List of top Questions asked in CAT- 2023

The number of positive integers less than 50, having exactly two distinct factors other than 1 and itself, is

Anil mixes cocoa with sugar in the ratio 3: 2 to prepare mixture A , and coffee with sugar in the ratio 7: 3 to prepare mixture B . He combines mixtures A and B in the ratio 2: 3 to make a new mixture C . If he mixes C with an equal amount of milk to make a drink, then the percentage of sugar in this drink will be

A lab experiment measures the number of organisms at 8 am every day. Starting with 2 organisms on the first day, the number of organisms on any day is equal to 3 more than twice the number on the previous day. If the number of organisms on the nth day exceeds one million, then the lowest possible value of n is

Let both the series \(a_1,a_2,a_3,....\) and \(b_1,b_2,b_3,....\) be in arithmetic progression such that the common differences of both the series are prime numbers. If \(a_5=b_9,a_{19}=b_{19}\) and \(b_2=0\) , then \(a_{11}\) equals

Let \(a_n=46+8n\) and \(b_n=98+4n\) be two sequences for natural numbers \(n ≤ 100\) . Then, the sum of all terms common to both the sequences is

In a rectangle ABCD, AB = 9 cm and BC = 6 cm. P and Q are two points on BC such that the areas of the figures ABP, APQ, and AQCD are in geometric progression. If the area of the figure AQCD is four times the area of triangle ABP, then BP : PQ : QC is

The sum of the first two natural numbers, each having 15 factors (including 1 and the number itself), is

Arvind travels from town A to town B, and Surbhi from town B to town A, both starting at the same time along the same route. After meeting each other, Arvind takes 6 hours to reach town B while Surbhi takes 24 hours to reach town A. If Arvind travelled at a speed of 54 km/h, then the distance, in km, between town A and town B is [This question was asked as TITA]

Anil invests Rs. 22000 for 6 years in a certain scheme with 4% interest per annum, compounded half-yearly. Sunil invests in the same scheme for 5 years, and then reinvests the entire amount received at the end of 5 years for one year at 10% simple interest. If the amounts received by both at the end of 6 years are same, then the initial investment made by Sunil, in rupees, is

The number of coins collected per week by two coin-collectors A and B are in the ratio 3 : 4. If the total number of coins collected by A in 5 weeks is a multiple of 7, and the total number of coins collected by B in 3 weeks is a multiple of 24, then the minimum possible number of coins collected by A in one week is

Any non-zero real numbers \(x, y\) such that \(y ≠ 3\) and \(\frac{x}{y}<\frac{x+3}{y-3}\), will satisfy the condition

Let \(a, b, m\) and \(n\) be natural numbers such that \(a >1\) and \(b >1\) . If \(a^m+b^n = 144^{145}\) , then the largest possible value of \(n − m\) is

Minu purchases a pair of sunglasses at Rs.1000 and sells to Kanu at 20% profit. Then, Kanu sells it back to Minu at 20% loss. Finally, Minu sells the same pair of sunglasses to Tanu. If the total profit made by Minu from all her transactions is Rs.500, then the percentage of profit made by Minu when she sold the pair of sunglasses to Tanu is

In a company, 20% of the employees work in the manufacturing department. If the total salary obtained by all the manufacturing employees is one-sixth of the total salary obtained by all the employees in the company, then the ratio of the average salary obtained by the manufacturing employees to the average salary obtained by the non-manufacturing employees is

Let C be the circle \(x^2+y^2+4x-6y-3=0\) and \(L\) be the locus of the point of intersection of a pair of tangents to \(C\) with the angle between the two tangents equal to \(60º\) . Then, the point at which \(L\) touches the line \(x = 6\) is

A boat takes 2 hours to travel downstream a river from port A to port B, and 3 hours to return to port A. Another boat takes a total of 6 hours to travel from port B to port A and return to port B . If the speeds of the boats and the river are constant, then the time, in hours, taken by the slower boat to travel from port A to port B is

In a right-angled triangle Δ ABC , the altitude AB is 5 cm , and the base BC is 12 cm . P and Q are two points on BC such that the areas of ΔABP, ΔABQ , and Δ ABC are in arithmetic progression. If the area of Δ ABC is 1.5 times the area of Δ ABP , the length of PQ , in cm , is

Geeta sells A \(→\) 20% (Profit) and B \(→\) 10% (Loss) at the same sp. If she increases SP such that A and B still sold at an equal price and profit of 10% made on B, then profit made on A will be?

The number of all natural numbers up to 1000 with non-repeating digits is

If a certain amount of money is divided equally among n persons, each one receives Rs 352 . However, if two persons receive Rs 506 each and the remaining amount is divided equally among the other persons, each of them receive less than or equal to Rs 330 . Then, the maximum possible value of n is

Ravi is driving at a speed of 40 km/h on a road. Vijay is 54 meters behind Ravi and driving in the same direction as Ravi. Ashok is driving along the same road from the opposite direction at a speed of 50 km/h and is 225 meters away from Ravi. The speed, in km/h, at which Vijay should drive so that all the three cross each other at the same time, is

Let \(n\) be the least positive integer such that \(168\) is a factor of \(1134^n\) . If \(m\) is the least positive integer such that \(1134^n\) is a factor of \(168^m\) , then \(m+ n \) equals

A triangle is drawn with its vertices on the circle C such that one of its sides is a diameter of C and the other two sides have their lengths in the ratio a:b. If the radius of the circle is r, then the area of the triangle is

The equation \(x^3+(2r+1)x^2+(4r-1)x+2=0\) has -2 as one of the roots. If the other two roots are real, then the minimum possible non-negative integer value of \(r\) is

A quadratic equation \(x^2+bx+c=0\) has two real roots. If the difference between the reciprocals of the roots is \(\frac{1}{3}\) , and the sum of the reciprocals of the squares of the roots is \(\frac{5}{9}\) , then the largest possible value of \((b+c)\) is