Aptitude - Odd Man Out and Series - Discussion

All the numbers are prime numbers except 81.

Prime number series is 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997 etc.

81 is divisible by 9, so it isn't a prime number. 9x9=81. the rest of the numbers can not be divided into evenly without a remainder. For example 5 is a prime because if you divide it by 2 you will have a remainder. 5 is only divisible by 5 or by 1.

also stated above was the formula: tn= t(n-1)+2n
where n= 1,2,3,4,...etc.
and t= 41,43,47,53,...etc.

If you plug in the numbers it doesn't equal the 2nd term which is 43.
let t= 1st term 41
n= 1

Example with above formula:tn= 41(1-1)+2(1)
41(0)+2 = 2?
I do understand t+2n
41+2(1)= 43
43+2(2)= 47
47+2(3)= 53

I am not trying to be picky, I was really trying to understand.
thanks for the above solutions!

To find odd man out series, we are using five procedures.
Those are,

1) Check the sequence is any cubes or squares.

2) To find the relation b/w two following numbers.

3) Any relation b/w the given number like,
Adding or multiply last two get the first digit.
Adding or multiply first two digits get the last digit.
Adding or multiply first and last digit get middle one.

4) That is prime numbers or not.

5) Those numbers are odd or even.

Mostly these types are using formed the odd man out series.

The prediction is right since,

I too tried by the logic such as:

41+2 = 43.
43+4 = 47.
47+6 = 53.
53+8 = 61.
61+10 = 71........71+2 = 73.

In this case when multiplier become 12 then the logic is violated so if we follow this prediction the answer should be 73, so I think this not proper prediction, and the prediction that mentioned in the key even proper than this.
So that is the pragmatic logic.

For anyone saying even 73 can be the answer, no it can't
if the series were;

41,43,47,53,61,71,73,97 the answer would have been 73.
but the series is:
41,43,47,53,61,71,73,81.

The last number 81 doesn't go with the 2,4,6,8,10,12,14.
Addition series.
So the answer is 81, with the explanation that 81 is a composite number.

If we solve like that:
43 - 41 = 2,
47 - 43 = 4,
53 - 47 = 6,
61 - 53 = 8,
71 - 61 = 10,
73 - 71 = 2.

So, that 73 makes an error for the exact difference between the given numbers so according to me, 73 is an answer .

Why its ans can't be 47?

41 4>1
43 4>3
47 4<7
53 5>3
61 6>1
71 7>1
73 7>3
81 8>1

Every 10th digit no is more than except 47, so the answer is 47. Why this answer is wrong?

t = 41 + 2 * 1 = 43
t = 43 + 2 * 2 = 47
t = 47 + 2 * 3 = 53
t = 53 + 2 * 4 = 61
t = 61 + 2 * 5 = 71
t = 71 + 2 * 6 = 83.

In the given Series there 73 followed by 71, so the answer must be 73.

It can be solved in this way too.

41+(1*1)+1 = 43
43+(2*1)+2 = 47
47+(3*1)+3 = 53
53+(4*1)+4 = 61
61+(5*1)+5 = 71
71+(6*1)+6 = 83.

And here 81. So, therefore, it is out of the series.

41, 43, 47, 53, 61, 71, 73, 81.

Difference b/w to number is even series..

43-41 = 2.
47-43 = 4.
53-47 = 6.
61-53 = 8.
71-61 = 10.
73-71 = 12.
81-73 = 9 its wrong so answer is (D).