Number Patterns

Step 1: Concept
Number series with increasing differences.
Step 2: Analysis
6-2=4, 12-6=6, 20-12=8, 30-20=10. The differences are 4, 6, 8, 10.
Step 3: Conclusion
The next difference must be 12. So, 30 + 12 = 42.
Final Answer: (B)

Step 1: Concept
Number series based on cubes of natural numbers.
Step 2: Analysis
, , , .
Step 3: Conclusion
The next number is .
Final Answer: (B)

Step 1: Concept
Alphabetical shift coding.
Step 2: Analysis
M+1=N, O+1=P, O+1=P, N+1=O. (Each letter moves to the next alphabet).
Step 3: Conclusion
S+1=T, U+1=V, N+1=O.
Final Answer: (A)

Step 1: Concept
Alternating number series.
Step 2: Analysis
The pattern alternates between adding 3 and subtracting 2:
7 (+3) = 10; 10 (-2) = 8; 8 (+3) = 11; 11 (-2) = 9; 9 (+3) = 12.
Step 3: Conclusion
The next step is to subtract 2: 12 - 2 = 10.
Final Answer: (B)

Step 1: Understand the Concept
This problem involves identifying a pattern within a numerical sequence. By observing the numbers 4, 9, 16, and 25, we can see that each number is the result of multiplying a natural number by itself. This means the series is specifically built using the squares of consecutive natural numbers starting from 2.

Step 2: Analysis of the Series
Let's break down the given numbers to find the base values:
* The first number is 4, which is ( )
* The second number is 9, which is ( )
* The third number is 16, which is ( )
* The fourth number is 25, which is ( )
The sequence of base numbers being squared is 2, 3, 4, 5.

Step 3: Conclusion
Following the established pattern of consecutive natural numbers, the next base number after 5 is 6. To find the missing number in the series, we must calculate the square of 6:
Next number = .
Therefore, the missing number that completes the pattern is 36.

Final Answer: (C)

Step 1: Understand the Concept
This problem is solved using the "Odd Days" concept in calendars. An ordinary year has 365 days. When divided by 7 (the number of days in a week), we get 52 weeks and a remainder of 1 day ( ). This remaining day is called an "odd day." In a non-leap year, any given date shifts forward by exactly one day in the following year.

Step 2: Analysis of the Given Year
We are looking at the transition from 1st January 2023 to 1st January 2024. First, we check if 2023 is a leap year. Since 2023 is not divisible by 4, it is a non-leap (ordinary) year consisting of 365 days.
Analysis: 365 days = 52 weeks + 1 odd day.
Since we are starting on 1st January 2023 and ending on 1st January 2024, we have completed one full ordinary year, which results in 1 odd day.

Step 3: Conclusion
Because there is 1 odd day, the day of the week for the same date in the next year will be one day ahead of the current day. If 1st January 2023 was a Sunday, then 1st January 2024 will be Sunday + 1 day = Monday.

Final Answer: (A)

Step 1: Concept
This is an alternating number series where two different mathematical operations are applied in a repeating pattern to find the next term.
Step 2: Analysis
By observing the transitions between consecutive numbers, we can identify a consistent pattern of addition and subtraction: • • • • •
Step 3: Conclusion
Following the established pattern of (+3, -2), the next operation after must be .
.
Final Answer: (B)

Concept: Inside number = sum of square roots of the corner numbers.

Step 1: First triangle.


Step 2: Second triangle.
Conclusion:

Concept: Bottom number = (product of top numbers) + (sum of top numbers)

Step 1: Check pattern.
Try refined pattern: Better pattern: Final correct pattern: Thus direct consistent pattern is: Applying proportional pattern gives: Conclusion:

Concept: The series follows an alternating pattern.
• Prime numbers: 11, 13, 17, 19, 23, 29
• Alternate terms: +2 pattern → 11 → 13, 17 → 19, 23 → 25 Thus, the next prime number after 23 is 29.

Concept: Increasing difference pattern.
• Differences:
• Next difference:

Concept:

Step 1: Substitute given values.
At : At : At :

Step 2: Solve equations.
Add (1) and (2): Substitute into (1): Substitute into (3): Multiply by 3:

Step 3: Find b and c.
Subtract (4) from (5):

Step 4: Final expression.