Shortcuts to Solve Classification / Odd Man Out Series Problems - Numbers

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Friends, in our last post we have discussed the shortcut techniques to solve Classification / Odd Man Out Series problems of Alphabets. Today we shall discuss some tips to solve the problems with numbers.

Note : This is the Second Lesson in this series. Please read basics at  Lesson 1 from here before reading this post

Single Numbers :

These are the easiest forms of odd man out series problems. You can easily find out the odd one in the first glance itself by checking the differences, basic rules of numbers (odd / even) etc...

Examples :

• 2, 4, 6, 9, 10 
• 1, 3, 6, 5, 7

Easy aren't they ? But now a days they are not asking such simple questions in exams.

What if they give you Bigger Numbers ?

Here you have to follow a 3 step process. 

1. Try to check the basic logic first
• Is there any relation between those numbers ?
• Whether any specific number is related to all the numbers ?
• Are the given numbers come under any specific category ?
• If you can't find the odd one in the first step, then go to step 2
2. Here check the Squares and Cubes (also check Squares+1s and Cubes+1s). If you still can't find the odd one, then go to step 3
3. Try remaining Mathematical Possibilities (like tables, divisibility rules etc..)
4. If you are unable to find out any relationship among given options, try to find out interrelationships among the digits of each number (read Example Problem 3)

Now let's see some examples

Problem 1 :

1. 13
2. 26
3. 39
4. 52
5. 65

 Solution : In the above list, 13 is the prime number. Remaining are not. So Option 1 is our answer.

Problem 2  :

1. 13
2. 23
3. 33
4. 43
5. 53

Solution : Check these numbers. Have you observed any logic ? Every number from the above list has 10 numbers difference from it's previous numbers. Great, we find one... But that's not the logic. So check whether the numbers are prime or not. So, here... all the given numbers are prime, except the number 33 (it is a composite number). So Option 3 is the answer. 

Problem 3 :

1. 176
2. 231
3. 572
4. 473
5. 653

Solution : Check the above numbers carefully. You can't find the correct answer by applying the first 2 steps. So here try to find out the logic... If you observe closely, you will find out that the middle number is the sum of the first and the last numbers. Check once....

1. 176
2. 231
3. 572
4. 473
5. 653

But you are not getting middle number in 5th Option (As 6+3 = 9, not 5). So this is the correct answer.

Problem 4 :

1. 123
2. 246
3. 147
4. 368
5. 159

Solution : Here also we tried all the steps but no answer. Hey wait, have you tried the above logic ???  Let's try

1. 1+3 = 4 (but the middle number is 2)
2. 2+6 = 8 (but the middle number is 4)
3. 1+7 = 8 (but the middle number is 4)
4. 3+8 = 11 (but the middle number is 6)
5. 9+1 = 10 (but the middle number is 5)

Not worked :(

Now see whether we can find anything with the newly obtained numbers....

4, 8, 8, 11, 10.... No relation.. But you could find out that one number except all are even numbers... So, may be this is our answer...  

Or if you want to go further, you can get another logic... Just divide these numbers with 2. 

1. 4/2 = 2
2. 8/2 = 4
3. 8/2 = 4
4. 11/2 = 5.5
5. 10/2 = 5

So, here.. except Option 4...  for remaining numbers, the middle number is the half of the total of remaining two numbers.

Note : If you can't get answer with above step, then you should experiment with different numbers and different mathematical operations. 

Problem 5 :

1. 119
2. 123
3. 143
4. 149
5. 133

Solution : 149 is a Prime number. Remaining numbers not

Problem 6 :

1. 29 : 812
2. 37 : 1332
3. 45 : 1980
4. 48 : 2256
5. 51 : 2551

If they ask question in the above format, then it means, there should be some relationship between the first and second number. 

Note : If you can't find any visible difference, then better to find out Squares.

