Directions: Study the following information carefully and answer the questions given below: In a hexagon arrangement, at each corner, a triangle is placed which is denoted by either two letters or two numbers. Below are given some of the conditions: I. If the number is a perfect square then only that number is increased by 1. II. If there is at least one vowel then change it to the preceding alphabet. III. If both digits are odd then reduce those digits by 2. IV. If any one of the consonants is smaller than N in alphabetical order then change it to the next alphabet. Note: If no condition is applied then there will be no change. Apply the above-given conditions to find the output. More than one condition can be applicable. For example:Input Output Triangle 1 1, 4 2, 5 Triangle 2 o, k n, l Triangle 3 6, 7 6, 7 Triangle 4 i, l h, m Triangle 5 s, v s, v Triangle 6 5, 5 3, 3 Input Triangle 1 c, d Triangle 2 u, b Triangle 3 7, 7 Triangle 4 h, f Triangle 5 w, q Triangle 6 8, 3
How many letters are the between the second letter of the output of triangle 2 and the first letter of the output of triangle 5?
19
Solving the Hexagon Arrangement Puzzle
The problem describes a hexagon arrangement with six triangles at its corners. Each triangle contains either two letters or two numbers. We are given a set of conditions that are applied to the input values to produce an output for each triangle.
Understanding the Conditions
- Condition I: If a number is a perfect square, increase only that number by 1.
- Condition II: If there is at least one vowel, change it to the preceding alphabet.
- Condition III: If both digits are odd, reduce those digits by 2.
- Condition IV: If any consonant is smaller than 'N' in alphabetical order, change it to the next alphabet.
Note that more than one condition can be applicable to a triangle's input.
Applying Conditions to Input Triangles
Let's apply the given conditions to the input for each triangle:
Triangle 1: c, d
The inputs are 'c' and 'd'. Both are consonants and are smaller than 'N' in alphabetical order.
- 'c' is a consonant smaller than 'N'. Applying Condition IV: 'c' changes to 'd'.
- 'd' is a consonant smaller than 'N'. Applying Condition IV: 'd' changes to 'e'.
Output for Triangle 1: d, e
Triangle 2: u, b
The inputs are 'u' and 'b'. 'u' is a vowel and 'b' is a consonant smaller than 'N'.
- 'u' is a vowel. Applying Condition II: 'u' changes to the preceding alphabet, which is 't'.
- 'b' is a consonant smaller than 'N'. Applying Condition IV: 'b' changes to the next alphabet, which is 'c'.
Output for Triangle 2: t, c
Triangle 3: 7, 7
The inputs are '7' and '7'. Both are numbers.
- '7' is not a perfect square. Condition I is not applied.
- Both digits are odd (7 and 7). Applying Condition III: Both '7's are reduced by 2. 7 - 2 = 5.
Output for Triangle 3: 5, 5
Triangle 4: h, f
The inputs are 'h' and 'f'. Both are consonants and are smaller than 'N'.
- 'h' is a consonant smaller than 'N'. Applying Condition IV: 'h' changes to 'i'.
- 'f' is a consonant smaller than 'N'. Applying Condition IV: 'f' changes to 'g'.
Output for Triangle 4: i, g
Triangle 5: w, q
The inputs are 'w' and 'q'. Both are consonants and are larger than 'N'.
- 'w' is a consonant larger than 'N'. Condition IV is not applied.
- 'q' is a consonant larger than 'N'. Condition IV is not applied.
- There are no vowels. Condition II is not applied.
No conditions are applied to Triangle 5.
Output for Triangle 5: w, q
Triangle 6: 8, 3
The inputs are '8' and '3'. Both are numbers.
- '8' is not a perfect square. Condition I is not applied.
- '3' is not a perfect square. Condition I is not applied.
- Both digits are not odd (8 is even). Condition III is not applied.
No conditions are applied to Triangle 6.
Output for Triangle 6: 8, 3
Summary of Outputs
| Triangle | Input | Output |
|---|---|---|
| Triangle 1 | c, d | d, e |
| Triangle 2 | u, b | t, c |
| Triangle 3 | 7, 7 | 5, 5 |
| Triangle 4 | h, f | i, g |
| Triangle 5 | w, q | w, q |
| Triangle 6 | 8, 3 | 8, 3 |
Finding the Number of Letters Between
The question asks for the number of letters between the second letter of the output of triangle 2 and the first letter of the output of triangle 5.
- Second letter of the output of Triangle 2 is 'c'.
- First letter of the output of Triangle 5 is 'w'.
We need to count the letters in the English alphabet that are strictly between 'c' and 'w'.
The letters are: d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v.
Counting these letters, we find there are 19 letters.
Alternatively, using alphabetical positions (a=1, b=2, ..., z=26):
- Position of 'c' is 3.
- Position of 'w' is 23.
The number of letters between 'c' and 'w' is (Position of 'w') - (Position of 'c') - 1 = 23 - 3 - 1 = 20 - 1 = 19.
Conclusion
There are 19 letters between the second letter of the output of triangle 2 ('c') and the first letter of the output of triangle 5 ('w').
Important Questions from Conditional Matrix
What is the sum of the second number of output of triangle 3 and the first number of output triangle 6?
What is the output of triangle 1?
What is the difference between the product of numbers of the output of triangle 3 and product of numbers of the output of triangle 6?
Select the option in which the numbers are related in the same way as are the numbers of the following sets.
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 – Operations on 13 such as adding /deleting /multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed)
(24, 8, 96)
(36, 4, 72)
Select the set in which the numbers are related in the same way as are the numbers of the following sets.
(30, 14, 8)
(84, 12, 36)
