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If a equals the sum of the even integers...

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by BlindVision » Wed Jun 17, 2009 10:56 am
If a equals the sum of the even integers from 2 to 20, inclusive, and b equals the sum of the odd integers from 1 to 19, inclusive, what is the value of a - b ?

A) 1

B) 10

C) 19

D) 20

E) 21


OA = B
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by ssmiles08 » Wed Jun 17, 2009 12:09 pm
some formulas you might want to remember to make your calculations easier:

# of integers: (highest multiple - lowest multiple)/increment + 1

average of evenly spaced sets: (highest + lowest)/2

now:

even numbers:

(20-2)/2 + 1 = 10 even integers.
(20+2)/2 = 11 is the average of the even set.
sum = avg*(#of elements) = 11*10 = 110 = a


odd numbers:
(19-1)/2 + 1 = 10 odd integers.
(19+1)/2 = 10 is the average of the odd set.
sum = avg*(#of elements) = 10*10 = 100 = b

a-b = 110 - 100 = 10. (B)
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by raleigh » Thu Jun 18, 2009 9:45 am
ssmiles approach is the quickest for these types of problems. If you don't feel comfortable with the formulas/approach, check out Manhattan GMAT's Number Properties book. It's a great book.
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Re: If a equals the sum of the even integers...

by kevincanspain » Thu Jun 18, 2009 1:19 pm
BlindVision wrote:If a equals the sum of the even integers from 2 to 20, inclusive, and b equals the sum of the odd integers from 1 to 19, inclusive, what is the value of a - b ?

A) 1

B) 10

C) 19

D) 20

E) 21

a - b = (20-19) + (18-17) + ... + (2 - 1) = 10

OA = B
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