   A word and number arrangement machine when given an input line of words and numbers rearranges them following a different rule in each step. The following is an illustration of input and rearrangement.

Input: always begin from bottom mount high

Step I: aabdho eimty inou ggnooy gmnou isst

Step II: 3   44   31   23   2   49

Step III: 48  18  72

Step IV: 3   9

Step V: 144

Step V is the last step of the arrangement.

Following the same pattern solve the given input.

Input: fear creates demons only hope defeat
Important for :
1
What will be the value obtained in final step of the arrangement?
» Explain it
C
Following the final solution we can say that 81 will be obtained in final step of the arrangement.

Hence, the correct answer is option C.

Final Solution:

Input: fear creates demons only hope defeat

Step I: aeiu aeeghix ehmnow bmoo eoks aeeguw

Step II: 36   19   38   15   10   2

Step III: 162  120  0

Step IV: 6  3

Step V: 81

Step V is the last step of the arrangement.

Common Explanation:

Reference:

Input: always begin from bottom mount high

Step I: aabdho eimty inou ggnooy gmnou isst

Inference:

In the Step I, firstly the consonants within each word in Input step are reversed in cyclic alphabetical order after that the words thus formed are arranged according to dictionary from left to right.

For example:

The word ‘Fear’ after reversing the consonants in cyclic alphabetical order and arranging the letters in alphabetical order becomes ‘aeiu’.

Using the same rule Step I of the given Input can be written as:

Input: fear creates demons only hope defeat

Step I: aeiu aeeghix ehmnow bmoo eoks aeeguw

Reference:

Step II: 3   44   31   23   2   49

Inference:

In the Step II, the difference of numbers obtained from the sum of the numeric position in alphabetic series of each vowel and the sum of the numeric position in alphabetic series of each vowel of the same word in Step I is taken.

For example:

The vowels in the word ‘aeiu’ are ‘a’, ‘e’, ‘i’ and ‘u’ and numeric position of ‘a’, ‘e’, ‘i’ and ‘u’ in alphabetic is ‘1’, ‘5’, ‘9’ and ‘21’ respectively so the sum of the numeric positions of vowels is 1 + 5 + 9 + 21 = 36. As, there are no consonants in the word ‘aeiu’ so we will consider 36 as the final number.

And, the vowels in the word ‘aeeghix’ are ‘a’, ‘e’, ‘e’ and ‘i’ and numeric position of ‘a’, ‘e’, ‘e’ and ‘i’ in alphabetic is ‘1’, ‘5’, ‘5’ and ‘9’ respectively, so the sum of the numeric positions of vowels is 1 + 5 + 5 + 9 = 20 and the consonants in the word ‘aeeghix’ are ‘g’, ‘h’ and ‘x’ and numeric position of ‘g’, ‘h’ and ‘x’ in alphabetic is ‘7’, ‘8’, and ‘24’ respectively, so the sum of the numeric position of consonants is 7 + 8 + 24 = 3. And, the difference of 39 and 20 is 19 so the number is 19.

Using the same rule Step II of the given Input can be written as:

Step II: 36   19   38   15   10   2

Reference:

Step III: 48  18  72

Inference:

In the Step III, the digits of first and second number are multiplied within the number and the numbers thus obtained are multiplied form a single number the same pattern is followed with third and fourth number, and fifth and sixth number.

For example:

First and second numbers from left end is Step II are ‘36’ and ‘19’ respectively and after multiplying the digits of ‘36’ and ‘19’ with the numbers we get ‘18’ and ‘9’, and after multiplying ‘18’ and ‘9’ we get 162. So the number is 162.

Using the same rule Step III of the given Input can be written as:

Step III: 162  120  0

Reference:

Step IV: 3   9

Inference:

The first and second numbers from left end in Step III are subtracted then the digits of the number thus formed are added within the number to form the first number from left end in step IV. and the same pattern is repeated with second and third number from left end in step III to form the second number from left end in step IV.

For example:

First and second numbers from left end in Step III are ‘162’ and ‘120’ respectively. The difference of ‘162’ and ‘120’ is 42 and the sum of the digits of ‘42’ is ‘4 + 2 = 6’. So the number is 6.

Using the same rule Step IV of the given Input can be written as:

Step IV: 6  3

Reference:

Step V: 144

Step V is the last step of the arrangement.

Inference:

In the Step V, the sum of the numbers in step IV is taken and the number thus formed is squared.

For example:

After adding the numbers 6 + 3 = 9 and the square of 9 is 81. So the number is 81.

Using the same rule Step V of the given Input can be written as:

Step V: 81

As it is given that Step V is the last step of the arrangement so the given input is completed.
2
What is the product of the numbers obtained in step IV?
» Explain it
D
Following the final solution we can say that the numbers obtained in step IV are ‘6’ and ‘3’.

Required Value = 6 × 3 = 18

Hence, the correct answer is option D.

Final Solution:

Input: fear creates demons only hope defeat

Step I: aeiu aeeghix ehmnow bmoo eoks aeeguw

Step II: 36   19   38   15   10   2

Step III: 162  120  0

Step IV: 6  3

Step V: 81

Step V is the last step of the arrangement.

Common Explanation:

Reference:

Input: always begin from bottom mount high

Step I: aabdho eimty inou ggnooy gmnou isst

Inference:

In the Step I, firstly the consonants within each word in Input step are reversed in cyclic alphabetical order after that the words thus formed are arranged according to dictionary from left to right.

For example:

The word ‘Fear’ after reversing the consonants in cyclic alphabetical order and arranging the letters in alphabetical order becomes ‘aeiu’.

Using the same rule Step I of the given Input can be written as:

Input: fear creates demons only hope defeat

Step I: aeiu aeeghix ehmnow bmoo eoks aeeguw

Reference:

Step II: 3   44   31   23   2   49

Inference:

In the Step II, the difference of numbers obtained from the sum of the numeric position in alphabetic series of each vowel and the sum of the numeric position in alphabetic series of each vowel of the same word in Step I is taken.

For example:

The vowels in the word ‘aeiu’ are ‘a’, ‘e’, ‘i’ and ‘u’ and numeric position of ‘a’, ‘e’, ‘i’ and ‘u’ in alphabetic is ‘1’, ‘5’, ‘9’ and ‘21’ respectively so the sum of the numeric positions of vowels is 1 + 5 + 9 + 21 = 36. As, there are no consonants in the word ‘aeiu’ so we will consider 36 as the final number.

And, the vowels in the word ‘aeeghix’ are ‘a’, ‘e’, ‘e’ and ‘i’ and numeric position of ‘a’, ‘e’, ‘e’ and ‘i’ in alphabetic is ‘1’, ‘5’, ‘5’ and ‘9’ respectively, so the sum of the numeric positions of vowels is 1 + 5 + 5 + 9 = 20 and the consonants in the word ‘aeeghix’ are ‘g’, ‘h’ and ‘x’ and numeric position of ‘g’, ‘h’ and ‘x’ in alphabetic is ‘7’, ‘8’, and ‘24’ respectively, so the sum of the numeric position of consonants is 7 + 8 + 24 = 3. And, the difference of 39 and 20 is 19 so the number is 19.

Using the same rule Step II of the given Input can be written as:

Step II: 36   19   38   15   10   2

Reference:

Step III: 48  18  72

Inference:

In the Step III, the digits of first and second number are multiplied within the number and the numbers thus obtained are multiplied form a single number the same pattern is followed with third and fourth number, and fifth and sixth number.

For example:

First and second numbers from left end is Step II are ‘36’ and ‘19’ respectively and after multiplying the digits of ‘36’ and ‘19’ with the numbers we get ‘18’ and ‘9’, and after multiplying ‘18’ and ‘9’ we get 162. So the number is 162.

Using the same rule Step III of the given Input can be written as:

Step III: 162  120  0

Reference:

Step IV: 3   9

Inference:

The first and second numbers from left end in Step III are subtracted then the digits of the number thus formed are added within the number to form the first number from left end in step IV. and the same pattern is repeated with second and third number from left end in step III to form the second number from left end in step IV.

For example:

First and second numbers from left end in Step III are ‘162’ and ‘120’ respectively. The difference of ‘162’ and ‘120’ is 42 and the sum of the digits of ‘42’ is ‘4 + 2 = 6’. So the number is 6.

Using the same rule Step IV of the given Input can be written as:

Step IV: 6  3

Reference:

Step V: 144

Step V is the last step of the arrangement.

Inference:

In the Step V, the sum of the numbers in step IV is taken and the number thus formed is squared.

