List of top Quantitative Aptitude Questions asked in CAT

In a watch, the minute hand crosses the hour hand for the third time exactly after every 3 hr 18 min and 15 s of normal time. What is the time gained or lost by this watch in one day?
A man has 9 friends: 4 boys and 5 girls. In how many ways can he invite them, if there has to be exactly 3 girls in the invitees?
The points of intersection of three lines \(2x + 3y - 5 = 0\), \(5x - 7y + 2 = 0\) and \(9x - 5y - 4 = 0\)
The price of a Maruti car rises by 30% while the sales of the car come down by 20%. What is the percentage change in the total revenue?
A man travels from A to B at a speed x km/hr. He then rests at B for x hours. He then travels from B to C at a speed 2x km/hr and rests for 2x hours. He moves further to D at a speed twice as that between B and C. He thus reaches D in 16 hr. If distances A-B, B-C and C-D are all equal to 12 km, the time for which he rested at B could be
A man travels three-fifths of a distance AB at a speed 3a, and the remaining at a speed 2b. If he goes from B to A and returns at a speed 5c in the same time, then
Two liquids A and B are in the ratio 5 : 1 in container 1 and 1 : 3 in container 2. In what ratio should the contents of the two containers be mixed so as to obtain a mixture of A and B in the ratio 1 : 1?
In a mile race, Akshay can be given a start of 128 m by Bhairav. If Bhairav can give Chinmay a start of 4 m in a 100 m dash, then who out of Akshay and Chinmay will win a race of one and half miles, and what will be the final lead given by the winner to the loser? (One mile is 1,600 m.)
I bought 5 pens, 7 pencils and 4 erasers. Rajan bought 6 pens, 8 erasers and 14 pencils for an amount which was half more what I had paid. What per cent of the total amount paid by me was paid for the pens?
The figure shows the rectangle ABCD with a semicircle and a circle inscribed inside in it as shown. What is the ratio of the area of the circle to that of the semicircle?

Given the quadratic equation \(x^2 - (A - 3)x - (A - 2)\), for what value of \(A\) will the sum of the squares of the roots be zero?
In a locality, two-thirds of the people have cable TV, one-fifth have VCR, and one-tenth have both. What is the fraction of people having atleast one among cable -TV and VCR?
Once I had been to the post office to buy five-rupee, two-rupee and one-rupee stamps. I paid the clerk Rs. 20, and since he had no change, he gave me three more one-rupee stamps. If the number of stamps of each type that I had ordered initially was more than one, what was the total number of stamps that I had when I left the post office?
The figure shows a circle of diameter AB and radius 6.5 cm. If chord CA is 5 cm long, find the area of triangle ABC.

If n is any odd number greater than 1, then \(n(n^2 - 1)\) is
The cost of diamond varies directly as the square of its weight. Once, this diamond broke into four pieces with weights in the ratio 1 : 2 : 3 : 4. When the pieces were sold, the merchant got Rs. 70,000 less. Find the original price of the diamond.
A wooden box of thickness 0.5 cm, length 21 cm, width 11 cm and height 6 cm is painted on the inside. The expenses of painting are Rs. 70. What is the rate of painting per square centimetres?
From a circular sheet of paper with a radius 20 cm, four circles of radius 5 cm each are cut out. What is the ratio of the uncut to the cut portion?
Instead of a metre scale, a cloth merchant uses a faulty 120 cm scale while buying, but uses a faulty 80 cm scale while selling the same cloth. If he offers a discount of 20%, what is his overall profit percentage?
A cube of side 12 cm is painted red on all the faces and then cut into smaller cubes, each of side 3 cm. What is the total number of smaller cubes having none of their faces painted?

Answer the questions based on the following information. A series \(S_1\) of five positive integers is such that the third term is half the first term and the fifth term is 20 more than the first term. In series \(S_2\), the nth term is defined as the difference between the (n+1)th term and the nth term of series \(S_1\), \(S_2\) is an arithmetic progression with a common difference of 30.

Answer the questions based on the following information. A salesman enters the quantity sold and the price into the computer. Both the numbers are two-digit numbers. But, by mistake, both the numbers were entered with their digits interchanged. Although, the total sales value remained the same, i.e. Rs. 1,148, the total inventory sold got reduced by 54.

Answer the questions based on the following information. A, S, M and D are functions of \(x\) and \(y\), and they are defined as follows.

\(A(x, y) = x + y\)

\(S(x, y) = x - y\)

\(M(x, y) = xy\)

\(D(x, y) = \dfrac{x}{y}, \quad y \neq 0\)

Direction for questions 108 and 109: Answer the questions based on the following information.

In a locality, there are five small cities: A, B, C, D and E. The distances of these cities from each other are as follows.

\(AB = 2\ \text{km}\), \(AC = 2\ \text{km}\), \(AD > 2\ \text{km}\), \(AE > 3\ \text{km}\), \(BC = 2\ \text{km}\), \(BD = 4\ \text{km}\), \(BE = 3\ \text{km}\), \(CD = 2\ \text{km}\), \(CE = 3\ \text{km}\), \(DE > 3\ \text{km}\)

Direction for questions: Answer the questions based on the following information. The data given in the table shows the investment details in country ‘Fortune Land’ of companies A, B, C, D, E and F. Figures in the table are in US dollars in billions.

 ABCDEF
Year 12.54.65.83.1110.67.8
Year 26.77.512.55.617.425.3
Year 311.518.721.27.729.860.1