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
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?
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Understanding the Hexagon Triangle Problem
The problem describes a hexagon arrangement where each corner has a triangle. Each triangle is represented by two elements, which can be letters or numbers. We are given a set of conditions that determine how these elements transform. We need to apply these conditions to the given input triangles and then perform a calculation based on the output of specific triangles.
Conditions for Transformation
Here are the conditions that can be applied to the elements in each triangle:
- Condition I: If a number is a perfect square, it is increased 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, or no condition might be applicable, in which case there is no change.
Applying Conditions to Each Triangle
Let's apply the conditions to the input for each triangle:
Triangle 1: Input is c, d.
- 'c' is a consonant and is smaller than 'N'. Condition IV applies. 'c' changes to 'd'.
- 'd' is a consonant and is smaller than 'N'. Condition IV applies. 'd' changes to 'e'.
Output of Triangle 1: d, e.
Triangle 2: Input is u, b.
- 'u' is a vowel. Condition II applies. 'u' changes to 't' (preceding alphabet).
- 'b' is a consonant and is smaller than 'N'. Condition IV applies. 'b' changes to 'c' (next alphabet).
Output of Triangle 2: t, c.
Triangle 3: Input is 7, 7.
- Both '7' and '7' are odd digits. Condition III applies.
- '7' is reduced by 2, becoming 5.
- The other '7' is also reduced by 2, becoming 5.
- Neither number is a perfect square, so Condition I does not apply.
Output of Triangle 3: 5, 5.
Triangle 4: Input is h, f.
- 'h' is a consonant and is smaller than 'N'. Condition IV applies. 'h' changes to 'i'.
- 'f' is a consonant and is smaller than 'N'. Condition IV applies. 'f' changes to 'g'.
Output of Triangle 4: i, g.
Triangle 5: Input is w, q.
- 'w' is a consonant but not smaller than 'N'. Condition IV does not apply.
- 'q' is a consonant but not smaller than 'N'. Condition IV does not apply.
- There are no vowels. Condition II does not apply.
- These are not numbers. Conditions I and III do not apply.
Output of Triangle 5: w, q (No change).
Triangle 6: Input is 8, 3.
- The digits are 8 and 3. Both are not odd (8 is even), so Condition III does not apply.
- 8 is not a perfect square. 3 is not a perfect square. Condition I does not apply.
- These are numbers, not letters, so Conditions II and IV do not apply.
Output of Triangle 6: 8, 3 (No change).
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 |
Calculating Products for Triangle 3 and Triangle 6
The question asks for the difference between the product of numbers in the output of Triangle 3 and the product of numbers in the output of Triangle 6.
Output of Triangle 3 is 5, 5.
Product of numbers in Triangle 3 output = 5 × 5 = 25.
Output of Triangle 6 is 8, 3.
Product of numbers in Triangle 6 output = 8 × 3 = 24.
Finding the Difference
Difference = (Product of Triangle 3 output) - (Product of Triangle 6 output)
Difference = 25 - 24
Difference = 1
Final Answer
The difference between the product of numbers of the output of triangle 3 and the product of numbers of the output of triangle 6 is 1.
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?
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?
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)
