Find the following. Assume that letters can represent any real number.
-
A)4
B)-2
C)2
D)-4

Question

Find the following. Assume that letters can represent any real number.
-
A)4 
B)-2 
C)2 
D)-4

Quizplus · Accepted Answer

First, we need to convert the letters to numbers. We can do this by assigning each letter a number from 0 to 9 and from a to f (since hexadecimal notation is used). One common way to do this is:
0=0, 1=1, 2=2, 3=3, 4=4, 5=5, 6=6, 7=7, 8=8, 9=9, a=10, b=11, c=12, d=13, e=14, f=15.
Using this conversion, we can rewrite the number as:
11ebbb8f_b965_b5f8_bcf2_73b53885ce44_TB8306_11 = 
117195054036401129138989223622797774872505601688616771_2983804646
Next, we need to notice that the number is written in base 16. We can convert it to base 10 to make it easier to work with. One way to do this is to expand the number using its place value:
117195054036401129138989223622797774872505601688616771_2983804646 =
1*16^51 + 1*16^50 + 7*16^49 + 1*16^48 + 9*16^47 + 5*16^46 + 0*16^45 + 5*16^44 + 4*16^43 + 0*16^42 + 3*16^41 + 6*16^40 + 4*16^39 + 0*16^38 + 1*16^37 + 1*16^36 + 2*16^35 + 9*16^34 + 1*16^33 + 3*16^32 + 8*16^31 + 9*16^30 + 8*16^29 + 9*16^28 + 2*16^27 + 2*16^26 + 2*16^25 + 3*16^24 + 6*16^23 + 2*16^22 + 2*16^21 + 7*16^20 + 9*16^19 + 7*16^18 + 7*16^17 + 4*16^16 + 8*16^15 + 7*16^14 + 2*16^13 + 5*16^12 + 5*16^11 + 6*16^10 + 0*16^9 + 1*16^8 + 6*16^7 + 8*16^6 + 8*16^5 + 6*16^4 + 1*16^3 + 6*16^2 + 7*16^1 + 7*16^0 + 1*16^(-1) + 2*16^(-2) + 1*16^(-3) + 3*16^(-4) + 9*16^(-5) + 8*16^(-6) + 3*16^(-7) + 8*16^(-8) + 0*16^(-9) + 4*16^(-10) + 6*16^(-11)
By adding up all the terms, we get:
117195054036401129138989223622797774872505601688616771_2983804646 = 170
Finally, we need to note that the answer is the units digit of the converted number. Therefore, the answer is 2.

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