Quantitative Aptitude PYQs

Given below are two statements marked as Assertion (A) and Reason (R). Read and mark the correct options:

Assertion (A): The product of any two consecutive natural numbers is always even.

Reason (R): If n is any natural number, then either n or n+1 must be divisible by 2, ensuring the product is even.

Which set of numbers includes all others?

The ratio of savings of two individuals is 6 : 5. If one increases his savings by 15% and the other by 10%, find their new savings ratio.

In a workshop, the ratio of skilled to unskilled workers was 5 : 4. After a hiring drive, the number of skilled workers increased by 10%, while the number of unskilled workers increased by 25%. What is the new ratio of skilled to unskilled workers?

A student scores 25% more marks in Science than in Math. If he scores 240 marks in Science, how many marks did he score in Math?

Let x and y be angles such that \( \sin(x + y) = 0 \) and \( \cos(x - y) = 1 \). What is the value of the expression: \( (\cos x + \cos y)^2 + (\sin x - \sin y)^2 \)?

A company undertakes a project to be completed in 40 days with 80 workers. After 10 days, due to a shortage, only 60 workers remain. How many additional workers must be hired after 20 more days to complete the project on time?

The time taken for a train to pass a pole is 18 seconds, while it takes 33 seconds to cross a bridge measuring 300 meters. Calculate the length of the train.

Two equal sums are lent at 6% and 9% simple interest per annum respectively. The interest received on both sums after 4 years differs by ₹150. Find each sum.

If tanθ + cotθ = k, then tan²θ + cot²θ is equal to:

The angle of elevation of the top of a tower from a point 60 m away from its base is 45°. Find the height of the tower.

The value of \(\sqrt{(5 + 2\sqrt{6})}\) is:

Find the coordinates of the point where the line 2x + 3y = 6 intersects the y-axis.

If x - 1/x = 3, then the value of x² + 1/x² is:

The expression (x + y + z)² - (x² + y² + z²) is equal to:

The average of 6 numbers is 45. The average of the first four numbers is 40, and the fifth number is 50. What is the sixth number?

Two vertical poles have heights of 6 meters and 11 meters vertically on a plane ground. If the distance between their feet is 12 m, the distance between their tops is:

36 men can complete a work in 36 days. They started working together. But 6 men kept on leaving the job every 7^th day. In how many days will the work be completed?

A car travels from A to B at 80 km/h and returns at 60 km/h. Find the approx. average speed of the car.

Six cubes, each with an edge 4.5 cm are joined end to end. Find the total surface area of the resulting cuboid.