Olympiad Test: Odd One Out -1

Each of the numbers is a prime number except 12.

Each of the numbers except 81 is a prime number.

In each number except 751, the difference of third and first digit is the middle one.

In each number except 383, the product of first and third digits is the middle one.

Each of the numbers except 72 is a perfect square.

(1 × 1) + 1, (2 × 2) + 1, (3 × 3) +1, (4 × 4) + 1, 
(5 × 5) + 1, (6 × 6) + 1, (7 × 7) + 1, (8 × 8) + 1
But, 64 is out of pattern.

Alternatively 23 is added and 17 is subtracted from the terms. So, 634 is wrong.

The numbers are 7 x 8, 8 x 9, 9 x 10, 10 x 11, 11 x 12, 12 x 13.
So, 150 is wrong.

The terms are alternatively multiplied by 1.5 and divided by 3. However, 18.5 do not satisfy it.

The differences between two successive terms from the beginning are 7, 5, 7, 5, 7, 5.
So, 40 is wrong.

The terms are successively divided by 12, 10, 8, 6, ...etc.
So, 24 is wrong, it should be 8 (48/6 = 8).

Let the given numbers be A, B, C, D, E, F, G.
Then, A, A x 1 + 1, B x 2 + 2, C x 3 + 3, D x 4 + 4, E x 5 + 5, F x 6 + 6 are the required numbers.
Clearly, 228 is wrong.

Go on subtracting 24, 21, 18, 15, 12, 9 from the numbers to get the next number.
190 – 24 = 166
166 – 21 = 145
145 – 18 = 127 [Here, 128 is placed instead of 127] 127 – 15 = 112
112 – 12 = 100 ... and so on.
Therefore, 128 is wrong.

Go on subtracting 3 and dividing the result by 2 to obtain the next number.
Clearly, 46 is wrong.

Numbers must be (14)², (13)², (12)², (11)², (10)², (9)², (8)².
So, 80 is wrong.

Go on multiplying the number by 2 and adding 1 to it to get the next number.
So, 27 is wrong.

Go on dividing by 6, 5, 4, 3, 2, 1 respectively to obtain the next number.
Clearly, 92 is wrong.

2^nd term = (1^st term) × 3 – 4 = 10 × 3 – 4 = 26 
3^rd term = (2^nd term) × 3 – 4 = 26 × 3 – 4 = 74 
4^th term = (3^th term) × 3 – 4 = 74 × 3 – 4 = 218
5^th term = (4^th term) ×3 – 4 = 218 × 3 – 4 = 650.
5^th term must be 650 instead of 654.

2^nd term = (1^st term) x 1 + 1 = 15 x 1 + 1 = 16 
3^rd term = (2^nd term) x 2 + 2 = 16 x 2 + 2 = 34 
4^th term = (3^th term) x 3 + 3 = 34 x 3 + 3 = 105.
5^th term = (4^th term) x 4 + 4 = 105 x 4 + 4 = 424 
6^th term = (5^th term) x 5 + 5 = 424 x 5 + 5 = 2125 
6^th term should 2125 instead of 2124.

Go on adding 7, 9, 11, 13, 15, 17, 19 respectively to obtain the next number.
So, 135 is wrong.