Mu Sigma Aptitude Puzzle: Previous Years' Questions with Answers 2024

Mu Sigma, a renowned analytics and decision sciences firm, is known for its rigorous placement process that often includes challenging aptitude and reasoning questions. Candidates aspiring to join Mu Sigma must prepare themselves for a variety of puzzles and logical reasoning problems. Here, we present some selected questions from previous years' Mu Sigma placement papers along with detailed solutions.

Mu Sigma Technical HR Interview Procedure: Apart from the written aptitude test, candidates also undergo technical and HR interviews as part of the selection process. The technical interview assesses candidates' knowledge in areas related to analytics, mathematics, and programming. On the other hand, the HR interview evaluates candidates' communication skills, problem-solving abilities, and their fit within the organizational culture of Mu Sigma.

Aptitude and Reasoning Questions:

Mu Sigma Placement Paper-Questions with answers
1. Sum of A and B is given by
A) *(@(A, B),2)
B) /(@(A,B),2)
C) @(*(A,B),2)
D) @(/(A,B),2
Ans. A.

Solution: he expression provided for the sum of A and B is:

A) $\ast (\mathrm{@}(�,�),2)$

Let's break down the expression:

• $\mathrm{@}$ represents an arithmetic operation (addition, subtraction, multiplication, or division).
• $\ast$ represents the first operand.
• $\mathrm{@}$ represents the second operand.

So, the expression can be interpreted as: "Perform an operation (@) on A and B, and then multiply the result by 2."

Given that we're looking for the sum of A and B, the correct operation to represent addition is likely multiplication (*), followed by multiplying the result by 2.

Therefore, the correct answer is:

A) $\ast (\mathrm{@}(�,�),2)$

2. Let x<0, 0<y<1, Z>1 which of the following is false:
A) (x2-z2)has to be positive.
B) yz can be less than one.
C) xy can never be zero
D) (y2-z2) is always negative
Ans. A.

Solution :

Let's evaluate each statement:

A) $({�}^2-{�}^2)$ has to be positive. Given $�<0$ and $�>1$, ${�}^2$ will always be positive and ${�}^2$ will always be positive since squaring any real number gives a positive result. However, ${�}^2$ will be greater than ${�}^2$ because $�>1$. Therefore, the difference $({�}^2-{�}^2)$ will always be negative. So, statement A is false.

B) $��$ can be less than one. Since $0<�<1$ and $�>1$, the product $��$ will always be less than $�$ but greater than 0. So, statement B is true.

C) $��$ can never be zero. Given $�<0$ and $0<�<1$, the product $��$ will always be negative because one of the factors is negative. Therefore, statement C is true.

D) $({�}^2-{�}^2)$ is always negative. Given $0<�<1$ and $�>1$, both ${�}^2$ and ${�}^2$ will be less than 1 and greater than 1, respectively. Subtracting a number greater than 1 from a number less than 1 will always result in a negative value. So, statement D is true.

Thus, the false statement is A) $({�}^2-{�}^2)$ has to be positive

3. If A’s income is 25% less than B’s ,by what % is B’s income greater than that of A ?
A) 35%
B) 25%
C) 30%
D) None of these
Ans. D.

Solution: Let's solve this problem step by step:

Let's assume B's income is 100 units (to make the calculation simpler).

If A's income is 25% less than B's, then A's income would be 75 units (since 25% of 100 is 25).

Now, we need to find by what percentage B's income is greater than A's.

The difference between B's income (100 units) and A's income (75 units) is 25 units.

To find the percentage difference, we'll divide the difference (25 units) by A's income (75 units) and then multiply by 100 to get the percentage:

$\text{Percentage difference}=\left(\frac{25}{75}\right)\times 100=\frac{1}{3}\times 100=33.33\mathrm{\%}$

Therefore, B's income is 33.33% greater than A's income.

Since none of the provided options exactly match the calculated percentage, the correct answer is:

D) None of these

Directions for Questions Nos: 4 to 5

Kya-Kya is an island in the south pacific .The inhabitants of Kya-Kya always Answer any question with two sentences, one of which is always true and other is always false.

