List of top Questions asked in CAT

N is a 3-digit number with non-zero digits. No digit is a perfect square and only 1 of the digits is a prime number. What is the number of factors of the smallest such number possible?
If \(N = 2^3 \times 3^7 \times 5^7 \times 7^9 \times 10!\), then how many factors of N are there which are perfect squares as well as multiples of 420?
How many taps did Clive receive for his question?
The number of distinct integers $n$ for which $\log_{\left(\frac14\right)}(n^2 - 7n + 11)>0$ is:
The number of non-negative values of n for which \(\log_{1/4}(n^2 - 7n + 14)>0\) is ____.
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?
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.
If $\log_{64} x^2 + \log_8 \sqrt{y} + 3 \log_{512} (\sqrt{y} z) = 4$, where $x, y$ and $z$ are positive real numbers, then the minimum possible value of $(x + y + z)$ is:
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 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?
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 \( (a^2 - b^2 + c^2) \).
Ankita is twice as efficient as Bipin, while Bipin is twice as efficient as Chandan. All three of them start together on a job, and Bipin leaves the job after 20 days. If the job got completed in 60 days, the number of days needed by Chandan to complete the job alone, is:
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?
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?
Who had solved the largest number of puzzles by the 20th minute from the start of the competition?

Human decision-making relies on cognitive shortcuts known as heuristics. While these shortcuts allow rapid decisions in uncertain situations, they also cause predictable errors. Understanding how heuristics shape judgment can help in designing better decision-making environments. 

What is the main idea? 

  1. Heuristics should be eliminated from human thinking.
  2. Heuristics are more harmful than useful.
  3. Understanding heuristics helps improve decision systems.
  4. Human decisions cannot be improved.
The ratio of the number of students in the morning shift and afternoon shift of a school was $13 : 9$. After 21 students moved from the morning shift to the afternoon shift, this ratio became $19 : 14$. Next, some new students joined the morning and afternoon shifts in the ratio $3 : 8$ and then the ratio of the number of students in the morning shift and the afternoon shift became $5 : 4$. The number of new students who joined is:
Four companies C1, C2, C3, C4 must interview candidates P, Q, R, S over four time slots (T1--T4).
Each candidate gets one unique slot and each company interviews exactly one candidate per slot.
Constraints:
1. P cannot be interviewed by C1 or C3.
2. Q must be interviewed in either T1 or T4.
3. R must be interviewed before S.
4. C4 only interviews in T2 or T3.
5. No company interviews the same candidate as last year:
(C1--P), (C2--Q), (C3--R), (C4--S).
How many valid interview schedules are possible?
Six employees A, B, C, D, E, F are to be assigned to three projects (P1, P2, P3), each with exactly two employees, under the following constraints:
A and D cannot be together;
B must be with C or F;
E must be in a project different from C;
F cannot be in P1.
How many valid assignments are possible?
A certain amount of money was divided among Pinu, Meena, Rinu, and Seema. Pinu received 20% of the total amount and Meena received 40% of the remaining amount. If Seema received 20% less than Pinu, the ratio of the amounts received by Pinu and Rinu is:
A shopkeeper sells an item at a profit of 20%. If he had bought it at 10% less and sold it for 60 more, his profit would become 60%. What is the cost price of the item?
Let $ABCDEF$ be a regular hexagon and $P$ and $Q$ be the midpoints of $AB$ and $CD$, respectively. Then, the ratio of the areas of trapezium $PBCQ$ and hexagon $ABCDEF$ is:
ABCD is a trapezium in which AB is parallel to DC, AD is perpendicular to AB, and $AB = 3DC$. If a circle inscribed in the trapezium touching all the sides has a radius of 3 cm, then the area, in sq. cm, of the trapezium is
Rahul starts on his journey at 5 pm at a constant speed so that he reaches his destination at 11 pm the same day. However, on his way, he stops for 20 minutes, and after that, increases his speed by 3 km per hour to reach on time. If he had stopped for 10 minutes more, he would have had to increase his speed by 5 km per hour to reach on time. His initial speed, in km per hour, was
The $(x, y)$ coordinates of vertices $P$, $Q$ and $R$ of a parallelogram $PQRS$ are $(-3, -2)$, $(1, -5)$ and $(9, 1)$, respectively. If the diagonal $SQ$ intersects the x-axis at $(a, 0)$, then the value of $a$ is: