Shortcuts in Reasoning for Competitive Exams – Input and Output

Shortcuts in Reasoning for Competitive Exams – Input and Output

Shortcuts in Reasoning Quantitative Aptitude English

INTRODUCTION

Problems related to input-output are frequently asked questions in various graduate level competitive examinations. They are not very tough stuff but take a good deal of time to be solved or sometimes students do not take attempt to solve them because of time consuming impression of such type of questions. But proper understanding of the subject makes you believe that such problems are not as tough and time consuming as they seem.

CONCEPT OF INPUT- OUTPUT PROBLEMS
In such problems:

• It is imagined that there is some kind of computer/word processing machine.
• An input is given to the computer/ word processing machine
• The computer/word processing machine performs repeated operations as per a certain pattern to give different output in different steps.

TYPES OF PROBLEMS

• Problems of shifting
• Problems of arrangement
• Problems of mathematical operation
• Miscellaneous.

PROBLEM OF SHIFTING

We know that in such type of problems, a word/number processing machine generate output through shifting. Shifting does mean an operation in which words or numbers of a given input give outputs in different steps through shifting their place to different place as per a fixed pattern.

Note: In shifting problems, the previous step of any step can possibly be determined, so we can move in backward or reverse order which is not possible in some of the other type of problems.

Methods to Solve
Lets take an example
Input: Blue Cat Good Other Have Cake
Step 1: Blue Other Good Cat Have Cake
Step 2: Blue Other Have Cat Good Cake
Step 3 : Cake Other Have Cat Good Blue
Step 4: Cake Cat Have Other Good Blue
Step 5 : Cake Cat Good Other Have Blue
Step 6: Blue Cat Good Other Have Cake
Shifting of element can easily be understood by making them equivalent to number like
Blue = 1, Cat = 2, Good = 3, Other = 4, Have = 5, Cake = 6

Input can be written as
1…..2……3……4…..5…..6
Blue Cat Good Other Have Cake
Step-1: 2 and 4 interchanged
Step-2 : 3 and 5 interchanged
Step-3 : 1 and 6 interchanged
Step-4 : 1,2 and 3 are repeated again.

PROBLEMS ON ARRANGEMENTS

Word Arrangement from Left Side:
EXAMPLE:

Here, we start arrangement from the word that comes 1st in the dictionary; then comes the word coming 2nd in the dictionary, then comes the word coming 3rd in the dictionary and so on. In this case, the arrangement start from left side. This is the reason in step I banana comes 1st as it comes 1st in the dictionary. In the 2nd step, orange comes at 3rd place because after the arrangement of step I the next word coming in the dictionary is mango but it get arranged automatically and hence there is no need to arrange it in step II. This is the reason after arranging banana in step I, we directly come to the word orange (coming 3rd in the dictionary) in step II. In the 3rd step, we arrange the word ‘pear’ (coming 4th in the dictionary) and the word tango get arranged automatically.

Word Arrangement from Right:
EXAMPLE:

In this case, the arrangement starts from right side. The word coming 1 st in the dictionary comes at the 1 st position from right. At the 2nd position from right comes the word coming 2nd in the dictionary and the process goes on till the arrangement gets completed. In the above given example, ‘Fame’ is the 1st word coming in the dictionary and hence it comes at the 1 st position from right in the step I. In the step II, the 2nd word coming in the dictionary (Game) comes at the 2nd position from right. Point to be noted that the word coming third in the dictionary will come at the 3rd position from right and this word is ‘Jam’. But ‘Jam’ automatically get arranged as per the given pattern when we arrange the word ‘Game’ in II step. This is the reason why we don’t arrange ‘Jam’ in the third step and jump directly to arrange the word. ‘Name’ that comes 4th in the dictionary. ‘Name’ occupies 4th position from right and the word ‘Shame’ automatically get arranged in the 3rd step. Hence, the word ‘Shame’ does not need to get arranged.

Word Arrangement from the Left-Right Alternate:
EXAMPLE:

Here, the arrangement is made by putting the first word at 1st place, then alphabetically last word at last place, then alphabetically second word at second place from left and the further arrangements goes on in the same manner. In the other words, are positioned from the left and from the right alternately. In the step I the word coming 1 st in the dictionary is ‘ a’ and it takes 1 st position from left. In the step II, the last word coming alphabetically is Sachin and it takes last position (1 st from right). In step III, the word coming 2nd in dictionary is ‘cricket’ that comes at 2nd position from left. In step IV, the word coming 3rd last in the dictionary takes the 3rd position from right. After the step IV, all the words get arranged in alphabetical order. Point to be noted that after step IV, there is no need to arrange the word ‘great’ as it get arranged automatically is step IV.

Arrangement in Increasing or Decreasing Order:
EXAMPLE :

This arrangement gives a clear idea of arrangement of numbers in increasing order. In step I, the smallest number (17) comes at the 1st position from left pushing the remaining to the right. In step II, the 2nd smallest number (18) comes at 2nd position from left pushing the remaining number to the right. In step III, the 4th smallest number (35) takes 4th position from left and the other two numbers 58 and 100 get arranged automatically.

Now, let us see decreasing order arrangement:

The same arrangement can take place from right side (or) in the reverse order as follow:

Number Arrangment from Left-Right Alternate:

Like words left-right alternate arrangement, number arrangement also takes place. The process of this arrangement is exactly the same as the arrangement takes place in case of words. Just see the following cases:

Case I:

Here, the smallest number (10) takes 1 st position from left in step I. In step II the largest number takes the last (1st from right) position. Again in step III the 2nd smallest number (15) comes at the 2nd position from left. In the step IV, the 2nd largest number (100) comes at the 2nd position from right and the remaining number (26 and 35) get arranged automatically.

In case II, the arrangements take place in the same way as the arrangements take place in case I. But the difference here is that case I is a left-right arrangement and case II is the right-left arrangement. In case II, the arrangement starts with the largest number (125) coming at the 1st position from right and this is step I. In step II, the smallest number (10) comes at the 1 st position from left. In step III the 2nd largest number (100) comes at the 2nd position from right. In step III, the third largest number (35) automatically comes at the 3rd position from right. In 4th step, the 2nd smallest number (15) comes at the 2nd position from left and 26 get arranged automatically coming at 3rd position from left.

Note:
Left-right (or right-left) arrangement of numbers also take place in the same manner when numbers are arranged in decreasing order.

Arrangement of Words and Numbers Simultaneously:
Just see the following outputs produced by a word and number machine.

Case I

In such case, numbers and words get arranged alternately. In step I, the smallest number (32) comes at the 1 st position from left pushing the remaining members of input towards right. In the step II, the word coming 1st alphabetically (that is the word ‘ Aradhna’) takes the 2nd position from left pushing the remaining member rightward. Point to be noted that the 2nd smallest number automatically comes at the third position from left while arranging the word ‘Aradhna’ and hence, there is no need to arrange the 2nd smallest number ‘50’. In step III, the word (Prema) coming 2nd alphabetically comes at the 4th position from left pushing the other members to the right. In step IV, the largest number (100) occupies the 5th position from left and the word (Vandana) coming last alphabetically comes at last position automatically finishing the complete arrangement.

Let us see some other cases of this type:

Case II:

In this case, largest number and the word coming last alphabetically get arranged alternately. Then the 2nd longest number and the word coming 2nd last alphabetically get arranged alternately and the process goes on till the arrangements of all the numbers and words get completed. In this case, arrangement completes in step III.

Case lll:

In this case, arrangement starts with the word coming 1 st alphabetically and such word is ‘ Aradhna’ that comes at the 1 st position from left is step 1. In step
II, the smallest number (32) comes at the 2nd position from left. Then, in step
III, the word coming 2nd alphabetically comes at the 3rd position from left and all the other members get arranged automatically.

Case IV:

In this case, word coming last alphabetically comes 1 st from left in step I and such word is ‘Vandana’. In step II, the largest number (100) comes at the 2nd position from left. In step III, the word coming 2nd last alphabetically occupies the 3rd position from left, and such word is ‘Prerna’. As the 2nd largest number (50) automatically get arranged as per the pattern going on and hence this is not needed to arranged in step IV. In step VI, the word coming 1st alphabetically comes at the 5 th position from left and such word is ‘Aradhna’. The smallest number (32) get arranged automatically coming at the last position from left in step IV. Thus, it is clear that in this case the word coming 1st alphabetically and the greatest number get arranged alternately in 1 st two steps; then 2nd last word alphabetically and 2nd largest number get arranged alternately finishing the whole arrangement in step IV.

CaseV:

In this case, the smallest number comes at the 1st position from left in step I and such number is 32. In step II, the word (Vandana) coming last alphabetically occupies the 2nd place from left. In the 2nd step, the 2nd smallest number (50) takes the 3rd position from left automatically and also the word coming 2nd last alphabatically takes the 4th position from left automatically. Hence, there is no need to arrange ‘50’ and ‘Prema’. In the III step, the largest number (100) occupies the 5th position from left completing the whole arrangement.

