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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.

OA C

Say before January, the fixed cost is $F and the variable cost is $V, and in January, the fixed cost is $F' and the variable cost is $V'.

Thus,

Before January, Total cost T = F + V and
After January, Total cost T' = F' + V' = F' + 95% of T = F' + 0.95V

We have to find out the value of [(T' - T)/T]*100%

Let's take each statement one by one.

1) The fixed cost of producing item X increased by 13% in January.

=> F' = 113% of F = 1.13F.

No information about variable cost. Insufficient.

2) Before the changes in January, the fixed cost of producing item X was 5 times the variable cost of producing item X.

=> F = 5V.

No information on after January. Insufficient.

(1) and (2) together

[(T' - T)/T]*100%

= [(F' + 0.95V - F - V)/(F + V)]*100%

= [(1.13F + 0.95V - F - V)/(F + V)]*100%

= [(0.13F - 0.05V)/(F + V)]*100%

= [(0.13*5V - 0.05V)/(5V + V)]*100%

= [(0.65V - 0.05V)/(6V)]*100%

= [0.6V)/(6V)]*100%

= 10%. Sufficient.

The correct answer: C

Hope this helps!

-Jay
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