For example:

After adding the numbers 6 + 3 = 9 and the square of 9 is 81. So the number is 81.

Using the same rule Step V of the given Input can be written as:

Step V: 81

As it is given that Step V is the last step of the arrangement so the given input is completed.
3
Which of the following numbers will represent ‘Fear’ in step II?
» Explain it
A
Following the final solution we can say that 36 will represent ‘Fear’ in step II.

Hence, the correct answer is option A.

Final Solution:

Input: fear creates demons only hope defeat

Step I: aeiu aeeghix ehmnow bmoo eoks aeeguw

Step II: 36   19   38   15   10   2

Step III: 162  120  0

Step IV: 6  3

Step V: 81

Step V is the last step of the arrangement.

Common Explanation:

Reference:

Input: always begin from bottom mount high

Step I: aabdho eimty inou ggnooy gmnou isst

Inference:

In the Step I, firstly the consonants within each word in Input step are reversed in cyclic alphabetical order after that the words thus formed are arranged according to dictionary from left to right.

For example:

The word ‘Fear’ after reversing the consonants in cyclic alphabetical order and arranging the letters in alphabetical order becomes ‘aeiu’.

Using the same rule Step I of the given Input can be written as:

Input: fear creates demons only hope defeat

Step I: aeiu aeeghix ehmnow bmoo eoks aeeguw

Reference:

Step II: 3   44   31   23   2   49

Inference:

In the Step II, the difference of numbers obtained from the sum of the numeric position in alphabetic series of each vowel and the sum of the numeric position in alphabetic series of each vowel of the same word in Step I is taken.

For example:

The vowels in the word ‘aeiu’ are ‘a’, ‘e’, ‘i’ and ‘u’ and numeric position of ‘a’, ‘e’, ‘i’ and ‘u’ in alphabetic is ‘1’, ‘5’, ‘9’ and ‘21’ respectively so the sum of the numeric positions of vowels is 1 + 5 + 9 + 21 = 36. As, there are no consonants in the word ‘aeiu’ so we will consider 36 as the final number.

And, the vowels in the word ‘aeeghix’ are ‘a’, ‘e’, ‘e’ and ‘i’ and numeric position of ‘a’, ‘e’, ‘e’ and ‘i’ in alphabetic is ‘1’, ‘5’, ‘5’ and ‘9’ respectively, so the sum of the numeric positions of vowels is 1 + 5 + 5 + 9 = 20 and the consonants in the word ‘aeeghix’ are ‘g’, ‘h’ and ‘x’ and numeric position of ‘g’, ‘h’ and ‘x’ in alphabetic is ‘7’, ‘8’, and ‘24’ respectively, so the sum of the numeric position of consonants is 7 + 8 + 24 = 3. And, the difference of 39 and 20 is 19 so the number is 19.

Using the same rule Step II of the given Input can be written as:

Step II: 36   19   38   15   10   2

Reference:

Step III: 48  18  72

Inference:

In the Step III, the digits of first and second number are multiplied within the number and the numbers thus obtained are multiplied form a single number the same pattern is followed with third and fourth number, and fifth and sixth number.

For example:

First and second numbers from left end is Step II are ‘36’ and ‘19’ respectively and after multiplying the digits of ‘36’ and ‘19’ with the numbers we get ‘18’ and ‘9’, and after multiplying ‘18’ and ‘9’ we get 162. So the number is 162.

Using the same rule Step III of the given Input can be written as:

Step III: 162  120  0

Reference:

Step IV: 3   9

Inference:

The first and second numbers from left end in Step III are subtracted then the digits of the number thus formed are added within the number to form the first number from left end in step IV. and the same pattern is repeated with second and third number from left end in step III to form the second number from left end in step IV.

For example:

First and second numbers from left end in Step III are ‘162’ and ‘120’ respectively. The difference of ‘162’ and ‘120’ is 42 and the sum of the digits of ‘42’ is ‘4 + 2 = 6’. So the number is 6.

Using the same rule Step IV of the given Input can be written as:

Step IV: 6  3

Reference:

Step V: 144

Step V is the last step of the arrangement.

Inference:

In the Step V, the sum of the numbers in step IV is taken and the number thus formed is squared.

For example:

After adding the numbers 6 + 3 = 9 and the square of 9 is 81. So the number is 81.

