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Last year the average (arithmetic mean) salary of the 10 [#permalink]
 05 Feb 2012, 09:58
Question Stats:
66% (01:52) correct
33% (01:47) wrong based on 3 sessions
Last year the average (arithmetic mean) salary of the 10 employees of Company X was $42,800. What is the average salary of the same 10 employees this year? (1) For 8 of the 10 employees, this year’s salary is 15 percent greater than last year’s salary. (2) For 2 of the 10 employees, this year’s salary is the same as last year’s salary. Official answer is E, but I think is C given that using both statements: of 10 employees, 2 kept the same salary but 8 increases by 15%, so the average salary would increase by 1.15*0.8 + 1.0*0.2, then new average salary would be:
42,800*(1.15*0.8 + 1.0*0.2)
42,800*1.12
47,936
Am I right or what am I missing? |
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Senior Manager
Status: May The Force Be With Me (D-DAY 15 May 2012)
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Re: Error in Official Guide 12th? [#permalink]
05 Feb 2012, 10:07
Hi, I think the OA is correct. You have the average which is $ 42,800 from which the sum of total salaries paid can be calculated Now statement 1 says 8 workers for a hike of 15%. We dont have individual salary's hence increase cannot be accurately applied thus leading to an incorrect average. => INSUFFICIENT Statement 2 says 2 workers did not get a raise. again we don't know anything about the rest of the workers => INSUFFICIENT Combining both we know that 8 got a hike & 2 didn't but again we dont know which ones, hence you cant calculate the mean. => INSUFFICIENT Hence E is correct Hope this helps 
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Re: Error in Official Guide 12th? [#permalink]
05 Feb 2012, 10:42
They are asking for new average salary.
If you increase all workers salary by 15%, no matter what is the salary for each one and maintaining the same number of workers, then the new average salary will be exactly 15% higher than past year.
Example:
Worker 1: 10,000
Worker 2: 20,000
Worker 3: 20,000
Avg: 16,667
With 15% Increase
Worker 1: 11,500
Worker 2: 23,000
Worker 3: 23,000
Avg: 19,167 = 16,667*1.15 (increased the 15%)
Given that in the question just 80% of workers increase their salaries by 15% and 2 maintained the same, you don't multiply the average by 15% or 1.15 as I did in the example, you weight this 15% by just 80%, then new average salary would be:
Last Year Salary * (1.15*0.8 + 1.00*0.2)
1.00 weighted by 0.2 because only 20% of the workers maintained the salary, the rest (80%) increased by 15% (1.15)
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Re: Error in Official Guide 12th? [#permalink]
05 Feb 2012, 11:09
Okay lets assume that 6 out of 10 of the salary were 42800. The last 4 salary will be 2 people with $5 and 2 people with 85600 salary. If the two highest paying employee plus the 6 average paying employee got a 15% raise then the average would be (6*42800*1.15 + 2*85600*1.15 + 2*5)/10 = 49219.85. If the two lowest employee plus the 6 average employee got the 15% raise then (6*42800*1.15 +2*85600+2*5*1.15)/10 = 46652.15.
What you're assuming from your equation is that every number will weigh the same, so that's why 8 of the numbers are worth 80%. This is wrong because weight is determine by the magnitude of the number compare to others. 8 number could weigh only 60% of the value or 99% of the total value. Without knowing how much the weight of those 8 numbers represent there is no solution.
Hence E
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Re: Error in Official Guide 12th? [#permalink]
05 Feb 2012, 12:18
Latinapp wrote: Hi guys, maybe I'm wrong but I disagree with the official answer:
Last year the average (arithmetic mean) salary of the 10 employees of Company X was $42,800. What is the average salary of the same 10 employees this year?
(1) For 8 of the 10 employees, this year’s salary is 15 percent greater than last year’s salary.
(2) For 2 of the 10 employees, this year’s salary is the same as last year’s salary.
Official answer is E, but I think is C given that using both statements: of 10 employees, 2 kept the same salary but 8 increases by 15%, so the average salary would increase by 1.15*0.8 + 1.0*0.2, then new average salary would be:
42,800*(1.15*0.8 + 1.0*0.2)
42,800*1.12
47,936
Am I right or what am I missing? Last year the average (arithmetic mean) salary of the 10 employees of Company X was $42,800. What is the average salary of the same 10 employees this year?(1) For 8 of the 10 employees, this year’s salary is 15 percent greater than last year’s salary. (2) For 2 of the 10 employees, this year’s salary is the same as last year’s salary. Given: total salary is $42,800*10. Question: new total salary=? Each statement together is not sufficient. When taken together. Consider two possible cases: 2 lowest salaries didn't change and 8 highest salaries increased by 15%; 2 highest salaries didn't change and 8 lowest salaries increased by 15%; Ask yourself, would new total salary be the same for both cases? No, because increase in amount for the first case will be more than increase in amount for the second case. Hence even taken together statements are not sufficient. Answer: E. Hope it's clear.
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Re: Error in Official Guide 12th?
[#permalink]
05 Feb 2012, 12:18
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