List of top Quantitative Aptitude Questions

What is the value of $2^{100} \mod 5$? 
 

When asked for his taxi number, the driver replied, “If you divide the number of my taxi by 2, 3, 4, 5, 6 each time you will find a remainder of one. But if you divide it by 11, the remainder is zero.” What is the taxi number?
A car \( A \) starts from a point \( P \) towards another point \( Q \). Another car \( B \) starts (also from \( P \)) 1 hour after the first car \( A \), and overtakes it after covering 30% of the distance \( PQ \). After that, the cars continue. On reaching \( Q \), car \( B \) reverses and meets car \( A \), after covering \( 2\frac{1}{3} \) of the distance \( QP \). Find the time taken by car \( B \) to cover the distance \( PQ \) (in hours).

At a college football game, $\tfrac{4}{5}$ of the lower-deck seats were sold. The lower deck contains $\tfrac{1}{4}$ of all stadium seats. Overall, $\tfrac{2}{3}$ of all stadium seats were sold. What fraction of the unsold seats in the stadium lay in the lower deck?

A vessel has a milk solution in which milk and water are in the ratio 4:1. By addition of water to it, milk solution with milk and water in the ratio 4:3 was formed. On replacing 14 L of this solution with pure milk, the ratio of milk and water changed to 5:3. What is the volume of the water added?
A leak was found in a ship when it was 77 km from the shore. The leak admits 2.25 tonnes of water in 5.5 minutes. 92 tonnes will suffice to sink the ship. The pumps can throw out water at 12 tonnes per hour. Find the average rate of sailing at which the ship may reach the shore as it begins to sink.

What is the remainder when $7^{100}$ is divided by 8? 
 

What is the sum of the series $1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \ldots$? 
 

A milkman buys milk contained in $10$ vessels of equal size. If he sells his milk at ₹ 5 per litre, he loses ₹ 200; if he sells it at ₹ 6 per litre, he would gain ₹ 150 on the whole. Find the number of litres contained in each vessel.
In the figure below, \( \angle MON = \angle MPO = \angle NQO = 90^\circ \), \( OQ \) is the bisector of \( \angle MON \), and \( QN = 10 \), \( OR = 40/\sqrt{7} \). Find \( OP \).

A man invests Rs. 5000 at 6% simple interest per annum. How much interest will he earn in 3 years? 
 

The side of an equilateral triangle is 10 cm long. By drawing parallels to all its sides, the distance between any two parallel lines being the same, the triangle is divided into smaller equilateral triangles, each of which has sides of length 1 cm. How many such small triangles are formed?

What is the value of $\sqrt{50 + \sqrt{50 + \sqrt{50 + \ldots}}}$? 
 

If \( \log_x(a - b) - \log_x(a + b) = \log_x\left(\frac{b}{a}\right) \), find \( \frac{a^2 + b^2}{b^2 + a^2} \)

What is the sum of digits of $2^{10}$? 
 

Train A running at $60$ km/h leaves Mumbai for Delhi at $6$ p.m. Train B running at $90$ km/h also leaves for Delhi at $9$ p.m. Train C leaves Delhi for Mumbai at $9$ p.m. If all three trains meet at the same time between Mumbai and Delhi (distance $=1260$ km), find the speed of Train C.
An aeroplane first flew with a speed of $440$ km/h and covered some distance. It still had to cover $770$ km less than what it had already covered, and it flew this remainder at $660$ km/h. The average speed for the entire flight was $500$ km/h. Find the total distance.

What is the probability that a leap year has 53 Sundays? 
 

\( A, B, C \) can independently do a work in 15, 20, and 30 days respectively. They work together for some time after which \( C \) leaves. A total of ₹18000 is paid for the work and \( B \) gets ₹6000 more than \( C \). For how many days did \( A \) work?

A number when divided by 7 leaves a remainder of 4. What is the remainder when its square is divided by 7? 
 

A man buys a certain quantity of apples, mangoes and bananas. If the mangoes were to cost the same as apples, he would have to forego the bananas to buy the same number of mangoes as he had bought earlier (for the same total amount). The amount spent by him on mangoes and bananas together is 50% more than the amount spent on apples. The total amount spent is ₹ 140. The number of mangoes bought is the same as the number of bananas. If he wishes to buy the same number of apples as well, how much additional amount would he have to spend?

A solid sphere of radius 12 inches is melted and cast into a right circular cone whose base diameter is \( \sqrt{2} \) times its slant height. If the radius of the sphere and the cone are the same, how many such cones can be made and how much material is left out?

A bag contains 4 red and 5 blue balls. Two balls are drawn without replacement. What is the probability that both are red? 
 

Rahul starts a business with ₹ 8000. After $6$ months, Sanjay joins with some capital. If their profits after one year are equal, find Sanjay's investment.

In a seating arrangement, 5 people (A, B, C, D, E) sit in a row. A and B must sit together, and C cannot sit at the ends. How many arrangements are possible?