CAT 2023 Question Paper (Available): Download CAT Question Paper with Solutions PDF

CAT 2023 Questions

• 1.

  Find the number of integer pairs (x, y) that satisfy the following system of inequalities:
  \[ \begin{cases} x \geq y \geq 3 \\ x + y \leq 14 \end{cases} \]
  

  View Solution

  ---

• 2.

  An item with a cost price of Rs.1650 is sold at a certain discount on a fixed marked price to earn a profit of 20% on the cost price. If the discount was doubled, the profit would have been Rs.110. The rate of discount, in percentage, at which the profit percentage would be equal to the rate of discount, is nearest to:

  • \(12\)
  • \(13\)
  • \(14\)
  • \(15\)
  View Solution

  ---

• 3.

  The monthly sales of a product from January to April were 120, 135, 150 and 165 units, respectively. The cost price of the product was Rs. 240 per unit, and a fixed marked price was used for the product in all the four months. Discounts of 20%, 10% and 5% were given on the marked price per unit in January, February and March, respectively, while no discounts were given in April. If the total profit from January to April was Rs. 138825, then the marked price per unit, in rupees, was

  • \(525\)
  • \(510\)
  • \(520\)
  • \(515\)
  View Solution

  ---

• 4.

  The ratio of the number of students in the morning shift and afternoon shift of a school was $13 : 9$. After 21 students moved from the morning shift to the afternoon shift, this ratio became $19 : 14$. Next, some new students joined the morning and afternoon shifts in the ratio $3 : 8$ and then the ratio of the number of students in the morning shift and the afternoon shift became $5 : 4$. The number of new students who joined is:

  • \(88\)
  • \(12\)
  • \(11\)
  • \(99\)
  View Solution

  ---

• 5.

  Let $3 \leq x \leq 6$ and $[x^2] = [x]^2$, where $[x]$ is the greatest integer not exceeding $x$. If set $S$ represents all feasible values of $x$, then which of the following is a possible subset of $S$?

  • \((3, \sqrt{10}) \cup [5, \sqrt{26}) \cup \{6\}\)
  • \((4, \sqrt{10}) \cup [5, \sqrt{27}) \cup \{6\}\)
  • \([3, \sqrt{10}] \cup [5, \sqrt{26}]\)
  • \([3, \sqrt{10}] \cup [4, \sqrt{17}] \cup \{6\}\)
  View Solution