What is the average (arithmetic mean) annual salary of the 6 employees

Question

What is the average (arithmetic mean) annual salary of the 6 employees of a toy company?

(1) If the 6 annual salaries were ordered from least to greatest, each annual salary would be $6,300 greater than the preceding annual salary.
(2) The range of the 6 annual salaries is $31,500.

ID: 700302
(DS03615)

ashisplb · Accepted Answer

1. We don't know individual values. So insufficient.

2. We know only the ranges. Value can be anything. So insufficient

1+2 salaries are 0,6300,12600,18900,25200,31500

6300,12600,18900,25200,31500,37800

So any values possible. So insufficient

Hence E

sudarshan22 · Answer

(1) If the 6 annual salaries were ordered from least to greatest, each annual salary would be $6,300 greater than the preceding annual salary.
x, x + 6300, x + 2 * 6300, x + 3 * 6300, x + 4* 6300, x + 5 * 6300
Avg = ( x + ( x + 5 * 6300 )) / 2 
= ( 2x + 5 * 6300 ) / 2
No information about x
  Insufficient

(2) The range of the 6 annual salaries is $31,500.
No information about individual salary 
  Insufficient

Combining both :
No new information, St 2) can be derived from St 1) itself
  Insufficient

Hence,   E  .

sudarshan22 · Answer

ashisplb  why would anyone do a job for zero salary ?
In fact it could be any value for the least paid and the increment of 6300 then on

jackspire · Answer

Hey  sudarshan22 ,
I liked your thought process.
Why would anyone will do a job with no salary?

ashisplb  - jokes apart. Good explanation.

sudarshan22 · Answer

jackspire SC alert : The above highlighted sentence is incorrect as per SC standards though, " would " and " will " together - Duhhhh

Jokes apart, Thanks much.

jackspire · Answer

Hey sudarshan22 , Thanks for the correction.

Probus · Answer

Hi,

Stmt1 : Lets say we try to find the salary of six emp. Then it can be calculated by X(n)=X(n-1)+ 6300
So the sixth salary will be X(6)=X(1)+5(6300)
or X(6)-X(1)= 31,500
Insufficient.

Since 1 and 2 are both the same statements, So choice E

Probus

Salsanousi · Answer

The average = Sum of salaries/6

Let first salary be x

The next salary will be x + 6,300 and so it goes to the 6th salary that equals x + 6,300*5

We have one variable that we don't know

Insufficient.

Statement 2)

Tells us the range X6 - X1 = 31,500

So we don't have anything specific about the salaries. Insufficient.

Now combine

The range is basically X6 - X1 = x + 6,300 *5 - x = 31,500

Basically tautology.

We don't know the value of x.

Insufficient.

Answer choice E

RashedVai · Answer

Statement (1) basically says " the range is 31500. We should paraphrase the disguise language. If both statement says the same thing then the answer must be (D) or(E)

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exc4libur · Answer

(1) If the 6 annual salaries were ordered from least to greatest, each annual salary would be $6,300 greater than the preceding annual salary.   insufic

ap: a+d(n-1)…
set: d,a+d,a+2d,a+3d,a+4d,a+5d
(a+d)-a=6300, d=6300

(2) The range of the 6 annual salaries is $31,500.   insufic

(1&2)    insufic

(a+5d)-a=31500, 5d=31500, d=6300; no info about 'a'

Ans (E)

KingAdam44 · Answer

Even from a guy who's terrible at quant (scored Q28 in my latest mock), this supposedly hard question is incredibly straightforward:

Statement 1 clearly doesn't provide any information that is necessary to find the average, we can just determine the gap between each salary: insufficient.
Statement 2: Just giving the range will give us the extreme salaries, but what about the 3 others? Insufficient as well!

Statements 1 & 2 together: 2 possible choices can result from this choice, so it's insufficient!

E for the win, solved in 40 seconds!

