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CAT 2022 Question Paper | Quant Slot 1

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Geometry HCF and LCM Factors Remainders Factorials Digits Ratios,Mixtures;Averages Percents; Profits; SICI Speed & Time; Races Logarithms and Exponents Pipes,Cisterns; Work,Time Set Theory Coordinate Geometry Mensuration Trigonometry Linear & Quadratic Equations Functions Inequalities Polynomials Progressions Permutation Probability
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CAT 2022 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 8 : Pinky is standing in a queue at a ticket counter. Suppose the ratio of the number of persons standing ahead of Pinky to the number of persons standing behind her in the queue is 3 : 5. If the total number of persons in the queue is less than 300, then the maximum possible number of persons standing ahead of Pinky is

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Explanatory Answer

The ratio of the number of persons standing ahead of Pinky to the number of persons standing behind her in the queue is 3 : 5.
Let’s assume that there are 3x number of people ahead of Pinky, then the number of people behind her will be 5x.
The total number of people in the queue is 8x + 1.
Since the total number of people in the queue is less than 300.
8x + 1 < 300
\( x \leq 37 \)
To find the maximum number of people ahead of Pinky, we take the maximum possible value of x, which is 37.
Therefore, the maximum number of people ahead of Pinky is 3 * 37 = 111