List of top Quantitative Aptitude Questions asked in CAT

A shop stores \(x\) kg of rice. The first customer buys half this amount plus half a kg of rice. The second customer buys half the remaining amount plus half a kg of rice. Then the third customer also buys half the remaining amount plus half a kg of rice. Thereafter, no rice is left in the shop. Which of the following best describes the value of \(x\)?
If the roots of the equation \(x^3 - ax^2 + bx - c = 0\) are three consecutive integers, then what is the smallest possible value of \(b\)?
Find: \(\sum_{k=1}^{2007} \sqrt{1 + \frac{1}{k^2} + \frac{1}{(k+1)^2}}\)
The number of common terms in the two sequences \(17, 21, 25, \ldots, 417\) and \(16, 21, 26, \ldots, 466\) is:
Let \(f(x)\) be a function satisfying \(f(x) f(y) = f(xy)\) for all real \(x, y\). If \(f(2) = 4\), then what is the value of \(f\left( \frac12 \right)\)?
Let \(a_1=p\) and \(b_1=q\), where \(p\) and \(q\) are positive quantities.
Define \(a_n=pb_{n-1},\ b_n=qb_{n-1}\), for even \(n>1\), and \(a_n=pa_{n-1},\ b_n=qa_{n-1}\), for odd \(n>1\).
If \(p=1/3\) and \(q=2/3\), then what is the smallest odd \(n\) such that \(a_n+b_n<0.01\)?
Let \(a_1=p\) and \(b_1=q\), where \(p\) and \(q\) are positive quantities.
Define \(a_n=pb_{n-1},\ b_n=qb_{n-1}\), for even \(n>1\), and \(a_n=pa_{n-1},\ b_n=qa_{n-1}\), for odd \(n>1\).
Which of the following best describes \(a_n+b_n\) for even \(n\)?
A quadratic function \(f(x)\) attains a maximum of 3 at \(x=1\). The value of the function at \(x=0\) is 1. What is the value of \(f(x)\) at \(x=10\)?
The price of Darjeeling tea (in rupees per kilogram) is \(100+0.10n\), on the \(n\)th day of 2007 (\(n=1, 2, \ldots, 100\)), and then remains constant. On the other hand, the price of Ooty tea (in rupees per kilogram) is \(89+0.15n\), on the \(n\)th day of 2007 (\(n=1, 2, \ldots, 365\)). On which date in 2007 will the prices of these two varieties of tea be equal?
Consider four digit numbers for which the first two digits are equal and the last two digits are also equal. How many such numbers are perfect squares?
Rahim plans to draw a square JKLM with a point O on the side JK but is not successful. Why is Rahim unable to draw the square?

A: The length of OM is twice that of OL.

B: The length of OM is 4 cm
Consider integers x, y and z. What is the minimum possible value of \( x^2 + y^2 + z^2 \)?

A: \( x + y + z = 89 \)

B: Among x, y, z two are equal.
ABC Corporation is required to maintain at least 400 Kilolitres of water at all times in its factory, in order to meet safety and regulatory requirements. ABC is considering the suitability of a spherical tank with uniform wall thickness for the purpose. The outer diameter of the tank is 10 meters. Is the tank capacity adequate to meet ABC's requirements?

A: The inner diameter of the tank is at least 8 meters.

B: The tank weighs 30,000 kg when empty, and is made of a material with density of 3 gm/cc.
The average weight of a class of 100 students is 45 kg. The class consists of two sections, I and II, each with 50 students. The average weight, \( W_I \), of Section I is smaller than the average weight, \( W_{II} \), of Section II. If the heaviest student, say Deepak, of Section II is moved to Section I, and the lightest student, say Poonam, of Section I is moved to Section II, then the average weights of the two sections are switched, i.e., the average weight of Section I becomes \( W_{II} \) and that of Section II becomes \( W_I \). What is the weight of Poonam?