1. 29² =  841 (but given number is 812)
2. 37²  = 1369 (but the given number is 1332)
3. 45² = 2025 (but the given number is 1980)
4. 48²= 2304 (but the given number is 2256)
5. 51² =  2601 (but the given number is 2551)

So squares are not matching with the numbers. But if you closely observe, you can see some similarities among these numbers. So, find out the difference, so that we could find some clue

1. 841-812 = 29 (First Number)
2. 1369-1332 = 37 (First Number)
3. 2025-1980 =  45 (First Number)
4. 2304-2256 = 48 (First Number)
5. 2601-2551 =  510 (Not the First Number)

So, Option 5 is the odd one.

Problem 7 :

1. 126
2. 72
3. 135
4. 171
5. 162 

Solution : At first glance we are unable to find any clues. So, check the interrelationships among these numbers (if any).

Note : People tend to mark Option 2 (72) as the answer because it consists only two numbers where as in remaining options the numbers are three. But please keep in mind that now a days they are not asking questions with such a simple logic. 

At a close observation, you can find that the total of the given numbers is 9

1. 1+2+6 = 9
2. 7+2 = 9
3. 1+3+5 = 9
4. 1+7+1 = 9
5. 1+6+2 = 9

So, there might be something with this 9.

Let's subtract this 9 with the given number... 

1. 126-9 = 117
2. 72-9 = 63
3. 135-9 = 126
4. 171-9 = 162
5. 162-9 = 153

you could find out some relation between option 4 and 5. But it's not enough.... So let's try division

1. 126/9 = 14
2. 72/9 = 8
3. 135/9 = 15
4. 171/9 = 19
5. 162/9 = 18

from the above answers, you can clearly say that 19 (Option 4) is a Prime Number. Where are remaining numbers are not.

Problem 8 : 

1. 48-134
2. 65-185
3. 128-374
4. 56-158
5. 81-223

Solution : With a close observation you can see that the second number is almost nearer to the three times of the first number.

1. 40 x 3 = 120 (given number is 134)
2. 60 x 3 = 180 (given number is 185)
3. 120x 3 = 360 (given number is 374)
4. 50 x 3 = 150 (given number is 158)
5. 80x 3 = 240 (given number is 223)

So, there should be some logic behind it

Multiply first numbers with 3

1. 48x3 = 144 (difference between result and second number is 144-134 = 10)
2. 65x3 = 195 (195-185 = 10)
3. 128x3 = 384 (384-374 = 10)
4. 56x3 = 168 (168-158 = 10)
5. 81x3=243 (243-223= 20)

So, Option 5 is the answer.

Problem 9 : 

1. 25-630
2. 36-1312
3. 16-260
4. 9-84
5. 49-2408

Solution : 

1. 25²=625 (625+5 = 630)
2. 36²=1296 (1296+16 = 1312)
3. 16² = 256 (256+4 = 260)
4. 9² = 81 (81+3 = 84)
5. 49² = 2401 (2401+7=2408)

So, here the odd one is Option 2

Problem 10 : 

1. 263
2. 242
3. 393
4. 661
5. 383

Solution : Check the relationship between the given numbers... Two numbers are of 200's and two numbers are of 300's and one is of 600. There is no relation. So, try to find out interrelationships among these numbers.

With close observation, you can find out that except the last number, for remaining numbers the first and last numbers are forming the middle number (First Number x Second number = Middle number)

1. 2x3 = 6
2. 2x2 = 4
3. 3x3 = 9
4. 6x1 = 6
5. 3x3 is not equal to 8

So, answer is Option 5

That's all for now friends. In our next post we shall discuss shortcuts to find out Odd ones in words. Happy Reading. 

Important Points to Note :

1. you should be good at speed maths. You hardly will get 30 seconds to solve these type of questions. You should not waste more time on calculations.
2. Mug up squares up to 30s and cubes upto 20s.
3. To make things easily understandable, we elaborated  each and every step in above problems. But in exams you should get the main idea in the first glance itself. You can easily attain this quality with regular practice. All the Best.

P. Rama Krishna

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