List of top Quantitative Aptitude Questions asked in CAT

An item is sold with a profit of \(40\%\). If the cost price is reduced by \(40\%\) and Rs. \(5\) are also reduced from it, then the profit will be increased to \(50\%\). Find the final cost price.

A bus leaves the bus stand at 9 am and travels at a constant speed of 60 km/h. It reaches its destination 3.5 hours later than its original time. The next day, it travels \( \frac{2}{3} \) of its route within \( \frac{1}{3} \) of its initial time and travels the rest of the route within 40 minutes. At what time does it reach its destination normally?

Two places A and B are 45 kms apart and connected by a straight road. Anil goes from A to B while Sunil goes from B to A. Starting at the same time, they cross each other in exactly 1 hour 30 minutes. If Anil reaches B exactly 1 hour 15 minutes after Sunil reaches A, the speed of Anil, in km per hour, is

When Rajesh's age was same as the present age of Garima, the ratio of their ages was 3 : 2. When Garima's age becomes the same as the present age of Rajesh, the ratio of the ages of Rajesh and Garima will become

\( 10^{68} \) is divided by 13, the remainder is  is

Consider two sets A = {2, 3, 5, 7, 11, 13} and B = {1, 8, 27}. Let f be a function from A to B such that for every element b in B, there is at least one element a in A such that f(a) = b. Then, the total number of such functions f is

For any non-zero real number x, let\( f(x) + 2f\left(\frac{1}{x}\right) = 3x.\)Then, the sum of all possible values of x  for which f(x) = 3, is

Anil invests Rs 22000 for 6 years in a scheme with 4% interest per annum, compounded half-yearly. Separately, Sunil invests a certain amount in the same scheme for 5 years, and then reinvests the entire amount he receives 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 equal, then the initial investment, in rupees, made by Sunil is

A container has a mixture of acid and water. If 2 liters of water are added, the acid content reaches 50%. After adding 18 liters of acid, the acid content increases to 80%. What was the initial acid to water ratio in the container?

A glass is filled with milk. Two-thirds of its content is poured out and replaced with water. If this process of pouring out two-thirds the content and replacing with water is repeated three more times, then the final ratio of milk to water in the glass, is

A vessel contained a certain amount of a solution of acid and water. When 2 litres of water was added to it, the new solution had 50% acid concentration. When 15 litres of acid was further added to this new solution, the final solution had 80% acid concentration. The ratio of water and acid in the original solution was

If \( x \) and \( y \) satisfy the equations
\(|x| + x + y = 15 \quad \text{(1)},\)
\(x + |y| - y = 20 \quad \text{(2)}.\)
Find the value of \( x - y \).

\(\sqrt{x + 6\sqrt{2}} - \sqrt{x - 6\sqrt{2}} = 2\sqrt{2}.\)
Find \( x \).

\(3^{3333}\) divided by 11, then the remainder would be?

The number of all positive integers up to 500 with non-repeating digits is

One direct question from the Number System was 10 to the power 100 divided by seven, candidates had to choose the correct answer for the problem.

For any natural Number 'n', let a_n be the largest number not exceeding \(\sqrt{n}\) , then a1 + a2 + a3... +a50 =

A company has 40 employees whose names are listed in a certain order. In the year 2022, the average bonus of the first 30 employees was Rs. 40000, of the last 30 employees was Rs. 60000, and of the first 10 and last 10 employees together was Rs. 50000. Next year, the average bonus of the first 10 employees increased by 100%, of the last 10 employees increased by 200% and of the remaining employees was unchanged. Then, the average bonus, in rupees, of all the 40 employees together in the year 2023 was

A fruit seller has a total of 187 fruits consisting of apples, mangoes and oranges. The number of apples and mangoes are in the ratio 5 : 2. After she sells 75 apples, 26 mangoes and half of the oranges, the ratio of number of unsold apples to number of unsold oranges becomes 3 : 2. The total number of unsold fruits is

When 3³³³ is divided by 11, the remainder is

Amal and Vimal together can complete a task in 150 days, while Vimal and Sunil together can complete the same task in 100 days. Amal starts working on the task and works for 75 days, then Vimal takes over and works for 135 days. Finally, Sunil takes over and completes the remaining task in 45 days. If Amal had started the task alone and worked on all days, Vimal had worked on every second day, and Sunil had worked on every third day, then the number of days required to complete the task would have been

The coordinates of the three vertices of a triangle are: (1, 2), (7, 2), and (1, 10). Then the radius of the incircle of the triangle is

The roots \(\alpha\), \(\beta\) of the equation \(3x^2 + \lambda x - 1 = 0\), satisfy \( \frac{1}{\alpha^2} + \frac{1}{\beta^2} = 15 \). The value of \( (\alpha^3 + \beta^3)^2 \) is

Aman invests Rs 4000 in a bank at a certain rate of interest, compounded annually.If the ratio of the value of the investment after 3 years to the value of the investment after 5 years is 25 : 36, then the minimum number of years required for the value of the investment to exceed Rs 20000 is

A glass is initially filled entirely with milk. In each step, \(\frac{2}{3}\) of the milk is replaced with water. This process is repeated 3 times. What is the final ratio of water to milk in the glass?