CAT 2026 · Slot 3 · Expected paper

CAT 2026 Slot 3 Quant Analysis: Expected Paper, Questions & Solutions

22 questions
13 MCQ
9 TITA
66 marks
10 medium
12 easy

Quant is split into 5 parts: Arithmetic (6), Algebra (10), Geo Mensu (3), TS&W (2), Modern Maths (1). Open a part for every question with options, answers and solutions, or a single question on its own page.

Arithmetic Questions

Q1
A vendor has 374 fruits in total, made up of apples, mangoes and oranges. Apples and mangoes are present in the ratio 5:2. She sells 150 apples, 52 mangoes and half of the oranges. The numbers of unsold apples and unsold oranges are then in the ratio 3:2. Find the total number of fruits remaining unsold.
Q6
In one month, the earnings of Ravi, Sunil and Manoj are in the ratio 8:6:5. They contribute 15%, 12% and 18% of their respective earnings towards the total house rent. In the following month, the rent remains unchanged, while their earnings increase by 10%, 12% and 15%, respectively. What percentage of their combined earnings is spent on rent in the following month? Give the answer to the nearest 0.1%.
Q9
Four numbers are such that the mean of the first two exceeds the first number by 1; the mean of the first three exceeds the mean of the first two by 2; and the mean of all four exceeds the mean of the first three by 3. Find the difference between the largest and the smallest of the four numbers.
Q11
A sum of Rs 10,000 is deposited in Bank P for some number of years at 5% simple interest per annum. On maturity, the entire amount is transferred to Bank Q for a further 5 years at 6% simple interest per annum. If the interest earned in Bank P and Bank Q are in the ratio 10:13, for how many years was the money deposited in Bank P?
Q17
A container is full of milk. One-third of its contents is removed and replaced with water. The contents are mixed thoroughly before each removal. The same operation is repeated three more times. Find the final ratio of milk to water.
Q19
An item is sold at a price that gives a 40% profit. If its cost had been 40% lower and it had been sold for Rs 5 less than the original selling price, the profit would have been 50%. Find the original selling price.

All 6 Arithmetic questions with solutions →

Algebra Questions

Q2
If x is positive and x^2+1/x^2=23, find x^7+1/x^7.
Q5
Solve log base (x-4) of (x^2-16) = log base (x-4) of (x+2) + 2. Find the sum of all valid values of x.
Q8
If 6^(4x) × 9^(3x+6) × 25^y = 27^(2z) × 10^(4x) × 125^(x-2), where x, y and z are natural numbers, find the minimum possible value of x+y+z.
Q10
Let f(x)=(x^2+5x)(x^2+5x+4). Solve √(f(x)+4)=2501 and find the sum of all real roots.
Q13
Three natural numbers p, q and r add up to 1000. The number r is a perfect square between 200 and 600, and p is at least 25% of q but at most 75% of q. Find the sum of the maximum and minimum possible values of p.
Q14
For real x, find the range of f(x)=(x-1)/(x^2+2x-2).
Q16
Let n be the least positive integer such that 180 is a factor of 270^n. If m is the least positive integer such that 270^n is a factor of 180^m, find m+n.
Q18
The number of integer solutions of 3 x (x^2+2)=7x^2 is ______.
Q21
A trader sells grain to three buyers. To the first buyer, the trader gives half the stock plus an extra 3 kg. To the second buyer, the trader gives half of the remaining stock plus an extra 3 kg. To the third buyer, the trader again gives half of the remaining stock plus an extra 3 kg, after which no grain is left. Find the initial quantity of grain.
Q22
An arithmetic progression has the property that the 3rd, 6th and 9th terms add up to 84, while the sum of its first 12 terms is 402. Find the sum of its first 4 terms.

All 10 Algebra questions with solutions →

Geo Mensu Questions

Q3
Let C be the circle x^2+y^2+4x−4y−8=0, and let L be the locus of the intersection point of a pair of tangents to C when the angle between the tangents is 60°. At which point does L touch the line x=6?
Q7
A quadrilateral ABCD is inscribed in a circle such that AB:CD=3:2 and BC:AD=4:3. If diagonals AC and BD intersect at E, find AE:CE.
Q12
In right-angled triangle ABC, AB=6 cm and BC=8 cm, with AB perpendicular to BC. Points P and Q lie on BC, and the areas of triangles ABP, ABQ and ABC are in arithmetic progression. If the area of triangle ABC is 1.5 times the area of triangle ABP, find PQ in cm.

All 3 Geo Mensu questions with solutions →

TS&W Questions

Q4
Pooja alone would need 12 days at 5 hours a day to finish a piece of work, while Nisha alone would need 10 days at 6 hours a day to finish the same work. They both contribute to completing the same piece of work, at constant hourly rates. Nisha puts in twice as many hours per day as Pooja, while Pooja works twice as many days as Nisha. If Pooja works 3 hours a day, how many days does Nisha work?
Q15
Towns P and Q are 45 km apart on a straight road. Vikram starts from P towards Q, while Deepak starts from Q towards P, at the same time. They meet after 1 hour 30 minutes. Vikram reaches Q exactly 1 hour 15 minutes after Deepak reaches P. Find Vikram's speed in km/h.

All 2 TS&W questions with solutions →

Modern Maths Questions

Q20
How many positive integers up to and including 1000 have no repeated digits?

All 1 Modern Maths question with solutions →

An expected paper by Cetking, not the actual CAT paper. CAT is conducted by the IIMs.