Using the same rule Step V of the given Input can be written as:

Step V: 81

As it is given that Step V is the last step of the arrangement so the given input is completed.
4
Which of the following words will be obtained in step I?
» Explain it
E
Following the final solution we can say that ‘aeeguw’ will be obtained in step I of the given arrangement.

Hence, the correct answer is option E.

Final Solution:

Input: fear creates demons only hope defeat

Step I: aeiu aeeghix ehmnow bmoo eoks aeeguw

Step II: 36   19   38   15   10   2

Step III: 162  120  0

Step IV: 6  3

Step V: 81

Step V is the last step of the arrangement.

Common Explanation:

Reference:

Input: always begin from bottom mount high

Step I: aabdho eimty inou ggnooy gmnou isst

Inference:

In the Step I, firstly the consonants within each word in Input step are reversed in cyclic alphabetical order after that the words thus formed are arranged according to dictionary from left to right.

For example:

The word ‘Fear’ after reversing the consonants in cyclic alphabetical order and arranging the letters in alphabetical order becomes ‘aeiu’.

Using the same rule Step I of the given Input can be written as:

Input: fear creates demons only hope defeat

Step I: aeiu aeeghix ehmnow bmoo eoks aeeguw

Reference:

Step II: 3   44   31   23   2   49

Inference:

In the Step II, the difference of numbers obtained from the sum of the numeric position in alphabetic series of each vowel and the sum of the numeric position in alphabetic series of each vowel of the same word in Step I is taken.

For example:

The vowels in the word ‘aeiu’ are ‘a’, ‘e’, ‘i’ and ‘u’ and numeric position of ‘a’, ‘e’, ‘i’ and ‘u’ in alphabetic is ‘1’, ‘5’, ‘9’ and ‘21’ respectively so the sum of the numeric positions of vowels is 1 + 5 + 9 + 21 = 36. As, there are no consonants in the word ‘aeiu’ so we will consider 36 as the final number.

And, the vowels in the word ‘aeeghix’ are ‘a’, ‘e’, ‘e’ and ‘i’ and numeric position of ‘a’, ‘e’, ‘e’ and ‘i’ in alphabetic is ‘1’, ‘5’, ‘5’ and ‘9’ respectively, so the sum of the numeric positions of vowels is 1 + 5 + 5 + 9 = 20 and the consonants in the word ‘aeeghix’ are ‘g’, ‘h’ and ‘x’ and numeric position of ‘g’, ‘h’ and ‘x’ in alphabetic is ‘7’, ‘8’, and ‘24’ respectively, so the sum of the numeric position of consonants is 7 + 8 + 24 = 3. And, the difference of 39 and 20 is 19 so the number is 19.

Using the same rule Step II of the given Input can be written as:

Step II: 36   19   38   15   10   2

Reference:

Step III: 48  18  72

Inference:

In the Step III, the digits of first and second number are multiplied within the number and the numbers thus obtained are multiplied form a single number the same pattern is followed with third and fourth number, and fifth and sixth number.

For example:

First and second numbers from left end is Step II are ‘36’ and ‘19’ respectively and after multiplying the digits of ‘36’ and ‘19’ with the numbers we get ‘18’ and ‘9’, and after multiplying ‘18’ and ‘9’ we get 162. So the number is 162.

Using the same rule Step III of the given Input can be written as:

Step III: 162  120  0

Reference:

Step IV: 3   9

Inference:

The first and second numbers from left end in Step III are subtracted then the digits of the number thus formed are added within the number to form the first number from left end in step IV. and the same pattern is repeated with second and third number from left end in step III to form the second number from left end in step IV.

For example:

First and second numbers from left end in Step III are ‘162’ and ‘120’ respectively. The difference of ‘162’ and ‘120’ is 42 and the sum of the digits of ‘42’ is ‘4 + 2 = 6’. So the number is 6.

Using the same rule Step IV of the given Input can be written as:

Step IV: 6  3

Reference:

Step V: 144

Step V is the last step of the arrangement.

Inference:

In the Step V, the sum of the numbers in step IV is taken and the number thus formed is squared.

For example:

After adding the numbers 6 + 3 = 9 and the square of 9 is 81. So the number is 81.

