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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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01 Mar 2012, 15:07
1
5
00:00

Difficulty:

15% (low)

Question Stats:

78% (01:30) correct 22% (01:18) wrong based on 206 sessions

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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
C?

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

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01 Mar 2012, 15:27
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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 ?

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,

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.

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

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27 Oct 2014, 21:58
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
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

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

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24 Feb 2018, 03:04
Sum of 1st n odd integers is n^2 & Sum of 1st n even integers is n^2+n

-> (sum of n even integers) - (sum of n odd integers) = (n^2+n) - (n^2) = n

Here, There are 8 even integers between 2 and 16 (inclusive) and 8 odd integers between 1 and 15 (inclusive).

-> n= 8

Ans:C
Re: If m equals the sum of the even integers from 2 to 16   [#permalink] 24 Feb 2018, 03:04
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