Full Quant CAT 2025 Slot 2 Question Paper PDF with Detailed Solutions

Breakup G strategy | Ratios + Table | Medium

The ratio of expenditures of Lakshmi and Meenakshi is 2 : 3, and the ratio of income of Lakshmi to expenditure of Meenakshi is 6 : 7. If excess of income over expenditure is saved by Lakshmi and Meenakshi, and the ratio of their savings is 4 : 9, then the ratio of their incomes is

Visual Lens G Strategy 1.2/0.8 | Profit Loss | Easy

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, as a percentage, at which the profit percentage would be equal to the rate of discount, is nearest to

Visual Lens G strategy | 1.2 / 0.8 Percentages | Moderate

A loan of Rs 1000 is fully repaid by two instalments of Rs 530 and Rs 594, paid at the end of first and second year, respectively. If the interest is compounded annually, then the rate of interest, in percentage, is _____

Breakup G Strategy | Concepts of Time Speed Distance | Easy

Rita and Sneha can row a boat at 5 km/h and 6 km/h in still water, respectively. In a river flowing with a constant velocity, Sneha takes 48 minutes more to row 14 km upstream than to row the same distance downstream. If Rita starts from a certain location in the river, and returns downstream to the same location, taking a total of 100 minutes, then the total distance, in km, Rita will cover is ______

Breakup G Strategy | Mixtures + Equations | Moderate

A mixture of coffee and cocoa, 16% of which is coffee, costs Rs 240 per kg. Another mixture of coffee and cocoa, of which 36% is coffee, costs Rs 320 per kg. If a new mixture of coffee and cocoa costs Rs 376 per kg, then the quantity, in kg, of coffee in 10 kg of this new mixture is

Breakup G strategy | Averages + Linear Equation | Easy

The average number of copies of a book sold per day by a shopkeeper is 60 in the initial seven days and 63 in the initial eight days, after the book launch. On the ninth day, she sells 11 copies less than the eighth day, and the average number of copies sold per day from second day to ninth day becomes 66. The number of copies sold on the first day of the book launch is ____

LCM G Strategy | Time & Work | Moderate

Ankita is twice as efficient as Bipin, while Bipin is twice as efficient as Chandan. All three of them start together on a job, and Bipin leaves the job after 20 days. If the job got completed in 60 days, the number of days needed by Chandan to complete the job alone is

Concept of Quadratic Equations | Hard

The equations 3x² − 5x + p = 0 and 2x² − 2x + q = 0 have one common root. The sum of the other roots of these two equations is

Concepts of Polynomial Equations + Quadratic | Hard

If 9^{x² + 2x – 3} − 4(3^{x² + 2x − 2}) + 27 = 0, then the product of all possible values of x is _____

Vedic Patterns G Strategy | Quadratic Equations | Hard

If m and n are integers such that (m + 2n)(2m + n) = 27, then the maximum possible value of 2m − 3n is ___

X maro G Strategy | Inequality | Easy

The set of all real values of x for which (x² − |x + 9| + x) > 0, is

Maxima Minima G Strategy | Easy

If a, b, c and d are integers such that their sum is 46, then the minimum possible value of (a − b)² + (a − c)² + (a − d)² is ______

Concept of Factors | Hard

The number of divisors of 2⁶ × 3⁵ × 5³ × 7², which are of the form (3r + 1), where r is a non-negative integer, is

Vedic Patterns G Strategy | Moderate

Suppose a, b, c are three distinct natural numbers, such that 3ac = 8(a + b). Then, the smallest possible value of 3a + 2b + c is _______

Visual Lens G Strategy | Hexagon Area | Moderate

Let ABCDEF be a regular hexagon and P and Q be the midpoints of AB and CD, respectively. Then, the ratio of the areas of trapezium PBCQ and hexagon ABCDEF is _______

Visual Lens G Strategy | Triangle

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

Concept of Angles of Circles | Moderate

Two tangents drawn from a point P touch a circle with center O at points Q and R. Points A and B lie on PQ and PR, respectively, such that AB is also a tangent drawn to the same circle. If ∠AOB = 50°, then ∠APB is _____

Concepts of Indices | Moderate

The sum of digits of the number (625)⁶⁵ × (128)³⁶ is ______

Concepts of Logs + Maxima Minima | Hard

If log₆₄(x²) + log₈(√y) + 3 log₅₁₂( √(y)z) = 4, where x, y and z are positive real numbers, then the minimum possible value of (x + y + z) is

Concepts of AP GP + Quadratic Equations | Hard

Let a_n be the nth term of a decreasing infinite geometric progression. If a₁ + a₂ + a₃ = 52 and a₁a₂ + a₂a₃ + a₃a₁ = 624, then the sum of this geometric progression is