Using the same rule Step V of the given Input can be written as:

Step V: 81

As it is given that Step V is the last step of the arrangement so the given input is completed.
5
What is the sum of the numbers obtained in step III?
» Explain it
B
Following the final solution we can say that the numbers obtained in step III are ‘162’, ‘120’ and ‘0’.

Required Value = 162 + 120 + 0 = 282

Hence, the correct answer is option B.

Final Solution:

Input: fear creates demons only hope defeat

Step I: aeiu aeeghix ehmnow bmoo eoks aeeguw

Step II: 36   19   38   15   10   2

Step III: 162  120  0

Step IV: 6  3

Step V: 81

Step V is the last step of the arrangement.

Common Explanation:

Reference:

Input: always begin from bottom mount high

Step I: aabdho eimty inou ggnooy gmnou isst

Inference:

In the Step I, firstly the consonants within each word in Input step are reversed in cyclic alphabetical order after that the words thus formed are arranged according to dictionary from left to right.

For example:

The word ‘Fear’ after reversing the consonants in cyclic alphabetical order and arranging the letters in alphabetical order becomes ‘aeiu’.

Using the same rule Step I of the given Input can be written as:

Input: fear creates demons only hope defeat

Step I: aeiu aeeghix ehmnow bmoo eoks aeeguw

Reference:

Step II: 3   44   31   23   2   49

Inference:

In the Step II, the difference of numbers obtained from the sum of the numeric position in alphabetic series of each vowel and the sum of the numeric position in alphabetic series of each vowel of the same word in Step I is taken.

For example:

The vowels in the word ‘aeiu’ are ‘a’, ‘e’, ‘i’ and ‘u’ and numeric position of ‘a’, ‘e’, ‘i’ and ‘u’ in alphabetic is ‘1’, ‘5’, ‘9’ and ‘21’ respectively so the sum of the numeric positions of vowels is 1 + 5 + 9 + 21 = 36. As, there are no consonants in the word ‘aeiu’ so we will consider 36 as the final number.

And, the vowels in the word ‘aeeghix’ are ‘a’, ‘e’, ‘e’ and ‘i’ and numeric position of ‘a’, ‘e’, ‘e’ and ‘i’ in alphabetic is ‘1’, ‘5’, ‘5’ and ‘9’ respectively, so the sum of the numeric positions of vowels is 1 + 5 + 5 + 9 = 20 and the consonants in the word ‘aeeghix’ are ‘g’, ‘h’ and ‘x’ and numeric position of ‘g’, ‘h’ and ‘x’ in alphabetic is ‘7’, ‘8’, and ‘24’ respectively, so the sum of the numeric position of consonants is 7 + 8 + 24 = 3. And, the difference of 39 and 20 is 19 so the number is 19.

Using the same rule Step II of the given Input can be written as:

Step II: 36   19   38   15   10   2

Reference:

Step III: 48  18  72

Inference:

In the Step III, the digits of first and second number are multiplied within the number and the numbers thus obtained are multiplied form a single number the same pattern is followed with third and fourth number, and fifth and sixth number.

For example:

First and second numbers from left end is Step II are ‘36’ and ‘19’ respectively and after multiplying the digits of ‘36’ and ‘19’ with the numbers we get ‘18’ and ‘9’, and after multiplying ‘18’ and ‘9’ we get 162. So the number is 162.

Using the same rule Step III of the given Input can be written as:

Step III: 162  120  0

Reference:

Step IV: 3   9

Inference:

The first and second numbers from left end in Step III are subtracted then the digits of the number thus formed are added within the number to form the first number from left end in step IV. and the same pattern is repeated with second and third number from left end in step III to form the second number from left end in step IV.

For example:

First and second numbers from left end in Step III are ‘162’ and ‘120’ respectively. The difference of ‘162’ and ‘120’ is 42 and the sum of the digits of ‘42’ is ‘4 + 2 = 6’. So the number is 6.

Using the same rule Step IV of the given Input can be written as:

Step IV: 6  3

Reference:

Step V: 144

Step V is the last step of the arrangement.

Inference:

In the Step V, the sum of the numbers in step IV is taken and the number thus formed is squared.

For example:

After adding the numbers 6 + 3 = 9 and the square of 9 is 81. So the number is 81.

Using the same rule Step V of the given Input can be written as:

Step V: 81

As it is given that Step V is the last step of the arrangement so the given input is completed.