4 You are walking on a road and come to a fork. You ask the inhabitants Ram, Laxman, Lila,”Which road will take me to the village?”
Ram says,”I never speak to strangers. I am new to this place”
Laxman says,”I am married to Lila. Take the left road”.
Lila says,”I am married to ram. He is not new to this place”
Which of the following is true?
A) Left road takes you to the village
B) Right road takes you to the village
C) Lila is married to laxman
D) None of above
Ans. A.
Ram stated that he never talked to strangers, but he spoke to a stranger. This contradiction indicates that his initial statement is false. Consequently, his other statement must be true. Following this logic, Lila's second statement is false, making her first statement true, indicating she is married to Ram. Consequently, Laxman's first statement is false, leading to the conclusion that his second statement is true, advising to take the left road..

Another way -

Let's analyze the statements made by Ram, Laxman, and Lila:

1. Ram says, "I never speak to strangers. I am new to this place."

   • If Ram never speaks to strangers, then his statement about being new to the place must be false, implying that he is not new to the place.
   • Thus, Ram's true statement is: "I never speak to strangers."
   • This means his false statement is: "I am new to this place."

2. Laxman says, "I am married to Lila. Take the left road."

   • If Laxman is married to Lila, then his statement about taking the left road must be true.
   • Thus, Laxman's true statement is: "I am married to Lila."
   • This means his false statement is: "Take the left road."

3. Lila says, "I am married to Ram. He is not new to this place."

   • If Lila is married to Ram, then her statement about Ram not being new to the place must be true.
   • Thus, Lila's true statement is: "He is not new to this place."
   • This means her false statement is: "I am married to Ram."

From the analysis:

• Ram's true statement implies that he is not new to the place.
• Laxman's true statement implies that the left road leads to the village.

Therefore, the correct answer is:

A) Left road takes you to the village

5. You find that your boat is stolen.You question three inhabitants of the island and they reply as follows:
John says,”I didn’t do it. Mathew didn’t do it”
Matthew says,”I didn’t do it. Krishna didn’t do it.”
Krishna says,”I didn’t do it .I don’t know who did it.”
Who stole your boat?
A) John
B) Matthew
C) Krishna
D) None of them.
Solution: 

Let's analyze the statements made by John, Matthew, and Krishna:

1. John says, "I didn’t do it. Mathew didn’t do it."

   • If John is telling the truth, then both he and Mathew are innocent.
   • If John is lying, then either he or Mathew could be guilty.

2. Matthew says, "I didn’t do it. Krishna didn’t do it."

   • If Matthew is telling the truth, then both he and Krishna are innocent.
   • If Matthew is lying, then either he or Krishna could be guilty.

3. Krishna says, "I didn’t do it. I don’t know who did it."

   • If Krishna is telling the truth, then he is innocent and genuinely doesn't know who stole the boat.
   • If Krishna is lying, then he could be guilty.

Since we can't definitively determine who is lying and who is telling the truth, we need to consider all possibilities:

• If John is lying, then either he or Mathew is guilty.
• If Matthew is lying, then either he or Krishna is guilty.
• If Krishna is lying, then he could be guilty.

However, if Krishna is telling the truth, then none of them are guilty.

Given this uncertainty, the only reasonable conclusion is:

D) None of them.

Since we cannot determine the truthfulness of the statements with certainty, we cannot identify the thief based solely on the provided information

6. Write a query to display the name of the students whose total marks is divisible by 25 (total marks may be 175, 200, 150…)

Sol . SELECT name FROM students WHERE total_marks % 25 = 0;

7. P(S1)
a++;
P(S2)
v++;
V(S2)
V(S1)
P-wait, V-signal, S1 and S2 are semaphores. Consider two threads running. Is there a deadlock .If yes in which situation does the deadlock occur.

