List of top Quantitative Aptitude Questions asked in CAT

Let \( S \) denote the infinite sum \( 2 + 5x + 9x^2 + 14x^3 + 20x^4 + \dots \), where \( |x|<1 \) and the coefficient of \( x^{n-1} \) is \( \frac{1}{2} n(n + 3) \), \( n = 1, 2, \dots \). Then S equals:
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?
Mayank, Mirza, Little and Jaspal bought a motorbike for rupee 60. Mayank paid one-half of the sum of the amounts paid by the other boys. Mirza paid one-third of the sum of the amounts paid by the other boys. Little paid one-fourth of the sum of the amounts paid by the other boys. How much did Jaspal have to pay?
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?
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:
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:
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?
On a 20 km tunnel, connecting two cities A and B, there are three gutters (1, 2, and 3). The distance between gutters 1 and 2 is half the distance between gutters 2 and 3. The distance from city A to its nearest gutter, gutter 1, is equal to the distance of city B from gutter 3. On a particular day, the hospital in city A receives information that an accident has happened at gutter 3. The victim can be saved only if an operation is started within 40 min. An ambulance started from city A at 30 km/hr and crossed gutter 1 after 5 min. If the driver had doubled the speed after that, what is the maximum amount of time would the doctor get to attend the patient at the hospital. Assume 1 min is elapsed for taking the patient into and out of the ambulance?
The nth element of a series is represented as \[ X_n = (-1)^{n} X_{n-1}. \] If \( X_0 = x \) and \( x>0 \), then which of the following is always true?
The length of the common chord of two circles of radii 15 cm and 20 cm, whose centres are 25 cm apart, 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:
The area of the triangle whose vertices are \( (a, a) \), \( (a + 1, a + 1) \) and \( (a + 2, a) \) is:

In the figure given below, ABCD is a rectangle. The area of the isosceles right triangle ABE = 7 cm²; EC = 3(BE). The area of ABCD (in cm²) is:

On a straight road XY, 100 m long, five heavy stones are placed 2 m apart beginning at the end X. A worker, starting at X, has to transport all the stones to Y, by carrying only one stone at a time. The minimum distance he has to travel is:
If there are 10 positive real numbers \( n_1<n_2<n_3 \dots<n_{10} \), how many triplets of these numbers \( (n_1, n_2, n_3), (n_2, n_3, n_4), \dots \) can be generated such that in each triplet the first number is always less than the second number, and the second number is always less than the third number?
In \( \triangle ABC \), the internal bisector of \( \angle A \) meets BC at D. If \( AB = 4 \), \( AC = 3 \) and \( \angle A = 60^\circ \), then the length of AD is:

The batting average (BA) of a Test batsman is computed from runs scored and innings played — completed innings and incomplete innings (not out) in the following manner:

\[ r_1 = \text{Number of runs scored in completed innings} \] \[ n_1 = \text{Number of completed innings} \] \[ r_2 = \text{Number of runs scored in incomplete innings} \] \[ n_2 = \text{Number of incomplete innings} \]

\[ BA = \frac{r_1 + r_2}{n_1} \]

To better assess a batsman’s accomplishments, the ICC is considering two other measures MBA1 and MBA2, defined as follows:

\[ MBA_1 = \frac{r_1}{n_1} + \frac{n_2}{n_1} \max \left( 0, \left( \frac{r_2}{n_2} - \frac{r_1}{n_1} \right) \right) \]

\[ MBA_2 = \frac{r_1 + r_2}{n_1 + n_2} \]

The petrol consumption rate of a new model car ’Palto’ depends on its speed and may be described by the graph below

The network diagram shows cities A, B, C, D, E, F with arrows as permissible travel. How many distinct paths exist from A to F?

A change-making machine contains 1-rupee, 2-rupee, and 5-rupee coins. Total coins = 300, total value = Rs. 960. If 1-rupee and 2-rupee coin counts are interchanged, value decreases by Rs. 40. Find the total number of 5-rupee coins.
Let $n$ be the number of different five-digit numbers divisible by 4, formed from digits 1, 2, 3, 4, 5, 6 with no repetition. Find $n$.
Ashish is given Rs. 158 in one-rupee denominations. He must allocate them into a minimum number of bags so any amount from Re 1 to Rs. 158 can be made without opening a bag. What is the minimum number of bags?