CAT 2020 Question Paper | Quants Slot 1

CAT Previous Year Paper | CAT Quants Questions | Question 9

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Question 9 : If x = (4096)7+4√3, then which of the following equals 64?

1. $$frac{x^{7/2}}{x^{4/√3}}$ 2. $\frac{x^{7}}{x^{4√3}}$ 3. $\frac{x^{7/2}}{x^{2√3}}$ 4. $\frac{x^{7}}{x^{2√3}}$ Best CAT Online Coaching Try upto 40 hours for free Learn from the best! 2IIM : Best Online CAT Coaching. Video Explanation Best CAT Coaching in Chennai CAT Coaching in Chennai - CAT 2022Limited Seats Available - Register Now! Explanatory Answer 642 = 4096 x =$4096)7 + 4√3
x = (642)7 + 4√3
√x = (64)7 + 4√3
√x( 1 ÷ (7 + 4√3)) = 64

1 ÷ (7 + 4√3) = $$frac{1}{7 + 4√3}$ = $\frac{1 ×$7 - 4√3$}{(7 + 4√3) × (7 - 4√3)}) = $$frac{7 - 4√3}{49 - 48}$ = 7 - 4√3 √x$ 1 ÷ (7 + 4√3)) = 64
√x(7 - 4√3) = 64
x(7/2 - (4√3)/2) = 64
x(7/2 - 2√3) = 64
$$frac{x^{7/2}}{x^{2√3}}$ The question is "If x =$4096)7+4√3, then which of the following equals 64?"

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