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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]

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New post 01 Mar 2012, 14:07
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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]

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New post 01 Mar 2012, 14:27
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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]

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New post 27 Oct 2014, 20:58
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?


2 * 1 = 2

2 * 8 = 16

There are 8 even integers from 2 to 16

For every even integer, there is a 1 less odd integer whose subtraction will give result 1

(16-15) + (14-13) ................. (2 - 1)

This is repeated 8 times = 8 * 1 = 8

Answer = C
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Re: If m equals the sum of the even integers from 2 to 16 [#permalink]

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New post 26 Jan 2018, 19:04
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Re: If m equals the sum of the even integers from 2 to 16   [#permalink] 26 Jan 2018, 19:04
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