To analyze the possibility of a deadlock, let's first understand the operations in the provided code snippet:

• P(S1): This operation decrements the semaphore S1. If S1 is already 0, the thread will block until S1 becomes greater than 0.
• a++: This operation increments the variable a.
• P(S2): This operation decrements the semaphore S2. If S2 is already 0, the thread will block until S2 becomes greater than 0.
• v++: This operation increments the variable v.
• V(S2): This operation increments the semaphore S2.
• V(S1): This operation increments the semaphore S1.
• P-wait: This operation represents the thread waiting for a condition to be true.
• V-signal: This operation represents the thread signaling that a condition has been met.

Now, let's analyze the possible scenarios:

1. If S1 and S2 are initialized to 1:

   • Thread 1 executes P(S1) and then a++.
   • Thread 2 executes P(S2) and then v++.
   • Both threads increment their respective variables and semaphores and proceed without deadlock.

2. If S1 and S2 are initialized to 0:

   • Thread 1 executes P(S1) and blocks.
   • Thread 2 executes P(S2) and blocks.
   • Neither thread can proceed, leading to a deadlock.

3. If S1 is initialized to 1 and S2 is initialized to 0:

   • Thread 1 executes P(S1) and then a++.
   • Thread 2 blocks on P(S2).
   • Thread 1 executes V(S1) and then V(S2).
   • Thread 2 proceeds after V(S2) and then executes v++.
   • Both threads proceed without deadlock.

4. If S1 is initialized to 0 and S2 is initialized to 1:

   • Thread 1 blocks on P(S1).
   • Thread 2 executes P(S2) and then v++.
   • Thread 2 executes V(S2) and then V(S1).
   • Thread 1 proceeds after V(S1) and then executes a++.
   • Both threads proceed without deadlock.

Therefore, deadlock occurs only in scenario 2 when both S1 and S2 are initialized to 0, and both threads block waiting for the other semaphore to be incremented

8. How do you find the port number of the remote host?

To find the port number of a remote host, you typically need to know which service or application you are trying to connect to on that host. Once you know the service or application, you can determine the port number associated with it.

Here are some common methods to find the port number of a remote host:

1. Documentation: Many services and applications document the default port numbers they use. You can consult the documentation of the service or application you are interested in to find out which port it uses.

2. Network Scanning Tools: Network scanning tools like Nmap or Netcat can be used to scan for open ports on a remote host. By running a port scan on the remote host, you can identify which ports are open and which services are running on those ports.

3. Online Port Lookup Tools: There are online services and websites that allow you to look up the port number associated with a specific service or application. You can search for the service or application name, and the tool will provide you with the default port number.

4. Protocol Standards: Some network protocols have assigned port numbers defined by standards organizations. For example, HTTP typically uses port 80, HTTPS uses port 443, SSH uses port 22, and so on. You can refer to the relevant protocol standard to find out the default port number.

5. Configuration Files: In some cases, the port number may be specified in configuration files on the remote host. For example, web servers often have configuration files where the port number is defined.

6. Network Administrators: If you have access to the network or system administrators of the remote host, you can ask them directly for the port number information.

Using one or more of these methods, you can usually determine the port number associated with a remote service or application

9. (Date; who)>logfile
Date; who>logfile
What is the difference between the two statements.

The two statements provided are used to redirect output to a file named "logfile" in a Linux or Unix-like shell environment. However, there is a subtle difference between the two statements:

1. Date; who > logfile:

   • This statement uses a semicolon (;) to separate two commands: date and who.
   • The date command prints the current date and time.
   • The who command displays information about currently logged-in users.
   • The output of both commands is redirected to the "logfile". If the "logfile" already exists, it will be overwritten with the new output.

2. Date; who > logfile:

   • This statement uses a semicolon (;) to separate two commands: date and who.
   • The date command prints the current date and time.
   • The who command displays information about currently logged-in users.
   • The output of both commands is appended to the "logfile". If the "logfile" already exists, the new output will be appended to the end of the file without overwriting existing content.

In summary, the difference lies in how the output is handled: the first statement overwrites the contents of the "logfile", while the second statement appends to the existing content of the "logfile".

