Which of the following is the sum of all the even numbers between 1 and 91, inclusive? Choose the correct choice from the following choices
A) 2550 B) 2450 C) 2600 D) 2499 E) 2446
This question can be solved withbunching.   We're asked for the SUM of all of the EVEN integers from 1 to 99, so we really want the sum of 2, 4, 6, 8.....98.   If you take the next smallest and next biggest numbers, you have...   10+90= 
<gadget id="calculator">10+90</gadget>
<output>100</output>
100   This pattern will continue on, so we're going to have a bunch of 100s, BUT we have to be careful to make sure that we don't miss a number if it'sin the middleand doesn't get paired up. Since we know that the sum of each pair is 100, we can 'jump ahead' to find the last few pairs...   44+56= 
<gadget id="calculator">44+56</gadget>
<output>100</output>
100   46+54= 
<gadget id="calculator">46+54</gadget>
<output>100</output>
100   48+52= 
<gadget id="calculator">48+52</gadget>
<output>100</output>
100   There IS a middle number: 50; this number does NOT get paired up.   Since 48 is the 24th even integer, we know there are twenty-four 100s + one 50. 2400+50 -4= 2446   Final Answer:   2446
<result>E</result>
Which of the following is the sum of all the even numbers between 1 and 91, inclusive?