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# If the sum of five consecutive positive integers is a, then

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If the sum of five consecutive positive integers is a, then [#permalink]

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21 Jul 2006, 12:00
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If the sum of five consecutive positive integers is a, then the sum of the next five consecutive integers in terms of a is

A) a + 1
B) a + 5
C) a + 25
D) 2a
E) 5a

The wording is a bit funky for me.. not sure what it exactly wants. Please explain if you can. Thanks!

Last edited by William509 on 21 Jul 2006, 12:30, edited 1 time in total.
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21 Jul 2006, 12:09
Let five integers are
x, x+1, x+2, x+3, x+4 Then
a = 5x+10
5x = a-10

Next five integers are
x+5, x+6, x+7, x+8, x+9
SUM = 5x + 35 = a-10+35
= a+25

But its not in the choices. There must be a typo.
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21 Jul 2006, 12:28
William509 wrote:

you mean (-a+25). Impossible.
Try taking any 5 positive numbers. There is typo in the answers. If the book gives explanation to justify (-a+25) burn that book.
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21 Jul 2006, 12:31
my fault. first time posting. i've corrected the choices.
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21 Jul 2006, 13:37
by manual calculation: a+25
let a be sum of 1,2,3,4,5
a=15
and the sum of 6,7,8,9,10 is 40.
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21 Jul 2006, 13:44
shampoo wrote:
by manual calculation: a+25
let a be sum of 1,2,3,4,5
a=15
and the sum of 6,7,8,9,10 is 40.

One more shoter method is
Set A = x,x+1, x+2, x+3, x+4
Set B is next five numbers x+5, x+6, x+7, x+8, x+9
Difference between 1st numbers of both sets = 5
Difference between 2nd numbers of both sets = 5
Difference between 3rd numbers of both sets = 5
Difference between 4th numbers of both sets = 5
Difference between 5th numbers of both sets = 5

So sum of set B will be 25 greater than that of A.
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21 Jul 2006, 13:44
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