List of top Quantitative Ability and Data Interpretation Questions on Quantitative Aptitude asked in XAT

$x, 17, 3x - y^2 - 2, and 3x + y^2 - 30$ are four consecutive terms of an increasing arithmetic sequence. The sum of the four numbers is divisible by:
Amitabh picks a random integer between 1 and 999, doubles it and gives the result to Sashi. Each time Sashi gets a number from Amitabh, he adds 50 and gives it back; Amitabh again doubles the received number. The first person whose result exceeds 1000 loses. Let $x$ be the smallest initial number that results in a win for Amitabh. The sum of the digits of $x$ is:
The sum of the possible values of \(x\) in the equation \(|x+7| + |x-8| = 16\) is:
There are two windows on the wall of a building that need repairs. A ladder 30 m long is placed against a wall such that it just reaches the first window which is 26 m high. The foot of the ladder is at point A. After the first window is fixed, the foot of the ladder is pushed backwards to point B so that the ladder can reach the second window. The angle made by the ladder with the ground is reduced by half, as a result of pushing the ladder. The distance between points A and B is:
Consider four natural numbers: $x$, $y$, $x+y$, and $x-y$. Two statements are given:
I. All four numbers are prime numbers.
II. The arithmetic mean of the numbers is greater than 4.
Which of the following statements would be sufficient to determine the sum of the four numbers?
Consider the formula, \( S = \dfrac{\alpha \times \omega}{\tau + \rho \times \omega} \) with positive integers. If \(\omega\) is increased and \(\alpha, \tau, \rho\) are kept constant, then \(S\):
There are two circles $C_1$ and $C_2$ of radii $3$ and $8$ units respectively. The common internal tangent $T$ touches the circles at points $P_1$ and $P_2$ respectively. The line joining the centers of the circles intersects $T$ at $X$. The distance of $X$ from the center of the smaller circle is $5$ units. What is the length of the line segment $P_1P_2$?
In quadrilateral $PQRS$, $PQ = 5$ units, $QR = 17$ units, $RS = 5$ units, and $PS = 9$ units. The length of the diagonal $QS$ can be:
Triangle $ABC$ is a right-angled triangle. $D$ and $E$ are the midpoints of $AB$ and $BC$ respectively. Read the following statements.
I. $AE = 19$ II. $CD = 22$ III. $\angle B$ is a right angle.
Which of the following statements would be sufficient to determine the length of $AC$?
Expression $\displaystyle \sum_{n=1}^{13} \frac{1}{n}$ can also be written as $\dfrac{x}{13!}$. What would be the remainder if $x$ is divided by $11$?
A rectangular swimming pool is 48 m long and 20 m wide. The shallow edge of the pool is 1 m deep. For every 2.6 m that one walks up the inclined base of the swimming pool, one gains an elevation of 1 m. What is the volume of water (in cubic meters), in the swimming pool? Assume that the pool is filled up to the brim.
The value of the expression: \[ \displaystyle \sum_{i=2}^{100} \frac{1}{\log_i(100!)} \] is:
A teacher noticed a strange distribution of marks in the exam. There were only three distinct scores: $6, 8,$ and $20$. The mode of the distribution was $8$. The sum of the scores of all the students was $504$. The number of students in the most populated category was equal to the sum of the number of students with lowest score and twice the number of students with the highest score. The total number of students in the class was:
Prof. Suman takes a number of quizzes for a course. All the quizzes are out of 100. A student can get an A grade in the course if the average of her scores is more than or equal to 90. Grade B is awarded to a student if the average of her scores is between 87 and 89 Both include(D). If the average is below 87, the student gets a C grade. Ramesh is preparing for the last quiz and he realizes that he will score a minimum of 97 to get an A grade. After the quiz, he realizes that he will score 70, and he will just manage a B. How many quizzes did Prof. Suman take?
A polynomial $y = ax^3 + bx^2 + cx + d$ intersects the x-axis at 1 and -1, and the y-axis at 2. The value of $b$ is:
The probability that a randomly chosen positive divisor of $10^{29}$ is an integer multiple of $10^{23}$ is: $a^2/b^2$. Then $b-a$ would be:
Circle C₁ has a radius of 3 units. The line segment PQ is the only diameter of the circle which is parallel to the X-axis. P and Q are points on curves given by the equations y = ax and y = 2ax respectively, where a < 1. The value of a is:
Consider a rectangle $ABCD$ of area $90$ units. The points $P$ and $Q$ trisect $AB$, and $R$ bisects $CD$. The diagonal $AC$ intersects the line segments $PR$ and $QR$ at $M$ and $N$ respectively. What is the area of the quadrilateral $PQNM$?
Two numbers, $297_B$ and $792_B$, belong to base $B$ number system. If the first number is a factor of the second number then the value of $B$ is:
There are two squares S1 and S2 with areas 8 and 9 units, respectively. S1 is inscribed within S2, with one corner of S1 on each side of S2. The corners of the smaller square divide the sides of the bigger square into two segments, one of length a and the other of length b (b > a). A possible value of b/a is:
Diameter of the base of a water-filled inverted right circular cone is $26$ cm. A cylindrical pipe, $5$ mm in radius, is attached to the surface of the cone at a point. The perpendicular distance between the point and the base (the top) is $15$ cm. The distance from the edge of the base to the point is $17$ cm, along the surface. If water flows at the rate of $10$ meters per minute through the pipe, how much time would elapse before water stops coming out of the pipe?
Aditya has a total of 18 red and blue marbles in two bags Each bag has marbles of both colors). A marble is randomly drawn from the first bag followed by another randomly drawn from the second bag, the probability of both being red is $5/16$. What is the probability of both marbles being blue?
In which of the following years the percentage increase in the number of Indians going abroad was greater than the percentage increase in the number of domestic tourists?
The mean of six positive integers is 15. The median is 18, and the only mode of the integers is less than 18. The maximum possible value of the largest of the six integers is
Ramesh bought a total of 6 fruits (apples and oranges) from the market. He found that he required one orange less to extract the same quantity of juice as extracted from apples. If Ramesh had used the same number of apples and oranges to make the blend, then which of the following correctly represents the percentage of apple juice in the blend?