If w is a positive integer and 10^w – 74 in decimal notation has digits whose sum is 440, what is the value of w?
Choose the correct option:
A) 40	B) 44	C) 45	D) 46	E) 50
Answer E = 50   We have (10^w)-74, where the sum of the digits is 440.   100-74= 
<gadget id="calculator">100-74</gadget>
<output>26</output>
26, so we already have   2+6= 
<gadget id="calculator">  2+6</gadget>
<output>8</output>
8 from the 440.   Because we have a power of 10, we will have numbers like 100, 1000, 10000 and so on. This minus 74 rests 26 and a lot of 9s. E.g: 1000-74= 9926.   So dividing the  432/9= 
<gadget id="calculator"> 432/9</gadget>
<output>48</output>
48, that`s the number of 9s. and we have 2 other numbers (2 and 6) wich were 00 before the subtraction.   So we have   48 + 2= 
<gadget id="calculator">  48 + 2</gadget>
<output>50</output>
50
<result>E</result>
If w is a positive integer and 10^w – 74 in decimal notation has digits whose sum is 440, what is the value of w?