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# There are 5 numbers - n, w, x, y, and z. What is the value

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There are 5 numbers - n, w, x, y, and z. What is the value [#permalink]  11 Dec 2005, 06:31
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There are 5 numbers - n, w, x, y, and z.
What is the value of (n-x)+(n-w)+(n-y)+(n-z) ?

1) n is the average of n, w, x, y, and z.
2) The 5 numbers are consecutive integers.
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[#permalink]  11 Dec 2005, 13:59
From Statement 1:
(n+w+x+y+z)/5 = n
w+x+y+z = 4n

(n-x)+(n-w)+(n-y)+(n-z)
= 4n-(w+x+y+z)
= 4n - 4n
= 0
Thus SUFF

From Statement 2:
if numbers are 1,2,3,4,5
(n-x)+(n-w)+(n-y)+(n-z)
= (-1)+(-2)+(-3)+(-4)
= -10

if numbers are -2,-1,0,1,2
(n-x)+(n-w)+(n-y)+(n-z)
= (-1)+(-2)+(-3)+(-4)
= -10
Thus SUFF

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[#permalink]  11 Dec 2005, 19:38
blshah wrote:
From Statement 1:
(n+w+x+y+z)/5 = n
w+x+y+z = 4n

From Statement 2:
if numbers are 1,2,3,4,5
(n-x)+(n-w)+(n-y)+(n-z)
= (-1)+(-2)+(-3)+(-4)
= -10

if numbers are -2,-1,0,1,2
(n-x)+(n-w)+(n-y)+(n-z)
= (-1)+(-2)+(-3)+(-4)
= -10
Thus SUFF

normally, when the question uses " consecutive" , you have to consider both increasing and decreasing orders
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Re: DS - n, w, x, y, z [#permalink]  12 Dec 2005, 02:23
gamjatang wrote:
There are 5 numbers - n, w, x, y, and z.
What is the value of (n-x)+(n-w)+(n-y)+(n-z) ?

1) n is the average of n, w, x, y, and z.
2) The 5 numbers are consecutive integers.

We have - A= 4n-(x+w+y+z)?
From 1) n=(n+x+w+y+z)/5 -> A=0 - Suff

2) Let's these numbers be
L,L+1,L+2,L+3,L+4 - where L - integer
If n=L
A=4L-(4L+1+2+3+4)=-10
If n=L+1
A=4(L+1)-(4L+2+3+4)=-5
and so on
so 2 is Insuff
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[#permalink]  12 Dec 2005, 10:45
I have no OA for this question. Sorry.
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[#permalink]  12 Dec 2005, 14:34
(1) Since n-the average, (n-x)+(n-w)=(y-n)+(z-n) if x & y are values below average, and y & z are values above average. Sum of differences between an average and numbers below average equates sum of differences between numbers above average and an average.

(n-x)+(n-w)+(n-y)+(n-z)=0 Sufficient.

(2) Insufficient.

A.
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[#permalink]  14 Dec 2005, 23:55
A

(n-x)+(n-w)+(n-y)+(n-z) = 4n-x-w-y-z

S1:
n = (x+w+y+z)/4 sp S1 = 0 SUFF

S2: The order of number is NOT given. Can't assume that n is lowest. INSUFF
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Re: DS - n, w, x, y, z [#permalink]  15 Dec 2005, 02:28
gamjatang wrote:
There are 5 numbers - n, w, x, y, and z.
What is the value of (n-x)+(n-w)+(n-y)+(n-z) ?

1) n is the average of n, w, x, y, and z.
2) The 5 numbers are consecutive integers.

Statement 1: n = n+w+x+y+z/5
=> 5n = n + w + x + y + z
=> 4n = w + x + y + z
We need to find (n-x)+(n-w)+(n-y)+(n-z)
= 4n - (w+x+y+z)
= 4n - 4n = 0

From Statement 2:
Let the sequence be n,w,x,y,z
we are given w = n + 1
x = n + 2
y = n + 3
z = n + 4
We need to find (n-x)+(n-w)+(n-y)+(n-z)
= 4n - (w+x+y+z)
= 4n - (n+1+n+2+n+3+n+4)
= 4n - (4n + 10)
= 10

Hence D.
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[#permalink]  15 Dec 2005, 05:04
I got the Answer today and it says (A) is the answer.

Here is the explanation.

Since n is the average of n, w, x, y, and z,
n=(n+w+x+y+z)/5
4n=(x+y+z+w)

(n-w)+(n-y)+(n-z)+(n-w)
= 4n-(x+y+z+w)
= 0
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Re: DS - n, w, x, y, z [#permalink]  19 Feb 2006, 20:25
gamjatang wrote:
There are 5 numbers - n, w, x, y, and z.
What is the value of (n-x)+(n-w)+(n-y)+(n-z) ?

1) n is the average of n, w, x, y, and z.
2) The 5 numbers are consecutive integers.

question : 4n -(x+w+y+z)= ?

stmt1,

n+w+x+y+z/5= n

so, w+x+y+z= 4n
4n-4n=0 suff

stmt2,

consider increasing and decreasing orders
you get 10 OR -10 for the final answer

Hence A
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[#permalink]  19 Feb 2006, 20:30
(n-x)+(n-w)+(n-y)+(n-z) = n-x + n-w + n-y + n-z = 4n-x-w-y-z

(1) n = (n+w+x+y+z)/5 -> 5n = n+w+x+y+z -> 4n = w+x+y+z

So 4n-x-w-y-z = w+x+y+z - x-w-y-z = 0

Sufficient.

(2) Number are consecutive. But we do nto know the order and so we can't solve. Insufficient.

Ans A
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[#permalink]  19 Feb 2006, 21:48
gamjatang,

Can you please explain what is the explanation for statement B not being sufficient?
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[#permalink]  19 Feb 2006, 22:06
Sirisha wrote:
gamjatang,

Can you please explain what is the explanation for statement B not being sufficient?

St2 is not valid because we do not know the order of the letters n,x,w,y,z. Nothing in the question stem and nothing in the statement tells us it is of this order: n,w,x,y,z. It could be any order.

If the order is n,w,x,y,z and the consecutive integers are 1,2,3,4,5 then 4n-w-x-y-z = -10. If the order is w,x,y,z,n and the consecutive integers are 1,2,3,4,5 then 4n-w-x-y-z = 10.
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[#permalink]  19 Feb 2006, 23:25
Thanks Wilfred. I always get confused whenever i see consecutive numbers in a GMAT question. The first question that comes to my mind is whether i should take them to be consecutive in the given order.
And I feel there is a difference between DS and General Problem solving questions on this. In General Problem solving, we take them to be consecutive. but, in DS not.
It will be great if anyone can explain more about this confusion.
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[#permalink]  20 Feb 2006, 00:14
Sirisha wrote:
Thanks Wilfred. I always get confused whenever i see consecutive numbers in a GMAT question. The first question that comes to my mind is whether i should take them to be consecutive in the given order.
And I feel there is a difference between DS and General Problem solving questions on this. In General Problem solving, we take them to be consecutive. but, in DS not.
It will be great if anyone can explain more about this confusion.

I believe that in GMAT land we cannot assume anything, unless the question says '...consecutive...in this order'.
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[#permalink]  20 Feb 2006, 06:55
yeah.. i think you are right. Thanks.
[#permalink] 20 Feb 2006, 06:55
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