Quantitative Aptitude PYQs

What is the smallest number that, when divided by 2, 3, 4, 5, 6, and 7 leaves remainder 1?

Find the value of \( 0.1 + 0.11 + 0.111 \)

If \( 2x + 3y = 50 \) and \( x, y \in N \), then what is the value of \( x \) for which \( y \) is minimum?

A milkman mixes water in pure blends milk and offers the mixture for sale at the original cost price of milk. If he mixes 0.75 liters of water in every 5.25 liters of milk and sells the entire mixture at the price of pure milk, what is his profit percentage?

Rs. \( x \) is invested at 14% simple interest and Rs. \( 2x \) at 7% compound interest per annum for 2 years. If the difference between the CI and SI is ₹392, what is the value of \( x \)?

The average marks of 30 students are 72. The top 5 students scored an average of 86 marks, while the last 5 students averaged 54.

What is the average of the remaining 20 students?

There are four consecutive odd numbers, denoted as \( x_1, x_2, x_3, \) and \( x_4, \) and three consecutive even numbers, represented by \( y_1, y_2, \) and \( y_3. \) The average of the odd numbers is six less than the average of the even numbers. Additionally, the total of the three even numbers is 16 less than the total of the four odd numbers. What is the average of \( x_1, x_2, x_3, \) and \( x_4 \)?

Mr. A invested ₹15,500 in stocks and ₹20,500 in mutual funds. If the uninvested amount is 40% of his total savings, what was his total savings?

The table below displays the student's scores from their first and second semester exams across four subjects in a particular year."

What is the student's approximate cumulative percentage of marks for the entire year?

A person sells 50 chairs for ₹10,000, suffering a loss of 15%. Estimate how many chairs should he sell for ₹9000 to make a profit of 10%?

A 40-liter mixture contains juice and water in the ratio \( 5:3 \). How much water (in liters) must be added to this mixture to change the ratio of juice to water to \( 2:3 \)?

A and B together finish work in 10 days. B and C in 12 days. A and C in 15 days. How many days will C take to do the work alone?

A bus starts from City A at 1:00 PM, and travels towards City B at a speed of 50 km/h. A car starts from City B at 2:30 PM and travels towards City A at a speed of 80 km/h. If the distance between City A and City B is 450 km, at what time will they cross each other?

Two runners, P and Q, start running from the same point on a circular track of 800 meters. They run in the same direction with speeds of 12 km/h and 9 km/h, respectively. If they run for 4 hours, how many times will they cross each other?

If \( (3x + \frac{2}{x} - 4) = 10 \), then what is the value of \( (9x^2 + \frac{4}{x^2} + 24) \)?

If \( x + \frac{1}{x} = \sqrt{2} \), determine the value of \( x^6 + \frac{1}{x^6} \)

From a point A on the ground, the angle of elevation to the top of a tower is 45°. After walking 40 meters toward the tower along the same straight line to a new point B, the angle of elevation becomes 60°. Find the approximate height of the tower and the distance from point A to the base of the tower.

Find the radius of a hemisphere whose volume is numerically equal to its total surface area.

Two solid hemispheres of radii \(R\) and \(2R\) are melted to form a sphere and a cone. The cone has the same radius as the new sphere, and its height is twice the sphere's radius. Find the radius of the newly formed sphere.

A company produces wooden signs shaped like regular octagons of side 20 cm. If wood costs \( ₹5/\text{cm}^2 \) and design costs ₹200 per piece, what is the total cost per sign?