List of top Quantitative Aptitude Questions asked in CAT

If \(f(x) = x^3 - 4x + p\), and \(f(0)\) and \(f(1)\) are of opposite signs, then which of the following is necessarily true?
A sprinter starts running on a circular path of radius \(r\) metres. Her average speed (in metres/minute) is \( \pi \) during the first 30 seconds, \( \frac{\pi}{2} \) during next one minute, \( \frac{\pi}{4} \) during next 2 minutes, \( \frac{\pi}{8} \) during next 4 minutes, and so on. What is the ratio of the time taken for the nth round to that for the previous round?
N persons stand on the circumference of a circle at distinct points. Each possible pair of persons, not standing next to each other, sings a two-minute song one pair after the other. If the total time taken for singing is 28 minutes, what is \( N \)?

In the adjoining figure, the lines represent one-way roads allowing travel only northwards or only westwards. Along how many distinct routes can a car reach point B from point A?

Let \( u = (\log_2 x)^2 - 6\log_2 x + 12 \) where \(x\) is a real number. Then the equation \(x^u = 256\), has

In the adjoining figure I and II, are circles with P and Q respectively. The two circles touch each other and have a common tangent that touches them at points R and S respectively. This common tangent meets the line joining P and Q at O. The diameters of I and II are in the ratio 4:3. It is also known that the length of PO is 28 cm.

The function \( f(x) \) is defined as follows:

\[ f(x) = \begin{cases} x & \text{for } 0 \le x \le 1 \\ 1 & \text{for } x \ge 1 \\ 0 & \text{otherwise} \end{cases} \]

The properties of the function are as follows:

\[ f_1(x) = f(-x) \quad \text{for all } x \] \[ f_2(x) = -f(x) \quad \text{for all } x \] \[ f_3(x) = f(f(x)) \quad \text{for all } x \]

In an examination, there are 100 questions divided into three groups A, B and C such that each group contains at least one question. Each question in group a carries 1 mark, each question in group B carries 2 marks and each question in group C carries 3 marks. It is known that the questions in group A together carry at least 60% of the total marks
What is the sum of $n$ terms in the series $\log m + \log \left( \frac{m^2}{n} \right) + \log \left( \frac{m^3}{n^2} \right) + \log \left( \frac{m^4}{n^3} \right) + \dots$?
If $13x + 2z = 5y^2$, then:
A real number $x$ satisfying $1 - \frac{1}{n}<x \leq 3 + \frac{1}{n}$, for every positive integer $n$, is best described by:
If $\log_x x - \log_10 \sqrt{x} = 2 \log_10 10$, then the possible value of $x$ is given by:
If both a and b belong to the set $\{1, 2, 3, 4\}$, then the number of equations of the form $ax^2 + bx + 1 = 0$ having real roots is:
If three positive real numbers $x$, $y$ and $z$ satisfy $y - x = z - y$ and $x + y = 4$, then what is the minimum possible value of $y$?
If $n$ is such that $36 \leq n \leq 72$, then $x = \frac{n^2 + 2\sqrt{n(n+4)} + 16}{n + 4\sqrt{n + 4}}$ satisfies:
The infinite sum $1 + \frac{4}{7} + \frac{9}{72} + \frac{16}{73} + \frac{25}{74} + \dots$ equals:
The number of roots common between the two equations $x^3 + 3x^2 + 4x + 5 = 0$ and $x^4 + 2x^3 + 7x + 3 = 0$ is:
If $\frac{1}{3} \log N + 3 \log M = 1 + \log 1000$, then:
Consider the sets $T_n = \{n, n+1, n+2, n+3, n+4\}$, where $n = 1, 2, 3, \dots, 96$. How many of these sets contain 6 or any integral multiple thereof (i.e., any one of the numbers 6, 12, 18, ...)?
What is the sum of all two-digit numbers that give a remainder of 3 when they are divided by 7?
Using only 2, 5, 10, 25, and 50 paisa coins, what will be the minimum number of coins required to pay exactly 78 paise, 69 paise and Rs. 1.01 to three different persons?
In a coastal village, every year floods destroy exactly half of the huts. After the flood water recedes, the same number of huts destroyed are rebuilt. The floods occurred consecutively in the last three years — 2001, 2002 and 2003. If floods are expected again in 2004, the number of huts expected to be destroyed is:
Let $a$, $b$, $c$, and $d$ be integers such that $a = 6b$, $a = 12c$, and $2b = 9d = 12e$. Then which of the following pairs contains a number that is not an integer?
If $x$ and $y$ are integers, then the equation $5x + 19y = 64$ has:
Two straight roads R1 and R2 diverge from a point A at an angle of 120°. Ram starts walking from point A along R1 at a uniform speed of 3 km/hr. Shyam starts walking at the same time from A along R2 at a uniform speed of 2 km/hr. They continue walking for 4 hr along their respective roads and reach points B and C on R1 and R2 respectively. There is a straight line connecting B and C. Then Ram returns to point A after walking along the line segments BC and CA. Shyam also returns to A after walking along line segments BC and CA. Their speeds remain unchanged. The time interval (in hours) between Ram's and Shyam's return to the point A is: