GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 23 Oct 2018, 00:28

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# (n-x)+(n-y)+(n-z)+(n-k) What is the value of the expression above?

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 50044
(n-x)+(n-y)+(n-z)+(n-k) What is the value of the expression above?  [#permalink]

### Show Tags

19 Nov 2017, 09:15
1
00:00

Difficulty:

35% (medium)

Question Stats:

82% (01:13) correct 18% (01:29) wrong based on 53 sessions

### HideShow timer Statistics

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

What is the value of the expression above?

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

(2) x, y, z, and k are consecutive integers.

_________________
PS Forum Moderator
Joined: 25 Feb 2013
Posts: 1216
Location: India
GPA: 3.82
(n-x)+(n-y)+(n-z)+(n-k) What is the value of the expression above?  [#permalink]

### Show Tags

19 Nov 2017, 09:22
1
Bunuel wrote:
(n-x)+(n-y)+(n-z)+(n-k)

What is the value of the expression above?

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

(2) x, y, z, and k are consecutive integers.

$$(n-x)+(n-y)+(n-z)+(n-k) = 4n -(x+y+z+k)$$ ------------(1)

Statement 1: implies that $$x+y+z+k=4n$$

so equation (1) becomes $$= 4n-4n=0$$. Sufficient

Statement 2: this does not gives the value of x, y, z, k and n. Hence insufficient

Option A
Intern
Joined: 16 Aug 2016
Posts: 15
Location: India
GMAT 1: 460 Q35 V19
GPA: 3.6
WE: Brand Management (Retail)
Re: (n-x)+(n-y)+(n-z)+(n-k) What is the value of the expression above?  [#permalink]

### Show Tags

19 Nov 2017, 13:08
Ques: (n-x)+(n-y)+(n-z)+(n-k)=?
Info: nothing

Before proceeding to the statements' evaluation, simplifying the expression, we get:
4n-(x+y+z+k)=?

St (1): The average (arithmetic mean) of x, y, z, and k is n.
Statement implies that $$\frac{x+y+z+k}{4}$$=n, or,
x+y+z+k=4n
Putting this in the question stem, we get 4n-4n=0.
Therefore, St (1) is sufficient to determine the value of the given expression, hence, answer choices AD remain [BCE eliminated].

St (2): x, y, z, and k are consecutive integers.
This statement implies that y=x+1, z=x+2, and k=z+3, and thus, x+y+z+k becomes 4x+6.
Now, putting in the question stem, we get, 4n-4x+6=?
As there's no information provided about n & x, they both can assume any value and we will get different results for the given expression.
Therefore, St (2) is insufficient, hence, answer choice A.
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6403
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: (n-x)+(n-y)+(n-z)+(n-k) What is the value of the expression above?  [#permalink]

### Show Tags

21 Nov 2017, 10:55
Bunuel wrote:
(n-x)+(n-y)+(n-z)+(n-k)

What is the value of the expression above?

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

(2) x, y, z, and k are consecutive integers.

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 5 variables and 0 equation, E is most likely to be the answer.
As E is the most likely answer, we should consider both conditions 1) and 2) together before considering each of them individually. If they are not sufficient when taken together, E is the answer.

Conditions 1) & 2)

$$\frac{(x+y+z+k)}{4} = n$$
$$x + y + z + k = 4n$$
Thus $$( n - x ) + ( n - y ) + ( n - z ) + ( n - k ) = 4n - ( x+ y + z + k ) = 4n - 4n = 0$$.
Both conditions together are sufficient.

Since this question is a statistics question (one of the key question areas), CMT (Common Mistake Type) 4(A) of the VA (Variable Approach) method tells us that we should also check answers A and B.

Condition 1)
Actually, the condition 1) only is used in the conditions 1) & 2).

$$\frac{(x+y+z+k)}{4} = n$$
$$x + y + z + k = 4n$$
Thus $$( n - x ) + ( n - y ) + ( n - z ) + ( n - k ) = 4n - ( x+ y + z + k ) = 4n - 4n = 0$$.

The condition 1) only is sufficient.

Condition 2)
We can't derive anything $$4n - ( x+ y + z + k )$$ from the condition, since we don't know $$n$$.
The condition 2) is not sufficient.

In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2), when taken together. Obviously, there may be occasions on which the answer is A, B, C or D.
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only \$99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Senior Manager
Joined: 06 Jul 2016
Posts: 382
Location: Singapore
Concentration: Strategy, Finance
Re: (n-x)+(n-y)+(n-z)+(n-k) What is the value of the expression above?  [#permalink]

### Show Tags

21 Nov 2017, 12:17
Bunuel wrote:
(n-x)+(n-y)+(n-z)+(n-k)

What is the value of the expression above?

Simplify the expression

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

Quote:
(1) The average (arithmetic mean) of x, y, z, and k is n.

(2) x, y, z, and k are consecutive integers.

S1) $$\frac{(x+y+z+k)}{4}$$ = n
=> x + y + z + k = 4n
Insert the value in the original expression
=> 4n - 4n = 0
Sufficient.

S2) x, y,z,k are consecutive integers
=> x, x+1, x+2, x+3
Inset the value in the original expression
=> 4n - (4x + 6)
Insufficient.

_________________

Put in the work, and that dream score is yours!

Re: (n-x)+(n-y)+(n-z)+(n-k) What is the value of the expression above? &nbs [#permalink] 21 Nov 2017, 12:17
Display posts from previous: Sort by