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# x is the sum of y consecutive integers. w is the sum of z

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Manager
Joined: 04 Jan 2008
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x is the sum of y consecutive integers. w is the sum of z [#permalink]

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13 Sep 2008, 02:51
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x is the sum of y consecutive integers. w is the sum of z consecutive integers. If y = 2z, and y and z are both positive integers, then each of the following could be true EXCEPT

(A) x=w
(B) x>w
(C) x/y is an integer
(D) w/z is an integer
(E) x/z is an integer

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VP
Joined: 17 Jun 2008
Posts: 1374

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14 Sep 2008, 01:12
dancinggeometry wrote:
x is the sum of y consecutive integers. w is the sum of z consecutive integers. If y = 2z, and y and z are both positive integers, then each of the following could be true EXCEPT

(A) x=w
(B) x>w
(C) x/y is an integer
(D) w/z is an integer
(E) x/z is an integer

A is impossible since sumof n consecutive numbers cannot be equal to sum of 2n consecutive integers !!!

IMO A
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cheers
Its Now Or Never

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Retired Moderator
Joined: 18 Jul 2008
Posts: 960

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14 Sep 2008, 09:40
Can you give me an example where answer B, and answer E are possible?

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Intern
Joined: 28 Jun 2008
Posts: 8

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14 Sep 2008, 12:44
1
KUDOS
(A)
X=W possible
X= Sum(1,2,3,4,5,6)=21, with Y=6
W= Sum(6,7,8)= 21, with Z=3
where Y=2Z

(B)
X>W, easy just choose numbers for X from 2 to 7, and done.

(C)
X/Y is an integer, we know that since Z and Y are integers, Z can be even or uneven, but Y can be only even in order for Y=2Z to be true. Now when you add consecutive Y numbers (where Y is even) and divide them by Y (just like an average calculation) you will get a non integer number. Answer is C
X= Sum(1,2,3,4,5,6)=21, with Y=6 21/6=3.5 a non-integer

(D)
W/Z is an integer, Z can be even or uneven, if it is even then W/Z won't be an integer, but if Z is uneven then.
W= Sum(6,7,8)=21, with Z=3 21/3=7, an integer

(E)
X/Z is an integer,
X= Sum(1,2,3,4,5,6)=21, with Y=6 and Z=3 21/3=7 an integer.
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Let us to't pell-mell...

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Senior Manager
Joined: 18 Jun 2007
Posts: 286

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14 Sep 2008, 14:03
Lets check A first.

Z--> [1,2,3,4,5] z = 5, Sum (w) = 15
Y--> [-1,-2,-3,0,1,2,3,4,5,6] y = 10(2z) and Sum(x) = 15

C it is. reasoning given by MRGiacalone

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Re: Zumit PS 015   [#permalink] 14 Sep 2008, 14:03
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