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If m equals the sum of the even integers from 2 to 16

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If m equals the sum of the even integers from 2 to 16 [#permalink] New post 01 Mar 2012, 14:07
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

77% (02:08) correct 23% (00:58) wrong based on 43 sessions
If m equals the sum of the even integers from 2 to 16, inclusive, and n equals the sum of the odd integers from 1 to 15, inclusive, what is the value of m - n ?

(A) 1
(B) 7
(C) 8
(D) 15
(E) 16

Any idea how can the answer be
[Reveal] Spoiler:
C?
[Reveal] Spoiler: OA

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Re: If m equals the sum of the even integers from 2 to 16 [#permalink] New post 01 Mar 2012, 14:27
Expert's post
enigma123 wrote:
If m equals the sum of the even integers from 2 to 16, inclusive, and n equals the sum of the odd integers from 1 to 15, inclusive, what is the value of m - n ?
(A) 1
(B) 7
(C) 8
(D) 15
(E) 16

Any idea how can the answer be
[Reveal] Spoiler:
C
?


Even integer from 2 to 16, inclusive (2, 4, 6, ..., 16) as well as odd integers from 1 to 15, inclusive (1, 3, 5, ..., 15) represent evenly spaced set (aka arithmetic progression). Now, the sum of the elements in any evenly spaced set is the mean (average) multiplied by the number of terms, where the mean of the set is (first+last)/2. (Check Number Theory chapter of Math Book for more: math-number-theory-88376.html)

There are 8 even integers from 2 to 16, inclusive, their sum equals to (first+last)/2*(number of terms)=(2+16)/2*8=72;

There are 8 odd integers from 1 to 15, inclusive, their sum equals to (first+last)/2*(number of terms)=(1+15)/2*8=64;

Difference: 72-64=8,

Answer: C.

Or: 2+4+6+8+10+12+14+16-(1+3+5+7+9+11+13+15)= (2-1)+(4-3)+(6-5)+(8-7)+(10-9)+(12-11)+(14-13)+(16-15)=1+1+1+1+1+1+1+1=8.

Answer: C.
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Re: If m equals the sum of the even integers from 2 to 16   [#permalink] 01 Mar 2012, 14:27
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If m equals the sum of the even integers from 2 to 16

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