A number-arrangement machine, when given an input string of numbers, arranges them following a particular pattern. The following is the illustration of an input and its arrangement. Input: 3 4 9 7 6 11 Step I 9 16 81 49 36 121 Step II 12 20 90 56 42 132 Step III 17 25 95 61 47 137 Step IV 15 23 93 59 45 135   As per the rules followed in the above steps, find the appropriate answer If 159 is one of the numbers in Step IV. which of the following can be input number?

A number-arrangement machine, when given an input string of numbers, arranges them following a particular pattern. The following is the illustration of an input and its arrangement. Input: 3 4 9 7 6 11 Step I 9 16 81 49 36 121 Step II 12 20 90 56 42 132 Step III 17 25 95 61 47 137 Step IV 15 23 93 59 45 135   As per the rules followed in the above steps, find the appropriate answer If 159 is one of the numbers in Step IV. which of the following can be input number? Correct Answer 12

EXPLANATION:

The logic in this question is:

⇒ In Step (I) we have done the square of all the digits.

⇒ In step (II) we added (input + Step 1), example 9 + 3 = 12.

⇒ In step (III) we added 5 to all the digits

⇒ In step (IV) we are subtracting 2 from all the digits.

Now, 159 is in Step (IV) so to calculate input we will go backward.

For step (III) we will add 2 in 159 which is equal to 161.

For step (II) we will subtract 5 from step (III) which give us 161 - 5 = 156

For Step (I) we will subtract 12 from 156 = 144

For input, we will calculate the square root of 144 = 12