List of top Quantitative Aptitude Questions

If the numerator of a fraction (in lowest form) is increased by \( \frac{1}{3} \) of itself and the denominator is decreased by \( \frac{1}{4} \) of itself, the fraction so obtained is \( \frac{21}{64} \). What is the difference between the denominator and the numerator of the original fraction?
Let \( A = \{1,2,5,6\}, B = \{1,2,3\} \) and \( C = (A \times B) \cap (B \times A) \). Which of the following is INCORRECT?
If \( a + b + c = 2 \), \( a^2 + b^2 + c^2 = 36 \), then the value of \( a^3 + b^3 + c^3 - 3abc \) is:
The mean of the following distribution is 25. \[ \begin{array}{|c|c|} \hline \text{Class} & \text{Frequency} \\ \hline 0-10 & 14 \\ 10-20 & p \\ 20-30 & 27 \\ 30-40 & 21 \\ 40-50 & 15 \\ \hline \end{array} \]
The graphs of \(2x - y = 1\) and \(3x - 2y = -1\) intersect at a point \(P\), which lies on the graph of the equation:
If \( \frac{46}{159} = \frac{1}{x} + \frac{1}{y} + \frac{1}{z^2} \), where \( x, y, z \) are positive integers, then the value of \( 2x + 3y - 4z \) is:
The expression \( \frac{\sec^6 \theta - \tan^6 \theta - 3 \sec^2 \theta \tan^2 \theta}{1 + 2 \sin^2 \theta - \sin^4 \theta + \cos^4 \theta} \) is equal to:
The ratio of the number of boys and the girls in a group is 5 : 8. If 4 more girls join the group and 5 boys leave the group, then the ratio of the number of boys to the number of girls becomes 1 : 2. Originally, what was the difference between the number of boys and girls in the group?
If \( f\left(1 - \frac{1}{x} \right) = \frac{5x + 1}{x}, \, x \neq 0 \), then \( f(x) = k - x \). What is the value of \( k \)?
Let \( U \) be the universal set, \( A \), \( B \), and \( C \) are the sets such that \( C \) is a subset of \( A \) and \( B \cap C = \emptyset \). If \( n(U) = 105 \), \( n(A) = 58 \), \( n(B) = 50 \), \( n(A \cap B) = 20 \) and \( n(A \cap C) = 32 \), then \( n(A \cup B) - n(B \cap C') = ? \)
From a point on a bridge across a river, the angles of depressions of the banks on opposite sides of the river are \(30^\circ\) and \(60^\circ\), respectively. If the height of the bridge from the banks is \( h \) metres and the width of the river is \( k \) metres, then \( h : k \) is equal to:
If \( 3\sin^2 x + 10\cos x - 6 = 0 \), \( 0^\circ<x<90^\circ \), then the value of \( \sec x + \cosec x + \cot x \) is:
Let \( x \) be the median of the data: 23, 17, 19, 11, 7, 3, 13, 2, 5, 29. Let \( y \) be the median of the same data set obtained by replacing 2 by 21 and 13 by 31. What is the value of \( |x - y| \)?
The heights (in cm) of 8 students are recorded as 162, 163, 160, 164, 160, 170, 161, 164. The standard deviation of the data is closest to:
A shopkeeper has two varieties of rice A and B. By selling A at ₹75 per kg, he loses 20%; and by selling B at ₹90 per kg, he gains 25%. If he mixes A and B in the ratio 4 : 5 and sells the mixture at ₹110.25 per kg, then his profit percentage is:
In a class of 100 students, 55 students passed in Mathematics and 65 passed in English. Five students failed in both the subjects. Let \( m \) be the number of students who passed in exactly one of the two subjects and \( n \) be the number of students who failed in at least one subject, then what is the value of \( (m - n) \)?
Given \( f(x) = \frac{-4x + 1}{4} \) and \( g(x) = \sqrt[3]{x} \), then \( (g \circ f^{-1})\left(\frac{3}{8}\right) = \)
A and B are two sets such that \( n(A) = 12 \), \( n(B) = 15 \) and \( n(A \cup B) = 20 \). Then, \( n(B \cap A') - n(A \cap B') = ?
In an arithmetic progression, the 4th term equals three times the first term and the 7th term exceeds two times the third term by one. The sum of its first ten terms is:
X and Y are two points that are 135 m apart on the ground on either side of a pole and in the same line. The angles of elevation of a bird sitting on the top of the pole from X and Y are \( 30^\circ \) and \( 60^\circ \) respectively. The distance of Y from the foot of the pole (in m) is:
Two persons A and B start moving at the same time towards each other from points x and y, respectively. After crossing each other, A and B now take \( \frac{4}{6} \) hours and 6 hours, respectively, to reach their respective destinations. If the speed of A is 72 km/h, then the speed (in km/h) of B is:
In a year, out of 160 games to be played, a cricket team wants to win 80% of them. Out of 90 games already played, the success rate is \( 66\frac{2}{3} %\). What should be the success rate for the remaining games in order to reach the target?
The sum of the first 10 terms of the series \[ \frac{7}{3} + \frac{7}{15} + \frac{1}{5} + \frac{1}{9} + \dots \quad \text{where} \quad \text{HCF}(a,b) = 1. \] What is the value of \( |a - b| \)?
A and B are two sets such that \( n(A) = 12 \), \( n(B) = 15 \) and \( n(A \cup B) = 20 \). Then, \( n(B \cap A') - n(A \cap B') = ?
If \( \sec \theta + \tan \theta = p \), then \( \frac{\sin \theta - 1}{\sin \theta + 1} \) is equal to: