← All CAT papers

CAT 2024 Slot 1 QA

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

Questions

  1. Q1. A fruit seller has a total of 187 fruits consisting of apples, mangoes and oranges. The number of apples and m…
  2. Q2. If (a+b \sqrt{n}) is the positive square root of (29-12 \sqrt{5}), where a and b are integers, and n is a natu…
  3. Q3. The sum of all real values of k for which \left(\frac{1}{8}\right)^k \times\left(\frac{1}{32768}\right)^{\frac…
  4. Q4. In the X Y-plane, the area, in sq. units, of the region defined by the inequalities y \geq x+4 and -4 \leq x^2…
  5. Q5. Renu would take 15 days working 4 hours per day to complete a certain task whereas Seema would take 8 days wor…
  6. Q6. In September, the incomes of Kamal, Amal and Vimal are in the ratio 8 : 6 : 5. They rent a house together, and…
  7. Q7. Consider two sets A=\{2,3,5,7,11,13\} and B=\{1,8,27\}. Let f be a function from A to B such that for every el…
  8. Q8. Let x, y, and z be real numbers satisfying $$ \begin{aligned} & 4\left(x^2+y^2+z^2\right)=a \\ & 4(x-y…
  9. Q9. The sum of all four-digit numbers that can be formed with the distinct non-zero digits a, b, c, and d, with ea…
  10. Q10. When 10^{100} is divided by 7 , the remainder is
  11. Q11. There are four numbers such that average of first two numbers is 1 more than the first number, average of firs…
  12. Q12. An amount of Rs 10000 is deposited in bank A for a certain number of years at a simple interest of 5% per annu…
  13. Q13. A shop wants to sell a certain quantity (in kg) of grains. It sells half the quantity and an additional 3 kg o…
  14. Q14. Suppose x_1, x_2, x_3, \ldots, x_{100} are in arithmetic progression such that x_5=-4 and 2 x_6+2 x_9=x_{11}+x…
  15. Q15. Two places A and B are 45 kms apart and connected by a straight road. Anil goes from A to B while Sunil goes f…
  16. Q16. The surface area of a closed rectangular box, which is inscribed in a sphere, is 846 sq cm , and the sum of th…
  17. Q17. A glass is filled with milk. Two-thirds of its content is poured out and replaced with water. If this process …
  18. Q18. For any natural number n, let a_n be the largest integer not exceeding \sqrt{n}. Then the value of a_1+a_2+\cd…
  19. Q19. ABCD is a rectangle with sides AB = 56 cm and BC = 45 cm, and E is the midpoint of side CD. Then, the length, …
  20. Q20. If the equations x^2+m x+9=0, x^2+n x+17=0 and x^2+(m+n) x+35=0 have a common negative root, then the value of…
  21. Q21. The selling price of a product is fixed to ensure 40% profit. If the product had cost 40% less and had been so…
  22. Q22. If x is a positive real number such that 4 \log _{10} x+4 \log _{100} x+8 \log _{1000} x=13, then the greatest…