Case VI:

In this case, the logic is that the greatest number (100) comes at the 1 st position from left in step I. In step II the word coming 1st alphabetically takes the 2nd position from left and the 2nd largest number (50) gets arranged automatically. Hence, in step III, we direct arrange the word coming 2nd last alphabetically (that word is ‘Prerna’) occupies the 4th position from left and the other two members (32 and ‘Vandana’) get arranged automatically finishing the whole arrangement.

Arrangement Based on the Number of Letters in Words:
Just have a look at the following patterns:

Case I:

Here, the words get arranged as per increasing number of letters.

words, the word having least number of letters comes 1 st from left in step I and such word is ‘be’. The word ‘let’ is bigger than ‘be’ and smaller than other words letterwise and hence, it takes 2nd position from left but it gets arranged automatically when the word ‘be’ is arranged in step I. In 2nd step, the word ‘love’ comes at the 3rd position from left as it is bigger than word ‘let’ letterwise. In step III, the letterwise bigger word (fried) than love comes at the fourth position from left. Similarly, mature comes at the 5th position from left and pattern comes at the last position automatically while arranging the word ‘mature’.

Case II:

In this case, the words get arranged in decreasing order in terms of letters. In other words, the word having the largest number of letters comes 1 st from left, then comes the word having 2nd largest number of letters, then comes the word having 3rd largest number of letters and the process goes on till the word having the least number of letters occupies the last position from left.

Case III:

Have you noticed something here? Here, the words get arranged in increasing order of litters. But when it comes to the case of two or more words having equal number of letters the priority is given alphabetically. It does mean that the word coming 1 st as per the alphabet will be put before the word coming 2nd. Similarly, the word coming 2nd alphabetically will be put before the word coming third. This is the reason why ‘let’ has been put before ‘set’ and ‘gate’ has been put before ‘hope’.

Case IV:

In this case, the words get arranged in decreasing order of letters. But when it comes to the case of two or more words having equal number of letters the priority is given to the word that comes later alphabetically. It does mean that the word coming 1 st alphabetically will be put after the word coming 2nd and the word coming 2nd will be put after the word coming 3rd. This is the reason why ‘hope’ has been put before ‘gate’ and ‘set’ has been put before ‘let’.

Important Note: The case ofarrangement discussed so far are the cases ofpush. In all the cases a new word jumps from its place in every step, occupies its new and due place and gives the remaining words and push either towards lej’t or right as per the requirement of the pattern. But in some cases of arrangement interchange does take place and that format is given below:

Arrangement with Interchange:
EXAMPLE:

In this case, the word (beautiful) coming 1 st in alphabetical order comes at the 1st position from left interchanging its place with the word ‘the’ and this is step I. In step II, the word (girl) coming 2nd in alphabetical order occupies the 2nd position from left interchanging with the word ‘most’. In step III, the word coming 3rd (is) comes at the third position from left interchanging with the word ‘the’ and finishing the complete arrangement in alphabetical order.
This type of cases can also be seen in number arrangements and in the arrangements of numbers and words simultaneously. The examples of these type of arrangements are given below:

EXAMPLE (Increasing order number arrangement)

Presentation:

The presentation gives you the clear idea of how interchange takes place in every step.

EXAMPLE (Decreasing order number arrangement)

Presentation:

PROBLEMS OF MATHEMATICAL OPERATION—
In this type of problems, the input has some numbers. Different steps are obtained by taking the numbers of the input and dilferent arithmetic operations are performed after that.

EXAMPLE:

In this case, in step I (each number of the input – 8). In step II, product of the digits of each number of the input. In step III, each number of the input is multiplied by 3. In step IV, each number of the input is added by 6. In step V, keep adding the digits of each number of the input till they are converted into single digit. In step VI, (digit sum of each number of input) . In step VII, each number of step II is added by 4.

MISCELLANEOUS PROBLEMS

In this type of problems, there is no fixed pattern of questions coming under this category. Infact, questions under this category comes before you as a real surprise.

In this case, in step I, first letter disappear. In step II, last letter disappear. In step III, vowels disappear. In step IV, consonants disappear. In step V, first two letters disappear.

Shortcut Approach

• First of all, observe the given input line of words or numbers and the last step of rearrangement, so that candidate may get an idea about the changes effected in various steps of rearrangement.
• In order to know what changes have been made in each step, observe two consecutive steps carefully.
• Now, correlate the input, the last step and anyone of the middle steps. This will enable you to identify the rule of arrangement.
• In shifting problems, it is possible to determine the previous/earlier steps including input. We can proceed/move backward or in reverse direction in shifting problems.
• In shifting problems for convenience, we assign numeric value to given words.