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CAT 2019 Slot 1 QA

Quantitative Ability · 34 questions · 60 minutes · +3 / −1 (no negative marking on type-in answers)

Questions

  1. Q1. In a class, 60% of the students are girls and the rest are boys. There are 30 more girls than boys. If 68% of …
  2. Q2. If (5.55) x = (0.555) y = 1000, then the value of \frac{1}{x} - \frac{1}{y} is
  3. Q3. With rectangular axes of coordinates, the number of paths from (1,1) to (8,10) via (4,6), where each step from…
  4. Q4. A club has 256 members of whom 144 can play football, 123 can play tennis, and 132 can play cricket. Moreover,…
  5. Q5. In a circle of radius 11 cm, CD is a diameter and AB is a chord of length 20.5 cm. If AB and CD intersect at a…
  6. Q6. Meena scores 40% in an examination and after review, even though her score is increased by 50%, she fails by 3…
  7. Q7. Corners are cut off from an equilateral triangle T to produce a regular hexagon H. Then, the ratio of the area…
  8. Q8. Let T be the triangle formed by the straight line 3x + 5y - 45 = 0 and the coordinate axes. Let the circumcirc…
  9. Q9. For any positive integer n, let f(n) = n(n + 1) if n is even, and f(n) = n + 3 if n is odd. If m is a positive…
  10. Q10. If the population of a town is p in the beginning of any year then it becomes 3+2p in the beginning of the nex…
  11. Q11. A person invested a total amount of Rs 15 lakh. A part of it was invested in a fixed deposit earning 6% annual…
  12. Q12. The product of two positive numbers is 616. If the ratio of the difference of their cubes to the cube of their…
  13. Q13. On selling a pen at 5% loss and a book at 15% gain, Karim gains Rs. 7. If he sells the pen at 5% gain and the …
  14. Q14. Two cars travel the same distance starting at 10:00 am and 11:00 am, respectively, on the same day. They reach…
  15. Q15. At their usual efficiency levels, A and B together finish a task in 12 days. If A had worked half as efficient…
  16. Q16. If a 1 + a 2 + a 3 + ... + a n = 3(2 n+1 - 2), then a 11 equals [TITA]
  17. Q17. The number of the real roots of the equation 2cos(x(x + 1)) = 2 x + 2 -x is
  18. Q18. The income of Amala is 20% more than that of Bimala and 20% less than that of Kamala. If Kamala's income goes …
  19. Q19. In a race of three horses, the first beat the second by 11 metres and the third by 90 metres. If the second be…
  20. Q20. If a 1 , a 2 , ......... are in A.P , \frac{1}{\sqrt{a_1} + \sqrt{a_2}} + \frac{1}{\sqrt{a_2} + \sqrt{a_3}} + …
  21. Q21. AB is a diameter of a circle of radius 5 cm. Let P and Q be two points on the circle so that the length of PB …
  22. Q22. One can use three different transports which move at 10, 20, and 30 kmph, respectively. To reach from A to B, …
  23. Q23. Amala, Bina, and Gouri invest money in the ratio 3 : 4 : 5 in fixed deposits having respective annual interest…
  24. Q24. If m and n are integers such that (\sqrt{2}) 19 3 4 4 2 9 m 8 n = 3 n 16 m (∜64) then m is
  25. Q25. A chemist mixes two liquids 1 and 2. One litre of liquid 1 weighs 1 kg and one litre of liquid 2 weighs 800 gm…
  26. Q26. Let x and y be positive real numbers such that log 5 (x + y) + log 5 (x - y) = 3, and log 2 y - log 2 x = 1 - …
  27. Q27. If the rectangular faces of a brick have their diagonals in the ratio 3 : 2 \sqrt{3} : \sqrt{15}, then the rat…
  28. Q28. Let S be the set of all points (x,y) in the x-y plane such that |x| + |y| ≤ 2 and |x| ≥ 1. Then, the area, in …
  29. Q29. The number of solutions of the equation |x|(6x 2 + 1) = 5x 2 is [TITA]
  30. Q30. Three men and eight machines can finish a job in half the time taken by three machines and eight men to finish…
  31. Q31. The product of the distinct roots of |x 2 - x - 6| = x + 2 is
  32. Q32. The wheels of bicycles A and B have radii 30 cm and 40 cm, respectively. While traveling a certain distance, e…
  33. Q33. Consider a function f(x+y) = f(x) f(y) where x , y are positive integers, and f(1) = 2. If f (a+1) + f (a+2) +…
  34. Q34. Ramesh and Gautam are among 22 students who write an examination. Ramesh scores 82.5. The average score of the…