Data Sufficiency

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?

Both statements together will be required to solve this.

Firstly, we need to know what is the percentage contribution of overheads and production in the total cost. This is provided by the second statement.

Secondly, we need to know individual changes to the overhead and production costs in January. Production cost changes are provided in the main question, overhead change is provided in statement 1.

So, we will need both statements.

Remember you do not need to solve a DS question, just check sufficiency!!

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.