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CAT 2022 Slot 3 QA

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

Questions

  1. Q1. Suppose k is any integer such that the equation 2 x^2+k x+5=0 has no real roots and the equation x^2+(k-5) x+1…
  2. Q2. The minimum possible value of \frac{x^2-6 x+10}{3-x}, for x\lt3, is
  3. Q3. Bob can finish a job in 40 days, if he works alone. Alex is twice as fast as Bob and thrice as fast as Cole in…
  4. Q4. A glass contains 500 cc of milk and a cup contains 500 cc of water. From the glass, 150 cc of milk is transfer…
  5. Q5. In an examination, the average marks of students in sections A and B are 32 and 60, respectively. The number o…
  6. Q6. Let r be a real number and f(x)=\left\{\begin{array}{cl}2 x-r & \text { if } x \geq r \\ r & \text { i…
  7. Q7. Suppose the medians BD and CE of a triangle ABC intersect at a point O. If area of triangle ABC is 108 sq. cm.…
  8. Q8. The arithmetic mean of all the distinct numbers that can be obtained by rearranging the digits in 1421, includ…
  9. Q9. Nitu has an initial capital of ₹ 20,000. Out of this, she invests ₹ 8,000 at 5.5 \% in bank A, ₹ 5,000 at 5.6 …
  10. Q10. Two cars travel from different locations at constant speeds. To meet each other after starting at the same tim…
  11. Q11. If \left(\sqrt{\frac{7}{5}}\right)^{3 x-y}=\frac{875}{2401} and \left(\frac{4 a}{b}\right)^{6 x-y}=\left(\frac…
  12. Q12. Moody takes 30 seconds to finish riding an escalator if he walks on it at his normal speed in the same directi…
  13. Q13. Consider six distinct natural numbers such that the average of the two smallest numbers is 14, and the average…
  14. Q14. If (3+2 \sqrt{2}) is a root of the equation a x^2+b x+c=0, and (4+2 \sqrt{3}) is a root of the equation a y^2+…
  15. Q15. If c=\frac{16 x}{y}+\frac{49 y}{x} for some non-zero real numbers x and y, then c cannot take the value
  16. Q16. A group of N people worked on a project. They finished 35 \% of the project by working 7 hours a day for 10 da…
  17. Q17. The average of all 3-digit terms in the arithmetic progression 38, 55, 72, ..., is
  18. Q18. In a triangle \mathrm{ABC}, \mathrm{AB}=\mathrm{AC}=8 \mathrm{cm}. A circle drawn with \mathrm{BC} as diameter…
  19. Q19. A school has less than 5000 students and if the students are divided equally into teams of either 9 or 10 or 1…
  20. Q20. A donation box can receive only cheques of ₹100, ₹250, and ₹500. On one good day, the donation box was found t…
  21. Q21. Two ships are approaching a port along straight routes at constant speeds. Initially, the two ships and the po…
  22. Q22. The lengths of all four sides of a quadrilateral are integer valued. If three of its sides are of length 1 cm,…