List of top Quantitative Aptitude Questions asked in CAT

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 $?

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?

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?

Cities A and B are in different time zones. A is located $3000 \ \text{km}$ 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.

Departure City	Time	Arrival City	Time
B	8:00 am	A	4:00 pm
A	3:00 pm	B	8:00 pm

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 at $50 \ \text{km/h}$.

Shabnam is considering three alternatives to invest her surplus cash for a week. She wishes to guarantee maximum returns on her investment. She has three options, each of which can be utilized fully or partially in conjunction with others.
Option A: Invest in a public sector bank. It promises a return of +0.10%.
Option B: Invest in mutual funds of ABC Ltd. A rise in the stock market will result in a return of +5% while a fall will entail a return of −3%.
Option C: Invest in mutual funds of CBA Ltd. A rise in the stock market will result in a return of −2.5% while a fall will entail a return of +2%.

Let $ S $ be the set of all pairs $(i,j)$ where $ 1 \leq i < j \leq n $ and $ n \geq 4 $. 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.

Mr. David manufactures and sells a single product at a fixed price in a niche market. The selling price of each unit is $ \text{Rs. } 30 $. The cost, in rupees, of producing $ x $ units is:

\[ C(x) = 240 + b x + c x^2 \] where $ b $ and $ c $ are constants.

Mr. David noticed that doubling the daily production from $ 20 $ to $ 40 $ units increases the daily production cost by $ 662\frac{2}{3}\% $. 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 Mr. David can sell as much as he can produce. His objective is to maximize the profit.

If $ p = \frac{1}{3} $ and $ q = \frac{2}{3} $, then what is the smallest odd $ n $ such that $ a_n + b_n<0.01 $?

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?

The price of Darjeeling tea (in rupees per kilogram) is $ 100 + 0.10n $ on the $ n^{\text{th}} $ day of 2007 ($ n = 1, 2, \ldots, 100 $), and then remains constant. The price of Ooty tea (in rupees per kilogram) is $ 89 + 0.15n $ on the $ n^{\text{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?

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 $ f(x) $ at $ x = 10 $?

Which of the following best describes $ a_n + b_n $ for even $ n $?

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?

How many pairs of positive integers $ m, n $ satisfy \[ \frac{1}{m} + \frac{4}{n} = \frac{1}{12}, \] where $ n $ is an odd integer less than 60?

Consider integers $ x, y, 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.

A punching machine is used to punch a circular hole of diameter 2 units from a square sheet of aluminium of width 2 units. The hole is positioned such that the circular hole touches one corner P of the square sheet, and the diameter of the hole originating at P is in line with a diagonal of the square.

An airline has a certain free luggage allowance and charges for excess luggage at a fixed rate per kg. Two passengers, Raja and Praja have 60 kg of luggage between them, and are charged Rs 1200 and Rs 2400 respectively for excess luggage. Had the entire luggage belonged to one of them, the excess luggage charge would have been Rs 5400.

If $\frac{a}{b} = \frac{1}{3}$, $\frac{b}{c} = 2$, $\frac{c}{d} = \frac{1}{2}$, $\frac{d}{e} = 3$ and $\frac{e}{f} = \frac{1}{4}$, then what is the value of $\frac{abc}{def}$?

Consider a sequence where the $n$th term $t_n = \frac{n}{n+2}$, $n = 1, 2, \dots$
The value of $t_3 \times t_4 \times t_5 \times \dots \times t_{53}$ equals:

Which among $2^{1/2}$, $3^{1/3}$, $4^{1/4}$, $6^{1/6}$, and $12^{1/12}$ is the largest?

A survey of 100 people was conducted to find out whether they had read recent issues of Golmal magazine in July, August, and September. Data: