CAT 2021 Question Paper | Quant Slot 1

CAT Previous Year Paper | CAT Quant Questions | Question 4

CAT 2021 Quant was dominated by Arithmetic followed by Algebra. In Arithmetic, the questions were dominated by topics like Speed-time-distance, Mixture and Alligations. This year, there was a surprise. The questions from Geometry were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.

Question 4 : If 5 - \\log _{10} \sqrt{1+x}) + 4 \\log _{10} \sqrt{1-x}) = \\log _{10} \frac{1}{\sqrt{1-x^{2}}}) , then 100 x equals


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Explanatory Answer

5 - \\log _{10} \sqrt{1 + x}) + 4\\log _{10} \sqrt{1 - x}) = \\log _{10} \frac{1}{\sqrt{1-x^{2}}})
5 - \\log _{10} \sqrt{1 + x}) + 4\\log _{10} \sqrt{1 - x}) = \\log _{10} { \left( \frac{1}{\sqrt{1-x}} \frac{1}{\sqrt{1+x}} \right)})
5 - \\log _{10} \sqrt{1 + x}) + 4\\log _{10} \sqrt{1 - x}) = - \\log _{10} \sqrt{1 - x}) - \\log _{10} \sqrt{1 + x})
4\\log _{10} \sqrt{1 - x}) + \\log _{10} \sqrt{1 - x}) = -5
\\log _{10} \sqrt{1 - x}) = -1
\\sqrt{1-x}) = \\frac{1}{10})
100x = 99.
Therefore the answer should be 99.


The question is " If 5 - \\log _{10} \sqrt{1+x}) + 4 \\log _{10} \sqrt{1-x}) = \\log _{10} \frac{1}{\sqrt{1-x^{2}}}) , then 100 x equals "

Hence, the answer is '99'

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