List of top Quantitative Aptitude Questions asked in CAT

If \( pqr = 1 \), the value of the expression \[ \frac{1}{1 + p + q} + \frac{1}{1 + q + r} + \frac{1}{1 + r + p} \] is equal to:

A piece of string is 40 cm long. It is cut into three pieces. The longest piece is three times as long as the middle-sized and the shortest piece is 23 cm shorter than the longest piece. Find the length of the shortest piece.

Three travellers are sitting around a fire, and are about to eat a meal. One of them has 5 small loaves of bread, the second has 3 small loaves of bread. The third has no food, but has 8 coins. He offers to pay for some bread. They agree to share the 8 loaves equally among the three travellers, and the third traveller will pay 8 coins for his share of the 8 loaves. All loaves were the same size. The second traveller (who had 3 loaves) suggests that he will be paid 3 coins, and that the first traveller be paid 5 coins. The first traveller says that he should get more than 5 coins. How much should the first traveller get?

Six persons are playing a card game. Suresh is facing Raghubir who is to the left of and to the right of Pramod. Ajay is to the left of Dhiraj. Yogendra is to the left of Pramod. If Dhiraj exchanges his seat with Yogendra and Pramod exchanges with Raghubir, who will be sitting to the left of Dhiraj?

After the division of a number successively by 3, 4 and 7, the remainders obtained are 2, 1 and 4 respectively. What will be the remainder if 84 divides the same number?

Ten straight lines, no two of which are parallel and no three of which pass through any common point, are drawn on a plane. The total number of regions (including finite and infinite regions) into which the plane will be divided by the lines is:

The number of real roots of the equation \( \frac{A^2}{x} + \frac{B^2}{x-1} = 1 \), where \( A \) and \( B \) are real numbers not equal to zero simultaneously, is:

A car rental agency has the following terms. If a car is rented for 5 hr or less, the charge is Rs. 60 per hour or Rs. 12 per kilometre whichever is more. On the other hand, if the car is rented for more than 5 hr, the charge is Rs. 50 per hour or Rs. 7.50 per kilometre whichever is more. Akil rented a car from this agency, drove it for 30 km and ended up paying Rs. 300. For how many hours did he rent the car?

Suppose for any real number \( x \), \( [x] \) denotes the greatest integer less than or equal to \( x \). Let \( L(x, y) = [x] + [y] \) and \( R(x, y) = [2x] + [2y] \). Then is it impossible to find any two positive real numbers \( x \) and \( y \) for which:

If \( x^2 + 5y^2 + z^2 = 2y(2x + z) \), then which of the following statements is (are) necessarily true? A. \( x = 2y \) B. \( x = 2z \) C. \( 2x = z \)

Shyam visited Ram during his brief vacation. In the mornings they both would go for yoga. In the evenings they would play tennis. To have more fun, they indulge only in one activity per day, i.e. either they went for yoga or played tennis each day. There were days when they were lazy and stayed home all day long. There were 24 mornings when they did nothing, 14 evenings when they stayed at home, and a total of 22 days when they did yoga or played tennis. For how many days Shyam stayed with Ram?

The owner of a local jewellery store hired three watchmen to guard his diamonds, but a thief still got in and stole some diamonds. On the way out, the thief met each watchman, one at a time. To each he gave \( \frac{1}{2} \) of the diamonds he had then, and 2 more besides. He escaped with one diamond. How many did he steal originally?

Neeraj has agreed to mow a lawn, which is a 20 m × 40 m rectangle. He mows it with a 1 m wide strip. If Neeraj starts at one corner and mows around the lawn toward the centre, about how many times would he go round before he has mowed half the lawn?

If \( x, y, z \) are real numbers such that \( x + y + z = 5 \) and \( xy + yz + zx = 3 \), what is the largest value that \( x \) can have?

Only a single rail track exists between stations A and B on a railway line. One hour after the north-bound super fast train N leaves station A for station B, a south-bound passenger train S reaches station A from station B. The speed of the super fast train is twice that of a normal express train E, while the speed of a passenger train S is half that of E. On a particular day, N leaves for B from A, 20 min behind the normal schedule. In order to maintain the schedule, both N and S increased their speeds. If the super fast train doubles its speed, what should be the ratio (approximately) of the speeds of passenger train S to that of the super fast train so that the passenger train S reaches exactly at the scheduled time at A on that day?

Instead of walking along two adjacent sides of a rectangular field, a boy took a short cut along the diagonal and saved a distance equal to half the longer side. Then the ratio of the shorter side to the longer side is:

Number S is obtained by squaring the sum of digits of a two-digit number D. If the difference between S and D is 27, then the two-digit number D is:

Four horses are tethered at four corners of a square plot of side 14 m so that the adjacent horses can just reach one another. There is a small circular pond of area 20 m² at the centre. Find the ungrazed area.

If \( f(x) = \log \left(\frac{(1 + x)}{(1 - x)}\right) \), then \( f(x) + f(y) \) is:

In a four-digit number, the sum of the first 2 digits is equal to that of the last 2 digits. The sum of the first and last digits is equal to the third digit. Finally, the sum of the second and fourth digits is twice the sum of the other 2 digits. What is the third digit of the number?

At his usual rowing rate, Rahul can travel 12 miles downstream in a certain river in 6 hr less than it takes him to travel the same distance upstream. If he could double his usual rowing rate for this 24 miles round trip, the downstream 12 miles would then take only 1 hr less than the upstream 12 miles. What is the speed of the current in miles per hour?

In some code, letters $a, b, c, d, e$ represent 2, 4, 5, 6, and 10 in some order. Given:
I. $a + c = e$,
II. $b - d = d$,
III. $e + a = b$.
Which is true?

A student took five papers in an examination, where the full marks were the same for each paper. His marks in these papers were in the proportion of 6 : 7 : 8 : 9 : 10. In all papers together, the candidate obtained 60% of the total marks. Then the number of papers in which he got more than 50% marks is:

Fresh grapes contain 90% water by weight while dried grapes contain 20% water. What is the weight of dry grapes available from 20 kg of fresh grapes?