List of top Quantitative Aptitude Questions asked in CAT

In triangle PQR, \( PQ = 12 \) cm, \( PR = 9 \) cm, and \( \angle Q + \angle R = 120^\circ \). Find the length of QR.

A train travels 360 km at a uniform speed. If the speed increases by 6 km/h, it takes 1 hour less. Find the original speed.

The sum of the squares of three consecutive integers is 194. Find the integers.

If \( g(x) = p(x) = qx^n \), and \( p \) and \( q \) are constants, then at \( x = 0 \), \( g(x) \) will be:

The sum of the first $n$ terms of an arithmetic progression is $2n^2 + n$. Find the 10th term.

Solve for $x$: $3x - 5 = 7 - 2x$.

A and B can do a job in 6 days. A alone takes 10 days. How long does B take?

A price is increased by 15 to Rs. 230. What was the original price?

A die is rolled twice. What is the probability of getting a sum of 9?

If \( x + \frac{1}{x} = 2 \), find the value of \( x^{10} + \frac{1}{x^{10}} \).

A number is increased by 25 and then decreased by 25. What is the net percentage change?

If information increases 20% per year, and memory space increases 10% per year from 2000 onwards (where 80% of total memory is already used), and usage grows at 45% more than current rate, when will there be shortage of memory?

A can complete a task in 15 days, B in 20 days. Together, how many days?

A pipe fills a tank in 8 hours, another empties it in 12 hours. If both are opened, how long to fill?

A shopkeeper sells two items at Rs. 1000 each. On one, he gains 25, and on the other, he loses 20. What is his overall profit or loss percentage?

An item is sold for Rs. 1200 at a 20 profit. Find the cost price.

A and B run a 1200m race. A gives B a 120m head start. A runs at 5 m/s, and B at 4 m/s. Who wins, and by how much time?

A car travels 240 km in 4 hours. What is its speed?

Two cars P and Q start from points A and B simultaneously. They meet 40 km from B. After meeting, they exchange speeds and return. They meet again 20 km from A. Find distance AB.

The area of a circle is 154 cm². Find its radius.

What is the maximum possible number of intersection points of 15 lines in a plane, assuming no two lines are parallel and no three are concurrent?

If the angle bisector of \( \angle P \) meets \( QR \) at point \( M \), find the length of \( PM \).

An aquarium of size 100 cm × 80 cm × 60 cm is tilted along the 80 cm edge. Water spills until the water line reaches 1/3 of the base width. Find the height of water reduced when box is restored.

If the equations below hold true for triangles ABC and DEF: \[ a(a + b + c) = d^2, b(a + b + c) = e^2, c(a + b + c) = f^2 \] Then which of the following is always true of triangle DEF?

Find the number of positive divisors of 720.