parulmahajan89 wrote:The total cost of producing item X is equal to the sum of item X's overhead cost and production cost. If the production cost of producing X decreased by 5% in January, by what percent did the total cost of producing item X change in that same month?
(1) The overhead cost of producing item X increased by 13% in January.
(2) Before the changes in January, the overhead cost of producing item X was 5 times the production cost of producing item X.
Can someone please help me with this?
Total = O+P.
We need to find the percentage change in T. We are told that P(new) = 0.95P . Percentage change in T = 100* (Tnew-T)/(T). So we need to find
Tnew in terms of T to get an answer.
With that in mind, let's look at the statements:
(1) The overhead cost of producing item X increased by 13% in January.
We are told that O(new) = 1.13O.
Tnew = 0.95P + 1.13O. Unless we know the ratio of O:P, we can't express Tnew in terms of T. Insufficient.
(2) Before the changes in January, the overhead cost of producing item X was 5 times the production cost of producing item X.
O = 5P. We don't know what the Onew is. Insufficient.
Together, statement two provides what we were looking for in statement one. Sufficient.
C is correct.
If you aren't convinced by C, here's furtherbproof:
Pnew = 0.95P
Onew = 1.13O = 1.13*5*P
T = O+P = 6P => P = T/6
Tnew = 0.95P + 1.13*5*P = (something)*P = (something)* T/6 .
Hence we find Tnew in terms of T. This will cancel out T from top and bottom in %change and we'll get a definite answer. Hence C is correct.
