Find the value of the sum , if .
A) 64
B) 60
C) 20
D) 8
E) 32

Question

Find the value of the sum  , if  . ​
A) 64 
B) 60 
C) 20 
D) 8 
E) 32

Quizplus · Accepted Answer

Since all the numbers except for the last two digits are the same, we only need to focus on the last two digits of each. We can convert each hexadecimal digit to its decimal equivalent: 
b = 11
0 = 0
3 = 3
9 = 9
6 = 6
f = 15
5 = 5
a = 10
7 = 7
8 = 8
3 = 3
f = 15
5 = 5
0 = 0
0 = 0
5 = 5
1 = 1
1 = 1

The sum of the last two digits of the first number is 3 + 9 = 12, which gives us a carryover of 1. 
The sum of the last two digits of the second number, including the carryover, is 7 + 2 + 1 = 10. 
Therefore, the sum of the two numbers is 10 with a carryover of 1. Since we are adding in hexadecimal, we can represent this as 1,0 (i.e. the carryover goes to the next digit). The answer can be written as D in hexadecimal or 13 in decimal. However, the question asks for the decimal value, so the answer is 8.

Find the Value of the Sum , If