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**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**

**What if they give you Bigger Numbers ?**

Here you have to follow a 3 step process.

**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
**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**Try remaining Mathematical Possibilities**(like tables, divisibility rules etc..)- 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 :**

**13****26****39****52****65**

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

**Problem 2 :**

**13****23****33****43****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 :**

- 176
- 231
- 572
- 473
- 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
**7**6 - 2
**3**1 - 5
**7**2 - 4
**7**3 - 6
**5**3

**Problem 4 :**

- 123
- 246
- 147
- 368
- 159

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

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

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.

- 4/2 = 2
- 8/2 = 4
- 8/2 = 4
- 11/2 = 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 :**

- 119
- 123
- 143
- 149
- 133

**Solution**: 149 is a Prime number. Remaining numbers not

**Problem 6 :**

- 29 : 812
- 37 : 1332
- 45 : 1980
- 48 : 2256
- 51 : 2551

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

- 29
^{2}= 841 (but given number is 812) - 37
^{2 }= 1369 (but the given number is 1332) - 45
^{2}= 2025 (but the given number is 1980) - 48
^{2}= 2304 (but the given number is 2256) - 51
^{2}= 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

- 841-812 = 29 (First Number)
- 1369-1332 = 37 (First Number)
- 2025-1980 = 45 (First Number)
- 2304-2256 = 48 (First Number)
- 2601-2551 = 510 (Not the First Number)

So, Option 5 is the odd one.

**Problem 7 :**

**126****72****135****171****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+2+6 = 9
- 7+2 = 9
- 1+3+5 = 9
- 1+7+1 = 9
- 1+6+2 = 9

So, there might be something with this 9.

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

- 126-9 = 117
- 72-9 = 63
- 135-9 = 126
- 171-9 = 162
- 162-9 = 153

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

- 126/9 = 14
- 72/9 = 8
- 135/9 = 15
- 171/9 = 19
- 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 :**

**48-134****65-185****128-374****56-158****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.

- 40 x 3 = 120 (given number is 134)
- 60 x 3 = 180 (given number is 185)
- 120x 3 = 360 (given number is 374)
- 50 x 3 = 150 (given number is 158)
- 80x 3 = 240 (given number is 223)

So, there should be some logic behind it

Multiply first numbers with 3

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

So, Option 5 is the answer.

**Problem 9 :**

**25-630****36-1312****16-260****9-84****49-2408**

**Solution :**

- 25
^{2}=625 (625+**5**= 630) - 36
^{2}=1296 (1296+**16**= 1312) - 16
^{2}= 256 (256+**4**= 260) - 9
^{2}= 81 (81+**3**= 84) - 49
^{2}= 2401 (2401+**7**=2408)

So, here the odd one is Option 2

**Problem 10 :**

**263****242****393****661****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)

- 2x3 = 6
- 2x2 = 4
- 3x3 = 9
- 6x1 = 6
- 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 :**

- 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.
- Mug up squares up to 30s and cubes upto 20s.
- 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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Thank u soo much for such a wonderful explanation.

ReplyDeleteHi first of all thank you so much for the posts for SBI clerk study material. i have been following all the post in this website.

ReplyDeleteI have found another logic in example no 3: Thought of sharing it:

In example 3 there is another logic to get to the answer

Another logic is:

1+7+6 = 14

2+3+1 = 6 ---> This must be the answer

5+7+2 = 14

4+7+3 = 14

6+5+3 = 15

I think this logic can also apply.

In problem 3 one more logic is following but then answer is different...every number has a sum of 14 except option 2....it is quite confusing to follow a particular method..

ReplyDeleteshivani di, you are my engel...... thank you so much and also thank your team member please try to clear the fundamental problems of all sections of reasoning and english like basic formula etc

ReplyDelete