List of top Quantitative Aptitude Questions asked in CAT

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 would be divided by the lines is

A child was asked to add first few natural numbers (i.e. \(1 + 2 + 3 + \dots\)) so long his patience permitted. As he stopped, he gave the sum as 575. When the teacher declared the result wrong, the child discovered he had missed one number in the sequence during addition. The number he missed was

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?

A rich merchant had collected many gold coins. He did not want anybody to know about him. One day, his wife asked, "How many gold coins do we have?" After a brief pause, he replied, "Well! If I divide the coins into two unequal numbers, then 48 times the difference between the two numbers equals the difference between the squares of the two numbers." The wife looked puzzled. Can you help the merchant's wife by finding out how many gold coins the merchant has?

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 \(20\text{ m} \times 40\text{ m}\) rectangle. He mows it with 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? (Round off the answer to two decimal digits)

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?

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

Only a single rail track exists between stations A and B on a railway line. One hour after the northbound 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 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

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 \(cm^2\); EC = 3(BE). The area of ABCD (in \(cm^2\)) 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

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 \(m^2\) at the centre. Find the ungrazed area.

The length of the common chord of two circles of radii 15 cm and 20 cm, whose centres are 25 cm apart, is

If there are 10 positive real numbers \( n_1 < n_2 < n_3 \ldots < n_{10} \), how many triplets of these numbers \( (n_1, n_2, n_3), (n_2, n_3, n_4) \) 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?

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?

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

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:

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:

If \( u, v, w \) and \( m \) are natural numbers such that \( u^m + v^m = w^m \), then which one of the following is true?

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:

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?