10. How do you find the machine MAC address
A) 0
B) 8
C) 16
D) 32
Ans. A

11. How many children did not try any of the rides. ?
A) 5
B) 10
C) 15
D) 20
Ans. 15.

12. kids * 3 rides = Rs. 60
(55-20=)35 kids * 2 rides = Rs. 70
60 + 70 = Rs. 130
So, Rs. (145 – 130 = ) 15 are left for the other (85 – 55 = ) 30 kids . so only 15 of them can take a ride and rest 15 will be left out.
145 rides were taken. 20 of them took all three, i.e. Rs. 60 were spent, so 145-60= Rs. 85 are left for the others. Total kids were 85, so rest were 65. out of these 65,

12. How many children took exactly one ride?
A) 5
B) 10
C) 15
D) 20
Ans. 15

13. Four cities are connected by a road network as shown in the figure. In how many ways can you start from any city and come back to it without travelling on the same road more than once ?
A) 8
B) 12
C) 16
D) 20
Ans. 12.
Consider the top city, the following are the 3 routes possible, starting from the leftmost edge. Since there are 3 edges emanating from each city and the figure is perfectly symmetrical, these 3 routes are possible from each edge, hence for any given city, the total number of routes = 4 * 3 = 12.

14. Directions for question nos 14 to 15
A, B, and C are three numbers, Let
@(A, B)= Average of A and B
*(A, B)=Product of A and B
/(A, B)=A divided by B

15  If A=2 and B=4 the value of @( / (*(A,B),B),A) would be
A) 2
B) 4
C) 6
D) 16
Ans. 2

16. What is the output of the following code?
x=0;y=1;
for(j=1;j<4;j++){
x=x+j;
y*=j;
}

Let's trace through the code:

1. Initialize variables:

   • x is initialized to 0.
   • y is initialized to 1.

2. Enter the loop:

   • j starts at 1.
   • In the first iteration (when j = 1):
     • x is updated: x = x + j = 0 + 1 = 1.
     • y is updated: y = y * j = 1 * 1 = 1.
   • In the second iteration (when j = 2):
     • x is updated: x = x + j = 1 + 2 = 3.
     • y is updated: y = y * j = 1 * 2 = 2.
   • In the third iteration (when j = 3):
     • x is updated: x = x + j = 3 + 3 = 6.
     • y is updated: y = y * j = 2 * 3 = 6.

3. Exit the loop:

   • The loop terminates when j is no longer less than 4.

Therefore, after the loop, the final values of variables x and y are:

• x = 6
• y = 6

17. There is a 200 miles long tunnel. one train enters the tunnel at a speed of 200mph while the other trains enter the tunnel in the opposite direction at a speed of 1000 mph. A bee travels at a speed of 1500 mph enters the tunnel goes to and back until it reaches the train. What is the distance covered by the bee when the two train collides (the bee survives)

18. List the two advantages of views.

18. Advantages of Views:

• Data Abstraction: Views provide a layer of abstraction by allowing users to interact with a subset of data from one or more tables. This abstraction helps in simplifying complex data structures and makes it easier to query and manipulate data.
• Enhanced Security: Views can be used to restrict access to sensitive or confidential data by exposing only specific columns or rows to users based on their privileges. This helps in enforcing security policies and ensuring that users only have access to the data they are authorized to see

19. Which layer is encryption and decryption done

Encryption and decryption are typically performed at the presentation layer of the OSI (Open Systems Interconnection) model or the application layer of the TCP/IP model. These layers are responsible for encoding and decoding data to ensure secure communication over the network

20. What are the various modes used to send data over the network

19. Modes Used to Send Data Over the Network: There are several modes used to send data over the network, including:

• Unicast: Data is sent from one sender to one receiver.
• Multicast: Data is sent from one sender to multiple specified receivers.
• Broadcast: Data is sent from one sender to all devices on the network.
• Anycast: Data is sent from one sender to the nearest of several receivers, typically used for load balancing or redundancy purposes