Praveenksinha · Answer

Statement 1:- 
let the least salary be X
now total salary will be =X+ X+6300 + X +12600..................
We can not find X
in sufficient

Statement Two
Insufficient as we only know the diff of salary between highest and lowest

Both:- 
Again Insufficient

Basshead · Answer

What is the average (arithmetic mean) annual salary of the 6 employees of a toy company?

(1) If the 6 annual salaries were ordered from least to greatest, each annual salary would be $6,300 greater than the preceding annual salary.

This statement doesn't tell us anything. Is the least salary $1? $6,300? We aren't able to determine this -- we only know that each salary is $6,300 than the preceding salary. INSUFFICIENT.

(2) The range of the 6 annual salaries is $31,500.

This statement tells us the Same thing as statement 1. INSUFFICIENT.

(1&2) We have two statements that provide THE same information. INSUFFICIENT.

MHIKER · Answer

(1) We can't determine total salary to determine average; Insufficient.

(2) We don't know the highest and the lowest figure; Insufficient.

Considering both:
If the lowest is x and the highest is x+37,800, Even though we can't establish an equation (x+37,800-x=31,500; 0=31,500); Insufficient

The answer is E.

ueh55406 · Answer

(1) If the 6 annual salaries were ordered from least to greatest, each annual salary would be $6,300 greater than the preceding annual salary. --- it's an AP with a common difference of 6300

let  a1= x 
 an=a1+ (n-1)d 
 n=6 
 a6=x+6300(5)= x+ 31,500

In an evenly spaced set, mean =  a1+a6/2 =  x+(x+31500)/2 =  2x+31500/2  this is as simplified as it can get. clearly without knowing x we can't go forward. Insuff.

(2) The range of the 6 annual salaries is $31,500

this is telling us more or less the same thing as the above one.  a6-a1= 31500 
if  a1=x 
 a6= x+31500

we will get back the same equation:

Arithmetic mean =  a1+a6/2 =  x+(x+31500)/2 =  2x+31500/2

Insufficient.

1+2 since we get the same info from both, we can hardly use the combo for something new. C is easy to eliminate.

we're left with E.

not going to lie, I thgt, there must be some way we could get AM, by either of these statements. but sadly, that isn't the case.

satyam43298 · Answer

Can anyone help me with this, I think the answer should be C, (after solving it).

BrentGMATPrepNow · Answer

Target question :    What is the average (arithmetic mean) annual salary of the 6 employees of a toy company?

When I scan the two statements, they both feel insufficient, AND I’m pretty sure I can identify some cases with conflicting answers to the  target question . So, I’m going to head straight to……

Statements 1 and 2 combined    
There are infinitely many scenarios that satisfy BOTH statements. Here are two: 
 Case a : The six salaries are  $6,300, $12,600, $18,900, $25,200, $31,500 and $37,800  (note: range = $37,800 - $6300 = $31,500). In this case, the answer to the target question is   the average annual salary is $22,050 
 Case b : The six salaries are  $12,600, $18,900, $25,200, $31,500, $37,800 and $44,100  (note: range = $44,100 - $12,600 = $31,500). In this case, the answer to the target question is   the average annual salary is $28,350 
Since we can’t answer the  target question  with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent

woohoo921 · Answer

BrentGMATPrepNow
To see if my approach is correct, I realized that both statements say the same thing.
For statement 2, I did:
# 1: n + 6,300
# 2: (n + 6,300) + 6,300
# 3: (n + 6,300) + 6,300 + 6,300
# 4: ...
# 5: ...
# 6: (n + 6,300) + (6,300*5)

Then I took the range of these six numbers --> (n +6,300) - [(n+6,300) + (6,300*5) = 31,500 --> 31,500 = 31,500
I ruled it off on this basis because we already know from statement 1 that any value can be taken on.

Thank you in advance for your help

BrentGMATPrepNow · Answer

As long as you concluded that statement 1 alone is insufficient, then the fact that statement 2 adds no additional information, makes the correct answer E

What is the average (arithmetic mean) annual salary of the 6 employees

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GMAT Data Sufficiency (DS) Questions

What is the average (arithmetic mean) annual salary of the 6 employees

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