I didn't entirely understand the explanation for this one. Can someone put it in other words? I know it has to do with weighted averages.
The total cost of producing item X is equal to the sum of item X's fixed cost and variable cost. If the variable cost of producing X decreased by 5% in January, by what percent did the total cost of producing item X change in January?
(1) The fixed cost of producing item X increased by 13% in January.
(2) Before the changes in January, the fixed cost of producing item X was 5 times the variable cost of producing item X.
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- Jeff
Weighted Averages
Christine -
Yes, another weighted average problem...they seem to be getting more popular. The problem tells you that the Cost of producing X is the sum of Fixed and Variable costs, so C = F +V. It then tells you that the variable cost (V) decreased by 5% in January, and asks you how the total cost changed. Before looking at the two following statements, think about what you need to know to answer the question. There are two possibilities a) Know the numeric value and F and V and be able to calculate their numeric change (ex. F = 100 and V = 500). or b) Know the ratio between F and V and the percentage change of each variable. (e.g. F is 60% of of total cost and went up by 5% and V is 40% of total cost and went down by 5%).
Keeping that in mind, look at (1): From (1) we know that fixed cost went up 13% and we know from the Problem statement that variable cost went down by 5%. However we don't know the relative size of fixed and variable costs. If the the fixed costs are large compared to variable costs, then total costs went up, but if variable costs are large compared to fixed costs, then total costs could have gone down. So (1) by itself is insufficient and we can rule out A&D.
Consider (2). This tells us the ratio between fixed and variable costs before the changes (5:1). The problem statement tells us how the variable cost changed, but (2) by itself doesn't tell us how fixed costs changed, so is insufficient by itself and we can rule out answer B.
Now consider them together. The problem statement gives us the percent change of variable cost. (1) gives us the percent change in fixed cost, and (2) tells us the starting ratio between fixed and variable costs. So you can calculate the percent change in total cost and (1) & (2) together are sufficient and the answer is C.
You can verify this by a numerical example. Let's say the initial variable cost is $100. Then from (2) we know the initial fixed cost is 5 * $100 = $500 and to total cost is $100 + $500 = $600. We then know that the variable costs goes down by 5%, so the new variable cost is $100 * (1-5%) = $95. From (1) we know the fixed cost goes up by 13% so 500 *(1 + 13%) = $560. The new total cost is $560 + $95 = $655. The % change from the original total cost is (655-600)/600 = 9 1/6 %.
The key take away from this problem is that you don't need to know the numerical values of the components to calculate the percent change if you know the ratio between the components.
/Jeff
Yes, another weighted average problem...they seem to be getting more popular. The problem tells you that the Cost of producing X is the sum of Fixed and Variable costs, so C = F +V. It then tells you that the variable cost (V) decreased by 5% in January, and asks you how the total cost changed. Before looking at the two following statements, think about what you need to know to answer the question. There are two possibilities a) Know the numeric value and F and V and be able to calculate their numeric change (ex. F = 100 and V = 500). or b) Know the ratio between F and V and the percentage change of each variable. (e.g. F is 60% of of total cost and went up by 5% and V is 40% of total cost and went down by 5%).
Keeping that in mind, look at (1): From (1) we know that fixed cost went up 13% and we know from the Problem statement that variable cost went down by 5%. However we don't know the relative size of fixed and variable costs. If the the fixed costs are large compared to variable costs, then total costs went up, but if variable costs are large compared to fixed costs, then total costs could have gone down. So (1) by itself is insufficient and we can rule out A&D.
Consider (2). This tells us the ratio between fixed and variable costs before the changes (5:1). The problem statement tells us how the variable cost changed, but (2) by itself doesn't tell us how fixed costs changed, so is insufficient by itself and we can rule out answer B.
Now consider them together. The problem statement gives us the percent change of variable cost. (1) gives us the percent change in fixed cost, and (2) tells us the starting ratio between fixed and variable costs. So you can calculate the percent change in total cost and (1) & (2) together are sufficient and the answer is C.
You can verify this by a numerical example. Let's say the initial variable cost is $100. Then from (2) we know the initial fixed cost is 5 * $100 = $500 and to total cost is $100 + $500 = $600. We then know that the variable costs goes down by 5%, so the new variable cost is $100 * (1-5%) = $95. From (1) we know the fixed cost goes up by 13% so 500 *(1 + 13%) = $560. The new total cost is $560 + $95 = $655. The % change from the original total cost is (655-600)/600 = 9 1/6 %.
The key take away from this problem is that you don't need to know the numerical values of the components to calculate the percent change if you know the ratio between the components.
/Jeff
2 posts Page 1 of 1