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Updated on: 11 Oct 2019, 03:27
Originally posted by Thoughtosphere on 05 Mar 2013, 03:31.
Last edited by Bunuel on 11 Oct 2019, 03:27, edited 2 times in total.
Last edited by Bunuel on 11 Oct 2019, 03:27, edited 2 times in total.
Renamed the topic, edited the question and the tags.
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
83% (01:28) correct
17%
(01:29)
wrong
based on 2312
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History
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Result
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A certain bakery has 6 employees. It pays annual salaries of $14,000 to each of 2 employees, $16,000 to 1 employee, and $17,000 to each of the remaining 3 employees. The average (arithmetic mean) annual salary of these employees is closest to which of the following?
(A) $15,200
(B) $15,500
(C) $15,800
(D) $16,000
(E) $16,400
(A) $15,200
(B) $15,500
(C) $15,800
(D) $16,000
(E) $16,400
First and foremost, lets not consider the three zeros, we'll add them afterwards
The generic method to solve this question would be adding the salaries and dividing by 6 - (14 x 2 + 16 + 17 x 3) x1000/6 This would give the right answer.
The other way, to solve this average problem, using lesser calculations is:
Since the salaries are 14, 16, 17, it would mean that the average is going to be more than 14. We have, 14 x 2 and 17 x 3.
Had it been, 14 x 3 and 17 x 3, we could have concluded, the average would be (14 + 17) / 2 = 15.5
But we have 14 x 2 and 16 x 1, which would mean, the average should increase by a small amount. This would eliminate most of the choices -A B E
We are left with 15800 and 16000.
An increase of 2 in the salary, will increase the average by 2 / 6 = .36
Thus you'll get the answer 15.86
We can avoid the last step calculation too, if we observe that the increase is from 14 to 16, and will that result in an increase of .5 ?
If you have some other good and faster method to solve this problem, please share.
The generic method to solve this question would be adding the salaries and dividing by 6 - (14 x 2 + 16 + 17 x 3) x1000/6 This would give the right answer.
The other way, to solve this average problem, using lesser calculations is:
Since the salaries are 14, 16, 17, it would mean that the average is going to be more than 14. We have, 14 x 2 and 17 x 3.
Had it been, 14 x 3 and 17 x 3, we could have concluded, the average would be (14 + 17) / 2 = 15.5
But we have 14 x 2 and 16 x 1, which would mean, the average should increase by a small amount. This would eliminate most of the choices -
We are left with 15800 and 16000.
An increase of 2 in the salary, will increase the average by 2 / 6 = .36
Thus you'll get the answer 15.86
We can avoid the last step calculation too, if we observe that the increase is from 14 to 16, and will that result in an increase of .5 ?
If you have some other good and faster method to solve this problem, please share.
Pro tip:
Combine official questions for familiarity with GMAT Club Tests for analytics and tougher Focus-level practice so the real exam feels manageable.
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LalaB
I see what you are doing and it is fine but the logic behind the approach is not very clear to me. (By the way, good call on dropping the '000s. They add no value and just make the solution cumbersome)
If I were to split it into two sets, they would be:
16, 16, 16, 16, 16, 16 - so that I know that the mean here is certainly none other than 16. 16 is the middle number and the means is expected to be something around it.
-2, -2, 0, +1, +1, +1 - because actually the first term is 14 i.e. 2 less and so on.
This adds up to -1 giving an average of -1/6
So average = 16 - 1/6 = 15.8333
(Essentially the same thing)
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Dipankar6435
Joined: 27 Jan 2013
Last visit: 21 Dec 2017
Posts: 58
Status:Breaking my head!!
Location: India
Concentration: General Management, Operations
Schools: ISB '16 (A) Ross '17 (D)
GMAT 1: 740 Q50 V40
GPA: 3.51
WE:Other (Transportation)
Thoughtosphere
I am wondering why we cannot just take the average of the numbers the conventional way instead of looking at novel ways to solve this simple problem
We can ignore the zeroes and just go ahead and compute (14*2 + 16 + 17*3) / 6....which approximately comes to a little less than 16 and we have our answer. Took me less than 30 secs
General Discussion
UmangMathur
Let the salary for each person be 14. Thus, the bakery ends up getting 2 + 3*3 = 11 as extra. This again has to be divided among 6 people. 12/6 = 2 which makes it 14+2 =16. Thus, as it is 11/6, it will be somewhere close to 16 and less than that. Also, 1/6 = 0.166. Thus 10/6 = 1.66 which gives the final salary after redistribution as 15.66. Thus, the answer is C.
