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05 Apr 2024, 01:30
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
51% (02:13) correct
49%
(02:02)
wrong
based on 254
sessions
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In a certain company, the average wages of employees in Town A is X, the average wages of employees in Town B is Y. If both types of employees are added together, is the new average salary smaller than (X + Y )/2?
(1) There are more employees in Town A than in town B
(2) Y − X = 4200
(1) There are more employees in Town A than in town B
(2) Y − X = 4200
05 Apr 2024, 04:36
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Multiplying the total employees in each town with their respective averages will give each groups total income. To get the average of both towns together, we add these two total incomes and divide by the combined number of employees. Mathemtically it would look like:
Let the number of employees in A = \(a\), and in B = \(b\).
\(\frac{Xa + Yb}{a+b}\)
Imagine that both towns have the same amount of people, ie \(a=b\), plugging that back into the above equation gives:
\(\frac{Xa + Ya}{a+a}\)
\(\frac{a(X+Y)}{2a}\)
\(\frac{X+Y}{2}\) which is exactly what pops up in the question stem. For the new average to be smaller, there need to be more employees in the town with the smaller average income.
(1) There are more employees in Town A than in town B
While this statement tells us that A has more people than B, without knowing more information about their respective average incomes we cannot solve this question.
INSUFFICIENT
(2) Y − X = 4200
This statement shows that town B has a greater average income than town A, however, as we do not know any information regarding the number of employees in each town, we cannot solve the question using this statement alone.
INSUFFICIENT
(1+2)
Putting the two statements together, we know that A has more employees than B, and a lower average income. This means that in terms of the average of the two towns, town A will be weighted more and thus will bring the average down. Meaning that \(\frac{X+Y}{2}>\frac{Xa + Yb}{a+b}\)
SUFFICIENT
ANSWER C
Let the number of employees in A = \(a\), and in B = \(b\).
\(\frac{Xa + Yb}{a+b}\)
Imagine that both towns have the same amount of people, ie \(a=b\), plugging that back into the above equation gives:
\(\frac{Xa + Ya}{a+a}\)
\(\frac{a(X+Y)}{2a}\)
\(\frac{X+Y}{2}\) which is exactly what pops up in the question stem. For the new average to be smaller, there need to be more employees in the town with the smaller average income.
(1) There are more employees in Town A than in town B
While this statement tells us that A has more people than B, without knowing more information about their respective average incomes we cannot solve this question.
INSUFFICIENT
(2) Y − X = 4200
This statement shows that town B has a greater average income than town A, however, as we do not know any information regarding the number of employees in each town, we cannot solve the question using this statement alone.
INSUFFICIENT
(1+2)
Putting the two statements together, we know that A has more employees than B, and a lower average income. This means that in terms of the average of the two towns, town A will be weighted more and thus will bring the average down. Meaning that \(\frac{X+Y}{2}>\frac{Xa + Yb}{a+b}\)
SUFFICIENT
ANSWER C
General Discussion
11 Apr 2024, 08:10
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Nidzo
why will A be weighted more?
