Difference of the sums

[sk8ternite]

The sum of all the integers between 101 and 147, exclusive, is how much greater than the sum of the odd integers between 115 and 133, inclusive?

a. 3224
b. 4216
c. 4340
d. 4588
e. 5580

[tohellandback]

sum of integers from 101 to 147, exclusive

45/2 (102+146)
45* 124

sum of odd integers from 115 to 133
total number of odd numbers=10
sum=10/2 (115+133)
5*248

difference is 35*124
answer is C

[sk8ternite]

sum of integers from 101 to 147, exclusive

45/2 (102+146)
45* 124

sum of odd integers from 115 to 133
total number of odd numbers=10
sum=10/2 (115+133)
5*248

difference is 35*124
answer is C

How did you get 10 odd numbers between 115 and 133? By manually counting or you had a formula?

[tohellandback]

sum of integers from 101 to 147, exclusive

45/2 (102+146)
45* 124

sum of odd integers from 115 to 133
total number of odd numbers=10
sum=10/2 (115+133)
5*248

difference is 35*124
answer is C

How did you get 10 odd numbers between 115 and 133? By manually counting or you had a formula?

(last term- first term)/(common difference) +1

[sk8ternite]

but that would be for all numbers, not only odd numbers

[tohellandback]

but that would be for all numbers, not only odd numbers

for all numbers the common difference will be 1
for odd or even numbers the common difference will be 2
for numbers divisible by 3, common difference will be 3 and so on

[sk8ternite]

I understand that to find all even numbers between 115 and 133, you divide 116 by 2 which is 58, and 132 by 2, which is 66, and you get 66-58+1= 9. But I am a little confused how you approach odd numbers?

[tohellandback]

I understand that to find all even numbers between 115 and 133, you divide 116 by 2 which is 58, and 132 by 2, which is 66, and you get 66-58+1= 9. But I am a little confused how you approach odd numbers?

looks like you need examples..
how many numbers are there between 135 and 967 inclusive
(967-135)/1 +1= 833

how many odd numbers between 135 and 967, inclusive
both are odd numbers
(967-135)/2 +1=417
How many even numbers between 135 and 967, inclusive
given numbers are not even, so find the first and last terms
first term is 136. last terms is 966
answer is

(966-136)/2 +1=416
I hope its clear now. if not, send me a pm.

[gmatv09]

IMO C

sum of all the integers between 101 and 147, exclusive
==> 45/2 [102 + 146] = 45/2 [248]


sum of the odd integers between 115 and 133, inclusive
==> n/2 [2a + (n-1)d]
==> 10/2 [2*115 + 9 * 2] = 5 [248]

difference betn sums = 4340

[real2008]

is it C

[sk8ternite]

OA is C

[smar83]

Well, the OA is C, but I got lost in the Process here:

" sum of odd integers from 115 to 133
total number of odd numbers=10
sum=10/2 (115+133)
5*248 "

I got :

1)the # of odd integers to be 10.
2) Then Average came out to be 124
3) Isnt the Sum = Average * # ? I got 1240 ? How did you get 124 ?

Thanks.

[smar83]

Ohh never mind. I got it.