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LalaB
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Joined: 23 Oct 2010
Last visit: 17 Jul 2016
Posts: 226
Location: Azerbaijan
Concentration: Finance
Schools: HEC '15 (A)
GMAT 1: 690 Q47 V38
İ am not sure that my method is ideal. So, I will be happy to hear experts' opinion on this -
we have a set 14 14 16 17 17 17
lets derive from it two sets -
1) 12 12 18 18 18 18 2) +2 +2 -2 -3 (+2 means we need +2 to get 14 from 12; -2 means we need -2 to get 16 from 18 etc)
12*2/6 +18*4/6 =4+12=16 ; 16 is the mean of the 1st set
-1/6 is the mean of the 2nd set
16-0.1666= 15.8333
ans is C
we have a set 14 14 16 17 17 17
lets derive from it two sets -
1) 12 12 18 18 18 18 2) +2 +2 -2 -3 (+2 means we need +2 to get 14 from 12; -2 means we need -2 to get 16 from 18 etc)
12*2/6 +18*4/6 =4+12=16 ; 16 is the mean of the 1st set
-1/6 is the mean of the 2nd set
16-0.1666= 15.8333
ans is C
Dipankar6435
We most certainly can and it is quite easy to do in this question. Nevertheless, people like to keep a repertoire of various methods that can be used to solve questions of a particular type. Depending on the values given in the question, innovative methods can be much faster than conventional approaches.
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LalaB
Current Student
Joined: 23 Oct 2010
Last visit: 17 Jul 2016
Posts: 226
Location: Azerbaijan
Concentration: Finance
Schools: HEC '15 (A)
GMAT 1: 690 Q47 V38
Dipankar6435
: Read the article -"Want a 750+? Do this question in 30 seconds", and u will get the answer
https://www.manhattangmat.com/blog/index.php/2013/03/04/want-a-750-do-this-question-in-30-seconds/
to VeritasPrepKarishma
Thanks for checking my approach and giving good advice!
VeritasPrepKarishma
I like this method but I have 2 questions.
1. When is it more time saving to use it? As numbers in these problems allow us to solve this problem very fast with the traditional method.
2. 16 - 1/6= 15.83 it takes me more time to calculate this than 95/6... Is there any faster way to calculate 16-1/6 other then (6*16+1)/6?
Thank you so much.
bytatia
How about: 147, 156, 160, 143, 180, 167
You might appreciate the deviations method more here. Also, check out this link for more on this method: https://anaprep.com/arithmetic-usefulne ... eviations/
You should know that 1/6 = .166666... or approximately .17
You must memorize some important fraction-percentage equivalents. Check here: https://youtu.be/HxnsYI1Rws8
1/6 is 16.7% which is .167 in decimal form.
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PareshGmat
Joined: 27 Dec 2012
Last visit: 10 Jul 2016
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WE:Information Technology (Computer Software)
Posts: 1,531
Thoughtosphere
Dropping the zero's
\(\frac{14*2 + 16*1 + 17*3}{6} = \frac{95}{6}\)
\(\frac{96}{6} = 16\); so \(\frac{95}{6}\) would be just below 16
15800 fits in best
Answer = C (Solved in 15 seconds)
Posts: 31
Someone posted the solution below to the question -- I understood the approach up until the last part of adding 10. Why does adding 10 works / what's the conceptual reason? Thank you!
SOLUTION:
As we are very good at Tables up to 10×10…
4*2=8
6*1=6
7*3=21
Total…35
Divide by 6=5.8333
Add 10…15.8333 …That’s all…
SOLUTION:
As we are very good at Tables up to 10×10…
4*2=8
6*1=6
7*3=21
Total…35
Divide by 6=5.8333
Add 10…15.8333 …That’s all…
VeritasPrepKarishma
Hello,
I mistook this problem to be a weighted average problem. As a result, I chose (E) 16,400 since there are 3 people getting paid 17,000$. Can someone please point out the error in this reasoning?
gatreya14
It is a weighted average problem.
