The sum W of the arithmetic sequence a, a+d, a+2d,..., a+(n-1)d is give by Wn = (n/2)*(2a + n-1)d. What is the sum of the integers 1 to 100 inclusive, with the even integers between 25 and 63 omitted.
Choose the correct choice from the following choices:
A) 4345  B) 4302  C) 4258  D) 4214  E) 4170
a method to do it under one minutes is to take advantage of the choices given...   lets work on the last digit as we have different units digit in each choice...   total sum of 1 to 100 inclusive will have 0 as the last digit..   this is so because the resultant will be 10*(sum of all single digits)... and since we are multiplying by 10,units digit will be 0...   now for single digit in sum W of even number from 25 to 63..   25 to 65 will have 4 times sum of single digit even int, 4*(2+4+6+8+0)=4*20..   here too the units digit is 0, but 64 has to be excluded from the total..   two ways from here on..   1) we are subtracting 0 from 0   so units digit should be 0, but we have to add 64..   so last/units digit =4..   2)we subtract 64 from sum of even int..   so units digit=80-4=76..   or units digit =6...   so our answer should have units digit as 10-6=4..   only D has 4 as units digit..   ans 4214
<result>D</result>
The sum W of the arithmetic sequence a, a+d, a+2d,..., a+(n-1)d is give by Wn = (n/2)*(2a + n-1)d. What is the sum of the integers 1 to 100 inclusive, with the even integers between 25 and 63 omitted.