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CAT 2022 Slot 1 QA

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

Questions

  1. Q1. Let ABCD be a parallelogram such that the coordinates of its three vertices A, B, C are (1, 1), (3, 4) and (−2…
  2. Q2. The number of ways of distributing 20 identical balloons among 4 children such that each child gets some ballo…
  3. Q3. A mixture contains lemon juice and sugar syrup in equal proportion. If a new mixture is created by adding this…
  4. Q4. For natural numbers x, y, and z, if x y+y z=19 and y z+x z=51, then the minimum possible value of x y z is
  5. Q5. Let a, b, c be non-zero real numbers such that b^2 \lt 4 a c, and f(x)=a x^2+b x+c. If the set S consists of a…
  6. Q6. Trains A and B start traveling at the same time towards each other with constant speeds from stations X and Y,…
  7. Q7. The average of three integers is 13 . When a natural number n is included, the average of these four integers …
  8. Q8. Pinky is standing in a queue at a ticket counter. Suppose the ratio of the number of persons standing ahead of…
  9. Q9. Ankita buys 4 kg cashews, 14 kg peanuts and 6 kg almonds when the cost of 7 kg cashews is the same as that of …
  10. Q10. The largest real value of a for which the equation |x+a|+|x-1|=2 has an infinite number of solutions for x is
  11. Q11. A trapezium \text{ABCD} has side \text{AD} parallel to \text{BC}, \angle \text{BAD}=90^{\circ}, \text{BC}=3 \t…
  12. Q12. For any real number x, let [x] be the largest integer less than or equal to x. If \sum_{n=1}^N\left[\frac{1}{5…
  13. Q13. In a village, the ratio of number of males to females is 5 : 4. The ratio of number of literate males to liter…
  14. Q14. Amal buys 110 kg of syrup and 120 kg of juice, syrup being 20% less costly than juice, per kg. He sells 10 kg …
  15. Q15. Let a and b be natural numbers. If a^2+a b+a=14 and b^2+a b+b=28, then (2 a+b) equals
  16. Q16. Alex invested his savings in two parts. The simple interest earned on the first part at 15% per annum for 4 ye…
  17. Q17. In a class of 100 students, 73 like coffee, 80 like tea and 52 like lemonade. It may be possible that some stu…
  18. Q18. For any natural number n, suppose the sum of the first n terms of an arithmetic progression is \left(n+2 n^2\r…
  19. Q19. All the vertices of a rectangle lie on a circle of radius R. If the perimeter of the rectangle is P, then the …
  20. Q20. The average weight of students in a class increases by 600 gm when some new students join the class. If the av…
  21. Q21. Let A be the largest positive integer that divides all the numbers of the form 3^k+4^k+5^k, and B be the large…
  22. Q22. Let 0 \leq a \leq x \leq 100 and f(x)=|x-a|+|x-100|+|x-a-50|. Then the maximum value of f(x) becomes 100 when …