List of top Quantitative Aptitude Questions

\( 10^{68} \) is divided by 13, the remainder is  is
In the $XY$-plane, the area, in sq. units, of the region defined by the inequalities $y \ge x + 4$ and $-4 \le x^2 + y^2 + 4(x - y) \le 0$ 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
Three circles of equal radii touch (but not cross) each other externally. Two other circles, X and Y, are drawn such that both touch (but not cross) each of the three previous circles. If the radius of X is more than that of Y, the ratio of the radii of X and Y 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 shopkeeper sells half of the grains plus \(3 \, \text{kg}\) of grains to Customer 1, and then sells another half of the remaining grains plus \(3 \, \text{kg}\) to Customer 2. When the 3rd customer arrives, there are no grains left. Find the total grains that were initially present.

When $10^{100}$ is divided by 7, the remainder is ?

There are 3 chess players in the 1st year, 4 chess players in the 2nd year, and 5 chess players in the 3rd year of college. What is the probability of selecting a team of 4 chess players if at least one player is from the 1st year?
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 train travelled a certain distance at a uniform speed. Had the speed been 6 km per hour more, it would have needed 4 hours less. Had the speed been 6 km per hour less,it would have needed 6 hours more. The distance, in km, travelled by the train is
The sum of the infinite series \( \frac{1}{5} \left( \frac{1}{5} - \frac{1}{7} \right) + \left( \frac{1}{5} \right)^2 \left( \frac{1}{5} - \frac{1}{7} \right)^2 - \left( \frac{1}{7} \right)^2 + \left( \frac{1}{5} \right)^3 \left( \frac{1}{5} - \frac{1}{7} \right)^3 + \dots \) is equal to
Consider the sequence\( t_1 = 1, t_2 = -1 and  t_n = \left( \frac{n-3}{n-1} \right) t_{n-2} for n \ge 3. \)Then, the value of the sum  \(\frac{1}{t_2}\) + \(\frac{1}{t_4}\) + \(\frac{1}{t_6}\) + ……. + \(\frac{1}{t_{2022}}\) + \(\frac{1}{t_{2024}}\), is
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
For some constant real numbers p, k and a, consider the following system of linear equations in  x  and  y: 
px - 4y = 2 
3x + ky = a 
A necessary condition for the system to have no solution for  (x, y), 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
Solve for x: \(3x - 7 = 2x + 5\).
If \(2x + 3y = 12\) and \(x = 3\), what is the value of y?
If \(\alpha\) and \(\beta\) are the roots of \(x^2 - 5x + 6 = 0\), what is the value of \(\alpha^2 + \beta^2\)?
20 litres of a 20% alcohol solution is mixed with 30 litres of a 30% alcohol solution. What is the alcohol concentration of the final mixture?
If \(x + \dfrac{1}{x} = 4\), then what is the value of \(x^2 + \dfrac{1}{x^2}\)?
A 40-litre mixture contains milk and water in the ratio 3 : 1. How many litres of water must be added to make the ratio 1 : 1?
In what ratio must rice costing Rs 30 per kg be mixed with rice costing Rs 40 per kg so that the mixture costs Rs 34 per kg?
How many 3-digit numbers can be formed using the digits 1, 2, 3, 4, 5 without repeating any digit?
A man travels from town P to town Q at 30 km/h and returns along the same road at 60 km/h. What is his average speed for the whole journey?