Ifaequals the sum of the even integers from 2 to 100, inclusive, andbequals the sum of the odd integers from 1 to 99, inclusive, what is the value of a - b ?  Choose one
A) 1
B) 50
C) 19
D) 20
E) 21
This is a solution from Beatthegmat:   even numbers:   (100-2)/2 + 1= 
<gadget id="calculator">(100-2)/2 + 1</gadget>
<output>50</output>
50 even integers.   (100+2)/2= 
<gadget id="calculator">(100+2)/2</gadget>
<output>51</output>
51 is the average of the even set.   sum= avg*(#of elements) = 51*50= 
<gadget id="calculator">51*50</gadget>
<output>2_550</output>
2550= a   odd numbers:   (99-1)/2 + 1= 
<gadget id="calculator">(99-1)/2 + 1</gadget>
<output>50</output>
50 odd integers.   (99+1)/2= 
<gadget id="calculator">(99+1)/2</gadget>
<output>50</output>
50 is the average of the odd set.   sum= avg*(#of elements) = 50*50= 
<gadget id="calculator">50*50</gadget>
<output>2_500</output>
2500= b   a-b = 2550 - 2500= 
<gadget id="calculator">2550 - 2500</gadget>
<output>50</output>
50. (50)
<result>B</result>
Ifaequals the sum of the even integers from 2 to 100, inclusive, andbequals the sum of the odd integers from 1 to 99, inclusive, what is the value of a - b ?