List of top Quantitative Aptitude Questions asked in CAT

Let ABCD be a parallelogram such that the coordinates of its three vertices A, B, C are (1, 1), (3, 4), and (−2, 8), respectively. Then, the coordinates of the vertex D are
The largest real value of a for which the equation\( |x+a|+|x−1|=2\) has an infinite number of solutions for x is
Let a and b be natural numbers. If \(a^2+ab+a=14\) and \(b^2+ab+b=28\), then (2a+b) equals
The minimum possible value of \(\frac{x^2−6x+10}{3−x}\),for x<3,is
If \((3+2\sqrt2)\) is a root of the equation ax2 + bx + c = 0 and \((4+2\sqrt3)\) is a root of the equation ay2 + my + n = 0,where a,b,c,m and n are integers, then the value of \((\frac{b}{m}+\frac{c−2b}{n})\) is
The length of each side of an equilateral triangle ABC is 3 cm. Let D be a point on BC such that the area of triangle ADC is half the area of triangle ABD. Then the length of AD,in cm,is
Ankita buys 4kg cashews, 14kg peanuts, and 6kg almonds when the cost of 7kg cashews is the same as that of 30kg peanuts or 9kg almonds. She mixes all three nuts and marks a price for the mixture in order to make a profit of ₹1752. She sells 4kg of the mixture at this marked price and the remaining at a 20% discount on the marked price, thus making a total profit of ₹744. Then the amount, in rupees, that she had spent buying almonds is
The average of a non-decreasing sequence of N numbers \(a_1,a_2,…,a_N\) is 300.If \(a_1\) is replaced by \(6a_1\), the new average becomes 400.Then,the number of possible values of \(a_1\) is
Suppose k is any integer such that the equation \(2x^2+kx+5=0\) has no real roots and the equation \(x^2+(k−5)x+1=0\) has two distinct real roots for x. Then, the number of possible values of k is
Manu earns ₹4000 per month and wants to save an average of ₹550 per month in a year. In the first nine months, his monthly expense was ₹3500, and he foresees that, tenth month onward, his monthly expense will increase to ₹3700. In order to meet his yearly savings target, his monthly earnings, in rupees, from the tenth month onward should be
Consider six distinct natural numbers such that the average of the two smallest numbers is 14 and the average of the two largest numbers is 28. Then,the maximum possible value of the average of these six numbers is
Trains A and B start traveling at the same time towards each other with constant speeds from stations X and Y, respectively. Train A reaches station Y in 10 minutes while train B takes 9 minutes to reach station X after meeting train A. Then the total time taken, in minutes, by train B to travel from station Y to station X is
Let r be a real number and \(f(x) = \begin{cases}     2x - r & \text{if } x \geq r \\     r & \text{if } x < r \end{cases}\).Then, the equation \(f(x)=f(f(x))\) holds for all real values of x where
Two ships meet mid-ocean,and then,one ship goes south and the other ship goes west,both travelling at constant speeds.Two hours later,they are 60 km apart.If the speed of one of the ships is 6km per hour more than the other one,then the speed,in km per hour,of the slower ship is
Consider the arithmetic progression 3,7,11,…and let \(A_n\) denote the sum of the first n terms of this progression.Then the value of \(\frac{1}{25}∑^{25}_{n=1}A_n\) is
Two cars travel from different locations at constant speeds. To meet each other after starting at the same time, they take 1.5 hours if they travel towards each other, but 10.5 hours if they travel in the same direction. If the speed of the slower car is 60km/hr, then the distance traveled, in km, by the slower car when it meets the other car while traveling towards each other, is
Suppose the medians BD and CE of a triangle ABC intersect at a point O. If area of triangle ABC is 108 sq. cm, then, the area of the triangle EOD, in sq. cm, is
Five students,including Amit,appear for an examination in which possible marks are integers between 0 and 50,both inclusive.The average marks for all the students is 38 and exactly three students got more than 32.If no two students got the same marks and Amit got the least marks among the five students,then the difference between the highest and lowest possible marks of Amit is
The arithmetic mean of all the distinct numbers that can be obtained by rearranging the digits in 1421, including itself, is
In an examination,the average marks of students in sections A and B are 32 and 60,respectively. The number of students in section A is 10 less than that in section B. If the average marks of all the students across both the sections combined is an integer,then the difference between the maximum and minimum possible number of students in section A is
Moody takes 30 seconds to finish riding an escalator if he walks on it at his normal speed in the same direction.He takes 20 seconds to finish riding the escalator if he walks at twice his normal speed in the same direction.If Moody decides to stand still on the escalator,then the time,in seconds,needed to finish riding the escalator is
The average of all 3-digit terms in the arithmetic progression 38,55,72,...,is
If \(c=\frac{16x}{y}+\frac{49y}{x} \)for some non-zero real numbers x and y,then c cannot take the value
Two ships are approaching a port along straight routes at constant speeds. Initially,the two ships and the port formed an equilateral triangle with sides of length 24 km. When the slower ship travelled 8 km,the triangle formed by the new positions of the two ships and the port became right-angled. When the faster ship reaches the port, the distance,in km,between the other ship and the port will be
A group of N people worked on a project.They finished \(35\%\) of the project by working 7 hours a day for 10 days.Thereafter,10 people left the group and the remaining people finished the rest of the project in 14 days by working 10 hours a day.Then the value of N is