A: \( W_{II} - W_I = 1.0 \)

B: Moving Deepak from Section II to I (without any move from I to II) makes the average weights of the two sections equal.
How many pairs of positive integers \( m, n \) satisfy \( \dfrac{1}{m} + \dfrac{4}{n} = \dfrac{1}{12} \), where \( n \) is an odd integer less than 60?
A confused bank teller transposed the rupees and paise when he cashed a cheque for Shailaja, giving her rupees instead of paise and paise instead of rupees. After buying a toffee for 50 paise, Shailaja noticed that she was left with exactly three times as much as the amount on the cheque. Which of the following is a valid statement about the cheque amount?
Suppose you have a currency, named Miso, in three denominations: 1 Miso, 10 Misos and 50 Misos. In how many ways can you pay a bill of 107 Misos?
A function \( f(x) \) satisfies \( f(1) = 3600 \), and \( f(1) + f(2) + \ldots + f(n) = n^2 f(n) \), for all positive integers \( n > 1 \). What is the value of \( f(9) \)?
Ten years ago, the ages of the members of a joint family of eight people added up to 231 years. Three years later, one member died at the age of 60 years and a child was born during the same year. After another three years, one more member died, again at 60, and a child was born during the same year. The current average age of this eight-member joint family is nearest to

Directions for the following two questions:

Mr. David manufactures and sells a single product at a fixed price in a niche market. The selling price of each unit is Rs. 30. On the other hand, the cost, in rupees, of producing x units is \( 240 + bx + cx^2 \), where b and c are some constants. Mr. David noticed that doubling the daily production from 20 to 40 units increases the daily production cost by 66.67%. However, an increase in daily production from 40 to 60 units results in an increase of only 50% in the daily production cost. Assume that demand is unlimited and that Mr. David can sell as much as he can produce. His objective is to maximize the profit.

Directions for the following two questions:

Let \( S \) be the set of all pairs \( (i, j) \) where \( 1 \leq i < j \leq n \), and \( n \geq 4 \) (\( i \) and \( j \) are natural numbers). Any two distinct members of \( S \) are called “friends” if they have one constituent of the pairs in common and “enemies” otherwise.

For example, if \( n = 4 \), then \( S = \{(1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)\} \). Here, \( (1, 2) \) and \( (1, 3) \) are friends, \( (1,2) \) and \( (2, 3) \) are also friends, but \( (1,4) \) and \( (2, 3) \) are enemies.

Directions for the following two questions: Cities A and B are in different time zones. A is located 3000 km east of B. The table below describes the schedule of an airline operating non-stop flights between A and B. All the times indicated are local and on the same day.

Assume that planes cruise at the same speed in both directions. However, the effective speed is influenced by a steady wind blowing from east to west. It reduces or increases the speed of plane by 50 km per hour depending on direction of flight.

DepartureArrival
CityTimeCityTime
B8:00 AMA3:00 PM
A4:00 PMB8:00 PM
Two circles with centres P and Q cut each other at two distinct points A and B. The circles have the same radii and neither P nor Q falls within the intersection of the circles. What is the smallest range that includes all possible values of the angle AQP in degrees?
Consider the set \( S = \{2, 3, 4, \ldots, 2n+1\} \), where \( n \) is a positive integer larger than 2007. Define \( X \) as the average of the odd integers in \( S \) and \( Y \) as the average of the even integers in \( S \). What is the value of \( X - Y \)?

In a tournament, there are \( n \) teams \( T_1, T_2, \ldots, T_n \), with \( n > 5 \). Each team consists of \( k \) players, \( k > 3 \). The following pairs of teams have one player in common: \( T_1 \) & \( T_2 \), \( T_2 \) & \( T_3 \), \( \ldots \), \( T_{n-1} \) & \( T_n \), \( T_n \) & \( T_1 \). No other pair of teams has any player in common. How many players are participating in the tournament, considering all the \( n \) teams together?