Professor Nitwit obtains a hash number of a given positive integer > 3 as follows. He subtracts 2 from the number (to get the new number), and multiplies the new number by 2 to get a term. He repeats this with the new number (to get newer numbers and terms) until the number becomes 2 or 1. The hash is defined as the sum of all the terms generated in this process. For example, with the number 5, he multiplies (5-2 =3) by 2 to get the first term 6. He multiplies (3-2=1) by 2 to get the second term 2. As the number has become 1, he stops. The hash is the sum of the two terms (6+2) or 8. If professor Nitwit is given 3 numbers 4, 9 and 13, what is the sum of the hash numbers he obtains for the three numbers?
Answers
The hash is defined as the sum of all the terms generated in this process
4-2=2
2*2-4
similarly
9-2=7
7*2=14
7-2=5
5*2=10
5-2=3
3*2=6
3-2=1
1*2=2
now third number
13-2=11
11*2=22
11-2=9
9*2=18
9-2=7
7*2=14
7-2=5
5*2=10
5-2=3
3*2=6
3-2=1
1*2=2
now add all the number to get hash nmber
hash number =2+6+10+14+18+22+2+6+10+14+4=108
You forgot to add the options to this question: Following are the options:
a. 297
b. 273
c. 290
d. 278
The answer to this question is D.
As we are subtracting 2 continuously from the resulting numbers, get a progression with a common difference of 2 and we need to multiply the sum by 2 to get hash number.
For example 5: (3 + 1) × 2 = 8
19 : (17 + 15 + 13 + ......+1) × 2 = 81 × 2 = 162
7 : (5 + 3 + 1) × 2 = 18
15: (13 + 11 + 9 + 7 + 5 + 3 + 1) × 2 = 98
Sum of the hash numbers = 278