C1 = 14k, w1 = 2
C2 = 16K, w2 = 1
C3 = 17K, w3 = 3
Cavg = (C1*w1 + C2*w2 + C3*w3)/(w1 + w2 + w3)
Cavg = (2*14 + 1*16 + 3*17)/(2 + 1 + 3)
Cavg = 15.833
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JeffTargetTestPrep
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Expert reply
Posts: 2,973
UmangMathur
We can set up the weighted average equation:
[2(14,000) + 16,000 + 3(17,000)]/6
(28,0000 + 16,000 + 51,000)/6 = 95,000/6 ≈15,800
Answer: C
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14 * 2 = 28
17 * 3 = 51
16 * 1 = 16
28 + 51 + 16 = 95
95 / 6 = 15.8
15.8 * 1000 = 15,800
Answer is C.
17 * 3 = 51
16 * 1 = 16
28 + 51 + 16 = 95
95 / 6 = 15.8
15.8 * 1000 = 15,800
Answer is C.
The weighted average problem can definitely be tricky when you have different numbers of employees earning different salaries. Let me walk you through the core approach to solve this.
Let's think about this step by step:
Notice how this isn't a simple average where you just add the three salary amounts and divide by 3. We need to account for how many employees earn each salary - this is what makes it a weighted average problem.
Step 1: Count your employees and their salaries
Here's what you need to see:
- 2 employees earn $14,000 each
- 1 employee earns $16,000
- 3 employees earn $17,000 each
Total employees = 2 + 1 + 3 = 6 (always verify this!)
Step 2: Calculate the total salary expenditure
Now multiply each salary by the number of people earning it:
\(2 \times 14,000 = 28,000\)
\(1 \times 16,000 = 16,000\)
\(3 \times 17,000 = 51,000\)
Total salaries = \(28,000 + 16,000 + 51,000 = 95,000\)
Step 3: Apply the average formula
Average = Total ÷ Number of items
Average = \(\frac{95,000}{6} = 15,833.33\)
Step 4: Find the closest answer
Your calculated average is $15,833.33. Looking at the choices, $15,800 (Choice C) is only about $33 away - clearly the closest match.
Answer: C
The key insight here is recognizing that you must weight each salary by the number of employees earning it before finding the average. This is fundamentally different from just averaging the three salary values!
You can check out the step-by-step solution on Neuron by e-GMAT to master the weighted average framework systematically - including common trap patterns where students incorrectly average the salary values directly. You can also explore other GMAT official questions with detailed solutions on Neuron for structured practice here.
_________________
Let's think about this step by step:
Notice how this isn't a simple average where you just add the three salary amounts and divide by 3. We need to account for how many employees earn each salary - this is what makes it a weighted average problem.
Step 1: Count your employees and their salaries
Here's what you need to see:
- 2 employees earn $14,000 each
- 1 employee earns $16,000
- 3 employees earn $17,000 each
Total employees = 2 + 1 + 3 = 6 (always verify this!)
Step 2: Calculate the total salary expenditure
Now multiply each salary by the number of people earning it:
\(2 \times 14,000 = 28,000\)
\(1 \times 16,000 = 16,000\)
\(3 \times 17,000 = 51,000\)
Total salaries = \(28,000 + 16,000 + 51,000 = 95,000\)
Step 3: Apply the average formula
Average = Total ÷ Number of items
Average = \(\frac{95,000}{6} = 15,833.33\)
Step 4: Find the closest answer
Your calculated average is $15,833.33. Looking at the choices, $15,800 (Choice C) is only about $33 away - clearly the closest match.
Answer: C
The key insight here is recognizing that you must weight each salary by the number of employees earning it before finding the average. This is fundamentally different from just averaging the three salary values!
You can check out the step-by-step solution on Neuron by e-GMAT to master the weighted average framework systematically - including common trap patterns where students incorrectly average the salary values directly. You can also explore other GMAT official questions with detailed solutions on Neuron for structured practice here.
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