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CAT 2024 Slot 3 QA

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

Questions

  1. Q1. The number of distinct integer solutions (x, y) of the equation |x+y|+|x-y|=2, is
  2. Q2. For some constant real numbers p, k and a, consider the following system of linear equations in x and y : $$ \…
  3. Q3. If (a+b \sqrt{3})^2=52+30 \sqrt{3}, where a and b are natural numbers, then a+b equals
  4. Q4. A circular plot of land is divided into two regions by a chord of length 10 \sqrt{3} meters such that the chor…
  5. Q5. In a group of 250 students, the percentage of girls was at least 44% and at most 60%. The rest of the students…
  6. Q6. If 10^{68} is divided by 13 , the remainder is
  7. Q7. The midpoints of sides AB, BC, and AC in △ ABC are M, N, and P, respectively. The medians drawn from A, …
  8. Q8. After two successive increments, Gopal's salary became 187.5% of his initial salary. If the percentage of sala…
  9. Q9. Sam can complete a job in 20 days when working alone. Mohit is twice as fast as Sam and thrice as fast as Ayna…
  10. Q10. A certain amount of water was poured into a 300 litre container and the remaining portion of the container was…
  11. Q11. Aman invests Rs 4000 in a bank at a certain rate of interest, compounded annually. If the ratio of the value o…
  12. Q12. Gopi marks a price on a product in order to make 20% profit. Ravi gets 10% discount on this marked price, and …
  13. Q13. The average of three distinct real numbers is 28. If the smallest number is increased by 7 and the largest num…
  14. Q14. The number of all positive integers up to 500 with non-repeating digits is
  15. Q15. A train travelled a certain distance at a uniform speed. Had the speed been 6 km per hour more, it would have …
  16. Q16. If 3^a=4,4^b=5,5^c=6,6^d=7,7^e=8 and 8^f=9, then the value of the product abcdef is
  17. Q17. Consider the sequence t_1=1, t_2=-1 and t_n=\left(\frac{n-3}{n-1}\right) t_{n-2} for n \geq 3. Then, the value…
  18. Q18. The number of distinct real values of x, satisfying the equation \max \{x, 2\}-\min \{x, 2\}=|x+2|-|x-2|, is
  19. Q19. Rajesh and Vimal own 20 hectares and 30 hectares of agricultural land, respectively, which are entirely covere…
  20. Q20. For any non-zero real number x, let f(x)+2 f\left(\frac{1}{x}\right)=3 x. Then, the sum of all possible values…
  21. Q21. A regular octagon ABCDEFGH has sides of length 6 cm each. Then the area, in sq. cm , of the square A C E G is
  22. Q22. The sum of all distinct real values of x that satisfy the equation 10^x+\frac{4}{10^x}=\frac{17}{2}, is