List of top Quantitative Aptitude Questions asked in CAT

In a village, the ratio of number of males to females is 5:4. The ratio of number of literate males to literate females is 2:3. The ratio of the number of illiterate males to illiterate females is 4:3. If 3600 males in the village are literate, then the total number of females in the village is

Amal buys 110kg of syrup and 120kg of juice, syrup being 20% less costly than juice, per kg. He sells 10kg of syrup at 10% profit and 20kg of juice at 20% profit. Mixing the remaining juice and syrup, Amal sells the mixture at ₹ 308.32 per kg and makes an overall profit of 64%. Then, Amal's cost price for syrup, in rupees per kg, is

Let a and b be natural numbers. If \(a^2+ab+a=14\) and \(b^2+ab+b=28\), then (2a+b) equals

For any natural number n,suppose the sum of the first n terms of an arithmetic progression is \((n+2n^2)\). If the \(n^{th}\) term of the progression is divisible by 9,then the smallest possible value of n is

All the vertices of a rectangle lie on a circle of radius R. If the perimeter of the rectangle is P, then the area of the rectangle is

The average weight of students in a class increases by 600 gm when some new students join the class. If the average weight of the new students is 3 kg more than the average weight of the original students, then the ratio of the number of original students to the number of new students is

Let \(0≤a≤x≤100\) and f(x)=\(|x−a|+|x−100|+|x−a−50|\).Then the maximum value of f(x) becomes 100 when a is equal to

In triangle \(ABC\), altitudes \(AD\) and \(BE\) are drawn to the corresponding bases. If \(∠BAC=45\degree\) and \(∠ABC=θ\), then \(\frac {AD}{BE}\) equals

Working alone,the times taken by Anu,Tanu and Manu to complete any job are in the ratio \(5:8:10\). They accept a job which they can finish in 4 days if they all work together for 8 hours per day. However,Anu and Tanu work together for the first 6 days,working 6 hours 40 minutes per day. Then,the number of hours that Manu will take to complete the remaining job working alone is

Regular polygons A and B have number of sides in the ratio \(1:2\) and interior angles in the ratio \(3:4\).Then the number of sides of B equals

If a and b are non-negative real numbers such that a+2b=6, then the average of the maximum and minimum possible values of (a+b) is

There are two containers of the same volume,first container half-filled with sugar syrup and the second container half-filled with milk.Half the content of the first container is transferred to the second container,and then the half of this mixture is transferred back to the first container.Next, half the content of the first container is transferred back to the second container.Then the ratio of sugar syrup and milk in the second container is

On day one,there are 100 particles in a laboratory experiment.On day n,where n≥2,one out of every n particles produces another particle.If the total number of particles in the laboratory experiment increases to 1000 on day m,then m equals

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

In an election,there were four candidates and \(80\%\) of the registered voters casted their votes.One of the candidates received \(30\%\) of the casted votes while the other three candidates received the remaining casted votes in the proportion \(1\ratio2\ratio3\).If the winner of the election received 2512 votes more than the candidate with the second highest votes, then the number of registered voters was

The number of integers greater than 2000 that can be formed with the digits 0,1,2,3,4,5 using each digit at most once,is

For some natural number n,assume that \((15,000)!\) is divisible by \((n!)!\) The largest possible value of n is

In an examination,there were 75 questions.3 marks were awarded for each correct answer,1 mark was deducted for each wrong answer and 1 mark was awarded for each unattempted question.Rayan scored a total of 97 marks in the examination.If the number of unattempted questions was higher than the number of attempted questions,then the maximum number of correct answers that Rayan could have given in the examination 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 number of integer solutions of the equation \((x^2−10)^{(x2−3x−10)}=1\) is

Mr.Pinto invests one-fifth of his capital at \(6\%\),one-third at \(10\%\) and the remaining at \(1\%\),each rate being simple interest per annum.Then,the minimum number of years required for the cumulative interest income from these investments to equal or exceed his initial capital 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

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 number of ways of distributing 20 identical balloons among 4 children such that each child gets some balloons but no child gets an odd number of balloons, is

For natural numbers x,y, and z, if xy+yz=19 and yz+xz=51, then the minimum possible value of xyz is