer is option 3 i.e. 35

(4a - 3b)2 =  (4a + 3b)2 - 4 × 4a × 3b

⇒ (4a + 3b)2 = (4a - 3b)2 + 4 × 4a × 3b 

⇒ (4a + 3b)2 = 1 + 48 × 1/2 = 1 + 24

⇒ (4a + 3b)2 = 25 or (4a + 3b) = 5

Now, (4a + 3b)3 = 64a3 + 27b3 + 3 × 4a × 3b × (4a + 3b)

⇒ 53 = 64a3 + 27b3 + 36 × (1/2) × 5

⇒ 64a3 + 27b3  = 125 - 90 = 35