List of top Quantitative Aptitude Questions asked in CAT

A mixture of coffee and cocoa, 16% of which is coffee, costs Rs 240 per kg. Another mixture of coffee and cocoa, of which 36% is coffee, costs Rs 320 per kg. If a new mixture of coffee and cocoa costs Rs 376 per kg, then the quantity, in kg, of coffee in 10 kg of this new mixture is:
The average number of copies of a book sold per day by a shopkeeper is 60 in the initial seven days and 63 in the initial eight days, after the book launch. On the ninth day, she sells 11 copies less than the eighth day, and the average number of copies sold per day from the second day to the ninth day becomes 66. The number of copies sold on the first day of the book launch is:

If \((2m+n) + (2n+m)=27\), find the maximum value of \((2m-3)\), assuming m and n are positive integers. 
 

A container has a mixture of milk and water in the ratio 5 : 2. If 14 liters of this mixture is removed and replaced with water, the ratio becomes 5 : 4. What is the initial quantity of the mixture?
There are 4 people M, S, P, R.
P gets 20% of the total.
M gets 40% of the remaining amount.
S gets 20% less than M.
R gets the remaining amount.
Find the ratio P : R.
Using digits 1 to 6 (each at most once), how many 4-digit numbers can be formed that are divisible by 4?
A and B can complete a work in 12 days and 18 days respectively. They start together, but A leaves after 4 days. How many more days will B take to finish the remaining work?
A container contains only milk. 2/3 of the mixture is removed and replaced with water. This process is done once and then repeated another 3 times. What is the final ratio of milk and water?
If the length of each side of a rhombus is 36 cm, and the area of the rhombus is 396 cm\(^2\), then what is the absolute value of the difference between the lengths of its diagonals?
In a cafeteria, there are 5 breads. One can choose 1 bread from the available breads, either small or large sized, and can choose up to 2 sauces from 6 available sauces. What is the number of different ways one can place an order?
The number of non-negative values of n for which \(\log_{1/4}(n^2 - 7n + 14)>0\) is ____.
Arun, Tarun and Varun work for 24, 21 and 15 days respectively and get paid 2160, 2400 and 2160 rupees respectively. They get paid the same even if they work for a partial day. If the work has to be completed within 10 days or less, what is the minimum amount that has to be paid to complete the entire task?
Stocks A, B and C, at 120, 90 and 80 rs respectively. A trader holds a portfolio consisting 60 shares of A, 20 of B and C together. If total value is 33000 what is the number of shares he holds.
In a class there were more than 10 boys than a certain number of girls. After 40% of the girls and 60% of the boys left, the remaining number of girls were 8 more than the remaining boys. Find the possible number of students initially in the class.
Find the real value(s) of x that satisfy the equation:
\[ \log_{2}(x^2 - 5x + 6) + \log_{1/2}(x - 2) = 3 \]
Given that a, b, and c are real numbers satisfying the equations:

\(2a - 5b + 11c = 0\)
\(11a + 10b - 2c = 5\)
Find the value of the expression \( (a^2 - b^2 + c^2) \).
Find the number of real values of x satisfying the equation:
\[ \log_{2}(x^2 - 5x + 6) + \log_{1/2}(x - 2) = 3 \]
A 200-litre container holds a solution that is 30% acid and the rest water. The solution undergoes the following three processes sequentially:
1. 20% of the water content is evaporated.
2. From the remaining mixture, 10% of the acid content is chemically extracted and removed.
3. Finally, 15% of the resulting solution is removed and replaced with water.
What is the volume of acid in the final solution?
In the sequence 1, 3, 5, 7, ..., k, ..., 57, the sum of the numbers up to k, excluding k, is equal to the sum of the numbers from k up to 57, also excluding k. What is k?
The sum of all possible real values of $x$ for which \[ \log_{x-3}(x^2 - 9) = \log_{x-3}(x + 1) + 2, \] is
The set of all real values of $x$ for which $(x^2 - |x+9| + x)>0$ is:
The ratio of expenditures of Lakshmi and Meenakshi is $2 : 3$, and the ratio of income of Lakshmi to expenditure of Meenakshi is $6 : 7$. If excess of income over expenditure is saved by Lakshmi and Meenakshi, and the ratio of their savings is $4 : 9$, then the ratio of their incomes is:
If $9^{x^2+2x-3} - 4\bigl(3^{x^2+2x-2}\bigr) + 27 = 0$, then the product of all possible values of $x$ is:
The equations $3x^2 - 5x + p = 0$ and $2x^2 - 2x + q = 0$ have one common root. The sum of the other roots of these two equations is:
In the set of consecutive odd numbers $\{1, 3, 5, \ldots, 57\}$, there is a number $k$ such that the sum of all the elements less than $k$ is equal to the sum of all the elements greater than $k$. Then, $k$ equals?