CAT 2025 Question Paper with Answer Key -Check Detailed Solutions and Analysis

CAT 2025 Questions

• 1.

  In a $\triangle ABC$, points $D$ and $E$ are on the sides $BC$ and $AC$, respectively. $BE$ and $AD$ intersect at point $T$ such that $AD : AT = 4 : 3$, and $BE : BT = 5 : 4$. Point $F$ lies on $AC$ such that $DF$ is parallel to $BE$. Then, $BD : CD$ is:

  • \(15 : 4\)
  • \(11 : 4\)
  • \(9 : 4\)
  • \(7 : 4\)
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• 2.

  In the sequence 1, 3, 5, 7, ..., k, ..., 57, the sum of the numbers up to k, excluding k, is equal to the sum of the numbers from k up to 57, also excluding k. What is k?
  

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• 3.

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

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• 4.

  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:

  • \(12\)
  • \(13\)
  • \(14\)
  • \(15\)
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• 5.

  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

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