Reasoning

Concept:
This question is based on syllogistic reasoning, which involves drawing logical conclusions from given statements. In syllogism problems, we analyze relationships between different groups or categories using logical rules. Important principles used in syllogism:

• The statement "All A are B" means every member of set A belongs to set B.
• The statement "Some B are C" means at least one member of set B belongs to set C.
• However, a statement about "some" elements cannot be generalized to represent "all" elements.

Step 1: Analyze the first statement.
This means the entire group of Teachers lies within the group Mentors.
Step 2: Analyze the second statement.
This means that only a portion of Mentors are Authors. It does not imply that all Mentors are Authors.

Step 3: Check the conclusion.
The conclusion states: But from the given information, we only know that:

• Teachers belong to the group of Mentors.
• Some Mentors are Authors.

It is possible that:

• The Mentors who are Authors are not Teachers.
• Teachers may belong to the portion of Mentors that are not Authors.

Therefore, the conclusion cannot be guaranteed.
Step 4: Logical interpretation using set relationships.
But there is no definite relation that confirms: Hence, the conclusion is not logically certain.
Step 5: Selecting the correct answer.

Concept:
Direction sense questions test the ability to track movements and determine the final position relative to the starting point. While solving such problems, it is helpful to imagine the directions on a compass or draw a simple diagram. The four primary directions are:

• North (N)
• South (S)
• East (E)
• West (W)

Important rules:

• When a person is facing South, turning left leads to the East.
• When a person is facing East, turning left leads to the North.

Step 1: Start from the initial position.
Assume the man starts from point A. He first walks: He reaches point B.
Step 2: First left turn.
When a person is facing South, a left turn leads to the East. He walks: He reaches point C.

Step 3: Second left turn.
Now he is facing East. Turning left from East leads to the North. He walks: He reaches point D.
Step 4: Determine the final position relative to the starting point.
The movements were: The 5 km South and 5 km North cancel each other out. Therefore, the final position is simply:
Step 5: Selecting the correct answer.
Thus, the man is located to the: of the starting point.

Concept:
Number series questions often follow a hidden pattern based on arithmetic operations such as addition, subtraction, multiplication, powers, or combinations of these operations. One common pattern is a sequence where each term is obtained by multiplying the previous term by a constant and then adding or subtracting a fixed number. Another useful way to analyze number series is to examine:

• Differences between consecutive terms
• Multiplicative relationships
• Patterns involving powers of numbers

Step 1: Observe the pattern in the given series.
Let us check if each term follows a multiplication pattern. Thus, the rule is:
Step 2: Apply the pattern to find the next term.


Step 3: Verify the pattern using another perspective.
The sequence can also be written as: Therefore, the next term should be:
Step 4: Selecting the correct answer.
Thus, the missing number in the series is 127.