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CAT 2023 Slot 3 QA

Quantitative Ability · 22 questions · 40 minutes · +3 / −1 (no negative marking on type-in answers)

Questions

  1. Q1. For a real number x, if \frac{1}{2}, \frac{\log _3\left(2^x-9\right)}{\log _3 4}, and \frac{\log _5\left(2^x+\…
  2. Q2. Let n and m be two positive integers such that there are exactly 41 integers greater than 8^m and less than 8^…
  3. Q3. For some real numbers a and b, the system of equations x+y=4 and (a+5) x+\left(b^2-15\right) y=8 b has infinit…
  4. Q4. If x is a positive real number such that x^8+\left(\frac{1}{x}\right)^8=47, then the value of x^9+\left(\frac{…
  5. Q5. A quadratic equation x^2+b x+c=0 has two real roots. If the difference between the reciprocals of the roots is…
  6. Q6. The sum of the first two natural numbers, each having 15 factors (including 1 and the number itself), is
  7. Q7. Let n be any natural number such that 5^{n-1} \lt 3^{n+1}. Then, the least integer value of m that satisfies 3…
  8. Q8. Rahul, Rakshita and Gurmeet, working together, would have taken more than 7 days to finish a job. On the other…
  9. Q9. Anil mixes cocoa with sugar in the ratio 3 : 2 to prepare mixture A, and coffee with sugar in the ratio 7 : 3 …
  10. Q10. The population of a town in 2020 was 100000 . The population decreased by y \% from the year 2020 to 2021 , an…
  11. Q11. A merchant purchases a cloth at a rate of Rs.100 per meter and receives 5 cm length of cloth free for every 10…
  12. Q12. There are three persons \mathrm{A}, \mathrm{B} and \mathrm{C} in a room. If a person \mathrm{D} joins the room…
  13. Q13. A boat takes 2 hours to travel downstream a river from port A to port B, and 3 hours to return to port A. Anot…
  14. Q14. A fruit seller has a stock of mangoes, bananas and apples with at least one fruit of each type. At the beginni…
  15. Q15. The number of coins collected per week by two coin-collectors A and B are in the ratio 3 : 4. If the total num…
  16. Q16. Gautam and Suhani, working together, can finish a job in 20 days. If Gautam does only 60% of his usual work on…
  17. Q17. Let \triangle A B C be an isosceles triangle such that A B and A C are of equal length. A D is the altitude fr…
  18. Q18. A rectangle with the largest possible area is drawn inside a semicircle of radius 2 \mathrm{~cm}. Then, the ra…
  19. Q19. In a regular polygon, any interior angle exceeds the exterior angle by 120 degrees. Then, the number of diagon…
  20. Q20. The value of 1+\left(1+\frac{1}{3}\right) \frac{1}{4}+\left(1+\frac{1}{3}+\frac{1}{9}\right) \frac{1}{16}+\lef…
  21. Q21. Let a_n=46+8 n and b_n=98+4 n be two sequences for natural numbers n \leq 100. Then, the sum of all terms comm…
  22. Q22. Suppose f(x, y) is a real-valued function such that f(3 x+2 y, 2 x-5 y)=19 x, for all real numbers x and y. Th…