List of top Questions asked in CAT

A group of 120 students attend at least one of three workshops: Data, Logic, and Verbal.
48 attend Data, 60 attend Logic, 50 attend Verbal.
20 attend both Data & Logic, 15 attend both Logic & Verbal, 12 attend both Data & Verbal, and 8 attend all three.
How many students attend exactly one workshop?

Four machines A, B, C, D produce items in a ratio.
A produces 40 more than B.
C produces 20% more than A.
D produces half of B.
If total production is 860 items,
how many items did Machine C produce?

Six people — P, Q, R, S, T, U — stand in a line.
P is somewhere ahead of Q.
Exactly two people stand between Q and R.
S is not adjacent to P or R.
T is not in the first or last position.
How many distinct valid arrangements are possible?

The number of non-negative values of n for which \(\log_{1/4}(n^2 - 7n + 14)>0\) is ____.

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.

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 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?

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?

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?

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?

Find the number of real values of x satisfying the equation:
\[ \log_{2}(x^2 - 5x + 6) + \log_{1/2}(x - 2) = 3 \]

A shopkeeper offers a 22% discount on the marked price of chairs. He gives 13 chairs to a customer at the discounted price of 12 chairs. If he still makes a profit of 26%, what is the marked price (MP) of a single chair, assuming its cost price (CP) is Rupees 100?

Find the real value(s) of x that satisfy the equation:
\[ \log_{2}(x^2 - 5x + 6) + \log_{1/2}(x - 2) = 3 \]

The sum of all real values of $k$ for which $(\frac{1}{8})^k \times (\frac{1}{32768})^{\frac{4}{3}} = \frac{1}{8} \times (\frac{1}{32768})^{\frac{k}{3}}$ is

\( 10^{68} \) is divided by 13, the remainder is  is

Amal and Vimal together can complete a task in 150 days, while Vimal and Sunil together can complete the same task in 100 days. Amal starts working on the task and works for 75 days, then Vimal takes over and works for 135 days. Finally, Sunil takes over and completes the remaining task in 45 days. If Amal had started the task alone and worked on all days, Vimal had worked on every second day, and Sunil had worked on every third day, then the number of days required to complete the task would have been

The roots \(\alpha\), \(\beta\) of the equation \(3x^2 + \lambda x - 1 = 0\), satisfy \( \frac{1}{\alpha^2} + \frac{1}{\beta^2} = 15 \). The value of \( (\alpha^3 + \beta^3)^2 \) is

If $(a + b\sqrt{3})^2 = 52 + 30\sqrt{3}$, where $a$ and $b$ are natural numbers, then $a + b$ equals ?

Renu would take 15 days working 4 hours per day to complete a certain task whereas Seema would take 8 days working 5 hours per day to complete the same task. They decide to work together to complete this task. Seema agrees to work for double the number of hours per day as Renu, while Renu agrees to work for double the number of days as Seema. If Renu works 2 hours per day, then the number of days Seema will work, is

If $(a + b\sqrt{n})$ is the positive square root of $(29 - 12\sqrt{5})$, where $a$ and $b$ are integers, and $n$ is a natural number, then the maximum possible value of $(a + b + n)$ is ?

The selling price of a product is fixed to ensure 40% profit. If the product had cost 40% less and had been sold for 5 rupees less, then the resulting profit would have been 50%. The original selling price, in rupees, of the product is

Bina incurs 19% loss when she sells a product at Rs. 4860 to Shyam, who in turn sells this product to Hari. If Bina would have sold this product to Shyam at the purchase price of Hari, she would have obtained 17% profit. Then, the profit, in rupees, made by Shyam is

Gopi marks a price on a product in order to make 20% profit. Ravi gets 10% discount on this marked price, and thus saves Rs 15. Then, the profit, in rupees, made by Gopi by selling the product to Ravi, is