List of top Quantitative Aptitude Questions asked in CAT

Consider the set $S = \{1, 2, 3, \dots, 1000\}$. How many arithmetic progressions can be formed from the elements of $S$ that start with $1$ and end with $1000$ and have at least $3$ elements?
Arun, Barun, and Kiranmala start from the same place and travel in the same direction at speeds of 30, 40, and 60 km/h respectively. Barun starts two hours after Arun. If Barun and Kiranmala overtake Arun at the same instant, how many hours after Arun did Kiranmala start?
An equilateral triangle $BPC$ is drawn inside a square $ABCD$. What is the value of $\angle APD$ in degrees?
When you reverse the digits of the number 13, the number increases by 18. How many other two-digit numbers increase by 18 when their digits are reversed?
The number of solutions of the equation $2x + y = 40$ where both $x$ and $y$ are positive integers and $x \leq y$ is:
Let $f(x) = \max(2x + 1, 3 - 4x)$, where $x$ is any real number. Then the minimum possible value of $f(x)$ is:
The number of employees in Obelix Menhir Co. is a prime number less than 300. The ratio of graduates and above to non-graduates can possibly be:
There are 6 tasks and 6 persons. Task 1 cannot be assigned to person 1 or 2; Task 2 must be assigned to either person 3 or person 4. Every person is assigned one task. How many ways can this assignment be done?
The graph of $y - x$ against $y + x$ is as shown (straight line with slope>0 through origin). Which of the given five graphs shows $y$ against $x$?
The sum of four consecutive two-digit odd numbers, when divided by 10, becomes a perfect square. Which of the following can possibly be one of these four numbers?
A group of 630 children is arranged in rows for a group photograph. Each row contains three fewer children than the row in front of it. Which number of rows is not possible?
The length, breadth, and height of a room are in the ratio $3 : 2 : 1$. If the breadth and height are halved while the length is doubled, then the total area of the four walls of the room will:
If $x = -0.5$, then which of the following has the smallest value?

Ram and Shyam run a race between points A and B, 5 km apart. Ram starts at 9:00 a.m. from A at a speed of 5 km/hr, reaches B, and returns to A at the same speed. Shyam starts at 9:45 a.m. from A at a speed of 10 km/hr, reaches B, and comes back to A at the same speed. 

If $R = \frac{30^{65} - 29^{65}}{30^{64} + 29^{64}}$, then:
If $a_1=1$ and $a_{n+1} - 3a_n + 2 = 4n$, find $a_{100}$.
Rightmost non-zero digits of $30^{270}$ is:
Let $x = \sqrt{4+\sqrt{4+\sqrt{4+......}}}$. Find $x$.
Let $g(x)$ be a function such that $g(x+1)+g(x-1) = g(x)$ for all real $x$. For what $p$ does $g(x+p) = g(x)$ hold for all $x$?
Square floor tiled with equal-size square tiles. Edge tiles are white, interior red. White tile count = red tile count. Possible number of tiles per edge?
A telecom provider hires male and female operators to answer 1000 calls/day. Male can handle 40 calls/day, female 50. Fixed pay: Rs. 250 (male), Rs. 300 (female). Per call pay: Rs. 15 (male), Rs. 10 (female). Must employ more than 7 of the 12 females available. How many male operators minimize cost?
Three Englishmen and three Frenchmen each know one unique secret. Only one Englishman knows French, no Frenchman knows English. They exchange secrets via person-to-person calls so all know all secrets. What is minimum number of calls?
Let $S$ be a set of integers $n$ with $1000 \leq n \leq 1200$ and all digits odd. How many $n \in S$ are divisible by 3?
Rectangular tiles of size $70$ cm × $30$ cm to be placed on floor $110$ cm × $130$ cm, aligned to edges. Max tiles without overhanging?

Circle diameter = 3 cm. AB and MN are diameters, perpendicular. CG ⟂ AB, AE:EB = 1:2, DF ⟂ MN, NL:LM = 1:2. Find DH in cm.