List of top Quantitative Aptitude Questions asked in CAT

Instead of a metre scale, a cloth merchant uses a 120 cm scale while buying, but uses an 80 cm scale while selling the same cloth. If he offers a discount of 20% on cash payment, what is his overall profit percentage?
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.
If a number 774958A96B is to be divisible by 8 and 9, the respective values of A and B will be
A cube of side 12 cm is painted red on all 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?
Which of the following values of x do not satisfy the inequality $(x^2 - 3x + 2>0)$ at all?

In the given figure, AB is diameter of the circle and points C and D are on the circumference such that $\angle CAD = 30^\circ$ and $\angle CBA = 70^\circ$. What is the measure of $\angle ACD$? 

In the adjoining figure, AC + AB = 5AD and AC – AD = 8. Then the area of the rectangle ABCD is

PQRS is a square. SR is a tangent (at point S) to the circle with centre O and TR = OS. Then the ratio of area of the circle to the area of the square is:

AB $\perp$ BC, BD $\perp$ AC and CE bisects $\angle C$, $\angle A = 30^\circ$. Then what is $\angle CED$?

ABCD is a square of area $4$, which is divided into four non-overlapping triangles as shown in the figure. Then the sum of the perimeters of the triangles is: 

Four sisters — Suvarna, Tara, Uma and Vibha are playing a game such that the loser doubles the money of each of the other players from her share. They played four games and each sister lost one game in alphabetical order. At the end of fourth game, each sister had Rs. 32.

$le(x, y) = \text{Least of} \ (x, y)$

$mo(x) = |x|$

$me(x, y) = \text{Maximum of} \ (x, y)$

What is the number $x$?
Statement I
I. The LCM of $x$ and 18 is 36.
Statement II
II. The HCF of $x$ and 18 is 2.
Is $x + y - z + t$ even?
Statement I
I. $x + y + t$ is even.
Statement II
II. $t$ and $z$ are od(d)
What is the first term of an arithmetic progression of positive integers?
Statement I
I. Sum of the squares of the first and the second term is 116.
Statement II
II. The fifth term is divisible by 7.
What is the price of bananas?
Statement I
I. With Rs. 84, I can buy 14 bananas and 35 oranges.
Statement II
II. If price of bananas is reduced by 50, then we can buy 48 bananas in Rs. 12.
What is the length of rectangle ABCD?
Statement I
I. Area of the rectangle is 48 square units.
Statement II
II. Length of the diagonal is 10 units.
What is the value of $x$, if $x$ and $y$ are consecutive positive even integers?
Statement I
I. $(x - y)^2 = 4$
Statement II
II. $(x + y)^2<100$
If $x, y$ and $z$ are real numbers, is $z - x$ even or odd?
Statement I I. $xyz$ is od(d)
Statement II
II. $xy + yz + zx$ is even.
What is the area of the triangle?
Statement I
I. Two sides are 41 cm each.
Statement II
II. The altitude to the third side is 9 cm long.
What is the profit percentage?
Statement I
I. The cost price is 80 of the selling price.
Statement II
II. The profit is Rs. 50.
A, B, C and D are four towns any three of which are non-collinear. Then the number of ways to construct three roads each joining a pair of towns so that the roads do not form a triangle is
Largest value of \( \min(2 + x^2, 6 - 3x) \), when \( x>0 \), is
A man can walk up a moving 'up' escalator in 30 s. The same man can walk down this moving 'up' escalator in 90 s. Assume that his walking speed is the same upwards and downwards. How much time will he take to walk up the escalator, when it is not moving?
What is the value of \( m \) which satisfies \( 3m^2 - 21m + 30<0 \)?