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The ratio of the number of employees of three companies X, Y, and Z is 3:4:8, respectively. Is the average age of all employees in these companies less than 40 years?
(1) The total age of all the employees in these companies is 600 years.
(2) The average age of employees in X, Y, and Z, is 40, 20, and 50 years, respectively.
(1) The total age of all the employees in these companies is 600 years.
(2) The average age of employees in X, Y, and Z, is 40, 20, and 50 years, respectively.
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26 Feb 2015, 13:12
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Hi pacifist85,
In this ratio question, we're dealing with numbers of employees. Since you CANNOT have a "fraction" of an employee, the ratio of 3:4:8 means that the number of employees at the first company MUST be a multiple of 3, the number at the second company MUST be an equivalent multiple of 4 and the number at the third company MUST be an equivalent multiple of 8.
So, we could have 3, 4 and 8 employees = 15 total
We could also have 6, 8 and 16 employees = 30 total
Etc.
In real basic terms, the total number of employees IS a positive multiple of 15. We just don't know WHICH positive multiple of 15.
We're asked if the average age of all the employees is UNDER 40. This is a YES/NO question.
Fact 1: Total age = 600
IF....
There are 15 employees, then the average age is 600/15 = 40 and the answer to the question is NO.
IF....
There are 30 employees, then the average age is 600/30 = 20 and the answer to the question is YES.
Fact 1 is INSUFFICIENT.
Fact 2: The average age at each company is 40, 20 and 50, respectively.
This information gives us an EXACT weighted average.
IF....
There are 15 employees, then the average is [3(40) + 4(20) + 8(50)]/15 = 600/15 = 40 and the answer to the question is NO.
Increasing the number of employees will NOT change the answer though, since the number of employees is based on the 3:4:8 ratio.
IF...
There are 30 employees, then the average is [6(40) + 8(20) + 16(50)]/30 = 1200/30 = 40 and the answer to the question is NO.
The answer to the question is ALWAYS NO.
Fact 2 is SUFFICIENT.
Final Answer:
GMAT assassins aren't born, they're made,
Rich
In this ratio question, we're dealing with numbers of employees. Since you CANNOT have a "fraction" of an employee, the ratio of 3:4:8 means that the number of employees at the first company MUST be a multiple of 3, the number at the second company MUST be an equivalent multiple of 4 and the number at the third company MUST be an equivalent multiple of 8.
So, we could have 3, 4 and 8 employees = 15 total
We could also have 6, 8 and 16 employees = 30 total
Etc.
In real basic terms, the total number of employees IS a positive multiple of 15. We just don't know WHICH positive multiple of 15.
We're asked if the average age of all the employees is UNDER 40. This is a YES/NO question.
Fact 1: Total age = 600
IF....
There are 15 employees, then the average age is 600/15 = 40 and the answer to the question is NO.
IF....
There are 30 employees, then the average age is 600/30 = 20 and the answer to the question is YES.
Fact 1 is INSUFFICIENT.
Fact 2: The average age at each company is 40, 20 and 50, respectively.
This information gives us an EXACT weighted average.
IF....
There are 15 employees, then the average is [3(40) + 4(20) + 8(50)]/15 = 600/15 = 40 and the answer to the question is NO.
Increasing the number of employees will NOT change the answer though, since the number of employees is based on the 3:4:8 ratio.
IF...
There are 30 employees, then the average is [6(40) + 8(20) + 16(50)]/30 = 1200/30 = 40 and the answer to the question is NO.
The answer to the question is ALWAYS NO.
Fact 2 is SUFFICIENT.
Final Answer:
GMAT assassins aren't born, they're made,
Rich
15 Jun 2014, 02:16
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Bookmarks
The ratio of the number of employees of three companies X, Y, and Z is 3:4:8, respectively. Is the average age of all employees in these companies less than 40 years?
Given that the ratio of the number of employees is \(3x:4x:8x\) for some positive multiple \(x\).
The question asks whether the average age, which is equal to \(\frac{(total \ age)}{(number \ of \ employees)} < 40\). This is equivalent to asking whether \(\frac{(total \ age)}{3x+4x+8x} < 40\), or in other words: is \((total \ age) < 600x\)?
(1) The total age of all the employees in these companies is 600 years.
The question simplifies to: is \(600 < 600x\)? Or equivalently, is \(1 < x\)?
We do not know that: if \(x=1\), then the answer is NO, but if \(x > 1\), then the answer is YES. Not sufficient.
(2) The average age of employees in X, Y, and Z, is 40, 20, and 50 years, respectively.
The above implies that \((total \ age)=40*3x+20*4x+50*8x=600x\), so the answer to the question is NO. Sufficient.
Answer: B
Given that the ratio of the number of employees is \(3x:4x:8x\) for some positive multiple \(x\).
The question asks whether the average age, which is equal to \(\frac{(total \ age)}{(number \ of \ employees)} < 40\). This is equivalent to asking whether \(\frac{(total \ age)}{3x+4x+8x} < 40\), or in other words: is \((total \ age) < 600x\)?
(1) The total age of all the employees in these companies is 600 years.
The question simplifies to: is \(600 < 600x\)? Or equivalently, is \(1 < x\)?
We do not know that: if \(x=1\), then the answer is NO, but if \(x > 1\), then the answer is YES. Not sufficient.
(2) The average age of employees in X, Y, and Z, is 40, 20, and 50 years, respectively.
The above implies that \((total \ age)=40*3x+20*4x+50*8x=600x\), so the answer to the question is NO. Sufficient.
Answer: B
