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# What is the value of the expression above?

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Manager
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What is the value of the expression above? [#permalink]

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19 Oct 2010, 05:34
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(n-x) + (n-y) + (n-c) + (n-k)
What is the value of the expression above?

(1) The average (arithmetic mean) of x, y, c, and k is n.
(2) x, y, c, and k are consecutive integers.
[Reveal] Spoiler: OA

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Manager
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Re: What is the value of the expression above? [#permalink]

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19 Oct 2010, 07:28

If we solve the expression
(n-x)+(n-y)+(n-z)+(n-K)
= n - x + n - y + n -z + N - k
= 4n - x-y-z-k
= 4n - (x+y+z+k)

Now, if we consider Option1
Avg. of x, y, z, and k is n
therefore, (x+y+z+k)/4 = n
and x+y+z+k = 4n

Now if we put this value in our equation we get
4n - 4n = 0
So we get value of expression as 0

Now if we consider option2
it leads us to nowhere... therefore this option doesn't give us any value.

Therefore answer is A i.e. Option 1 is sufficient to give the answer

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Re: What is the value of the expression above? [#permalink]

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19 Oct 2010, 11:19
A

I SUFF - > 4n - (x+y+z+k) = Q
n - (x+y+z+k)/4 = Q/4
n - n = Q => 0

II INSUFF - > Even though we could say y = x+1, z = x+2 so forth; making the expression 4 n - (4x+6). But we do not know what is n or x
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Manager
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Re: What is the value of the expression above? [#permalink]

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20 Oct 2010, 05:54
yes .. it is A only...
(n-x)+(n-y)+(n-z)+(n-K) = 4n - ( X+Y+Z+K)
from I.) The average of x,y,z, and k is n. ===> (X+Y+Z+K)/4 = N
====> X+Y+Z+K = 4n

so the value of (n-x)+(n-y)+(n-z)+(n-K) = 4n - ( X+Y+Z+K)
= 4n - 4n = 0

So (1) is sufficient

from (2), I know only that x, y, z, and k are consecutive integers.

wht is the starting value or what is the last value and what is the N value..
So, clarly it not sufficient..

So ans A alone

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Re: What is the value of the expression above? [#permalink]

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20 Oct 2010, 07:08
A.

4n-(x+y+z+k)

1. (x+y+z+k)/4=n ----> (x+y+z+k)=4n -----> 4n-4n=0 (Sufficient)
2. the statement doesn't give us any relationship between x,y,z&k and n. (Insufficient)

Even if 2. gave us some kind of relationship between one of these variables and n
you will end up with multiple values.

n, n+1, n+2, n+3 --------> 4n-(4n+6)=-6
n-1, n, n+1, n+2 --------> 4n-(4n+2)=-2
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Re: (n-x) + (n-y) + (n-c) + (n-k) What is the value of the expression [#permalink]

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09 Feb 2017, 09:34
(n-x) + (n-y) + (n-c) + (n-k) = 4n - (x + y + c + k)

St1: x + y + c + k = 4n
4n - (x + y + c + k) = 4n - 4n = 0
Sufficient

St2: x, y, c, and k are consecutive integers. --> Clearly insufficient.

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Re: What is the value of the expression above? [#permalink]

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13 Feb 2017, 17:11
pzazz12 wrote:
(n-x) + (n-y) + (n-c) + (n-k)
What is the value of the expression above?

(1) The average (arithmetic mean) of x, y, c, and k is n.
(2) x, y, c, and k are consecutive integers.

We need to determine the value of (n-x) + (n-y) + (n-c) + (n-k), which can be simplified to:

4n - x - y - c - k

Statement One Alone:

The average (arithmetic mean) of x, y, c, and k is n.

We can create the following equation:

(x + y + c + k)/4 = n

x + y + c + k = 4n

Notice that 4n - x - y - c - k = 4n - (x + y + c + k), so we can substitute x + y + c + k with 4n and we have:

4n - (x + y + c + k) = 4n - 4n = 0

Statement one alone is sufficient to answer the question.

Statement Two Alone:

x, y, c, and k are consecutive integers.

Knowing that x, y, c, and k are consecutive integers is not enough information to determine the value of (n-x) + (n-y) + (n-c) + (n-k) because we still don’t know each individual value of x, y, c, and k, nor do we know anything about n. Statement two alone is not sufficient to answer the question.

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Re: What is the value of the expression above?   [#permalink] 13 Feb 2017, 17:11
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