CAT 2026 Slot 1 Quant Analysis: Expected Paper, Questions & Solutions

A and B are two regular polygons with $a$ and $b$ sides respectively. The interior angle of polygon B is $\tfrac{4}{3}$ times the interior angle of polygon A. If $b = 3a$, what is each interior angle of a polygon with $a + 3b$ sides?

In triangle ABC, $AB = 12$ cm, $AC = 15$ cm and $BC = 18$ cm. Find the length of the median AD (in cm).

Three sides of a quadrilateral are 3 cm, 2 cm and 6 cm, and the fourth side is an integer. How many lengths are possible for the fourth side?

For positive integers $a$, $b$ and $c$, if $ab + bc = 13$ and $bc + ca = 45$, what is the minimum possible value of $abc$?

The number of divisors of $2^4 \times 3^5 \times 5^3 \times 7^2$ that are of the form $4r + 1$, where $r$ is a non-negative integer, is:

For a 4-digit number greater than 1000, the sum of the thousands, hundreds and tens digits is 13, and the sum of the hundreds, tens and units digits is 15. The tens digit is 4 more than the units digit. What is the difference between the largest and smallest possible values of the number?

In a student council election, five candidates contested for a single position. 75% of the students enrolled in the institution voted. One candidate secured 20% of the votes polled, while the votes obtained by the remaining four candidates were in the ratio $2:3:4:6$. The candidate with the highest votes got 120 votes more than the candidate with the second-highest votes. What is the total number of students enrolled in the institution?

In a school, 56% of the students are boys and 32% of all students secured first class. If 25% of the boys secured first class and 162 girls secured first class, find the total number of students in the school.

The average of three distinct real numbers is 50. If the smallest number is increased by 16 and the largest is reduced by 7, the order of the numbers stays the same, the new arithmetic mean becomes 9 more than the middle number, and the difference between the smallest and largest numbers becomes 55. What is the largest number in the original set?

Shubham invests ₹5000 in a bank at a certain rate of interest, compounded annually. The ratio of the investment's value after 2 years to its value after 4 years is $25 : 49$. What is the minimum number of years for the value to exceed ₹25000?

Volga, a famous pastry parlour in Hamirpur, sells three varieties of pastry: Chocolate, Vanilla and Mix Fruit. Their demand in January was in the ratio $13 : 16 : 21$. In February the demand rose by 100%, 50% and $33\tfrac{1}{3}\%$ respectively. In March, demand for both Chocolate and Mix Fruit rose by 25%, while Vanilla's demand became equal to the mean of the three varieties. Find the percentage increase in Vanilla's demand from February to March.

Sarah buys two qualities of pomegranate, A and B, for ₹4450. The weights (in kg) of A and B are in the ratio $3 : 5$, and the cost per kg of A is 30% more than that of B. She sells A at a 12% profit and B at an 18% profit. What is Sarah's overall profit?

Let $f(x) = x^2 + ax + b$ and $g(x) = f(x + 1) - f(x - 1)$. If $f(x) \ge 0$ for all real $x$ and $g(15) = 48$, then the smallest possible value of $b$ is:

Find $n$ if $7^{3n-1} - 343^{\,n-1} = 2352$.

Let $c$ and $k$ be positive integers such that $c^2 + ck + c = 40$ and $3k^2 + ck + k = 100$. What is the value of $\dfrac{c + 2k}{2}$?

A donation box can receive only cheques of ₹100, ₹250 and ₹1000. On the last day of the month, the box contained exactly 90 cheques totalling ₹42600. If the number of ₹1000 cheques was the maximum possible, what is the sum of the numbers of ₹100 and ₹250 cheques?

A rectangular tank has two inlet pipes (A and B) and one outlet pipe C. Pipe A fills the tank twice as fast as pipe B, and pipe B fills the tank three times as fast as pipe C empties it. Anuj opens pipes A and B in the 1st hour, pipes B and C in the 2nd hour, and pipes A and C in the 3rd hour. He repeats this 3-hour cycle for 9 hours, after which he opens only the two inlet pipes (A and B), and the remaining part of the tank fills in 5 hours. What fraction of the tank's total capacity is filled by pipe A alone?

A flight was scheduled to depart at 10:00 AM and travel 6300 km. Due to maintenance, departure was delayed until 1:00 PM. To make up time, the pilot increased the average speed by 200 km/h over the original plan, which limited the delay at the destination to just 1 hour. If instead the pilot had increased the speed by a further 100 km/h, at what time would the flight have arrived?

Two trains running in opposite directions on parallel tracks cross each other in 12 seconds. The faster train is 180 m long and crosses a lamp post in 9 seconds. If the slower train's speed is 8 km/h less than the faster train's, what is the length of the slower train, in metres (closest integer)?

The number of common terms in the two sequences $18, 24, 30, 36, \ldots, 606$ and $14, 24, 34, 44, \ldots, 604$ is:

If $z$ is a negative number such that $2^{\,z^2 \log_5 7} = 7^{\log_2 5}$, then $z$ equals:

How many integers $n$ satisfy $(n - 3)(n - 6) - 3(n - 3) \le 0$?