Had a question on a data sufficiency question

[vinaybhat343]

I'm having a lot of difficulty understanding the logic behind how to find the solution to this problem. How you go about solving this?


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.





Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.


Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.


Both statements TOGETHER are sufficient, but NEITHER one ALONE is sufficient.


EACH statement ALONE is sufficient.


Statements (1) and (2) TOGETHER are NOT sufficient.

[mondegreen]

I'm having a lot of difficulty understanding the logic behind how to find the solution to this problem. How you go about solving this?

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.

Total Cost = Overhead(o)+Production(p)

Fact Statement 1 tells us that the o increased by 13% and we know that p decreased by 5%. However, we have no data for reference to calculate the change in percentage for the Total Cost. Insufficient.

Fact Statement 2 tells us that before the change, o = 5p.Thus, before the change, the total cost = 6p. Still, no reference to calculate the change in percentage.Insufficient.

Taking both together, we know that before the change, Total Cost = 6p, after the change, New T.C = 1.13o+0.95p = 1.13*5p+0.95p = 6.6p. Thus, the change in percentage can be calculated. Actually, you don't need to calculate the values.We just have to check whether it is SUFFICIENT to get the percentage change.

C.

[jlucero]

Great explanation, mondegreen. Let us know if there are more questions on this one.

[GulbaghG268]

Hi
I saw this question in the mock CAT, my query is why can't the overhead cost be fixed and Option B be sufficient to give the solution. The argument that is being given on other forums where this question is being discussed is you can not assume that the OH costs are not changing, it nowhere states in the question stem that both the values changed, why are we assuming that the OH costs are varying?

Are such questions which are debatable expected in the GMAT??

Great explanation, mondegreen. Let us know if there are more questions on this one.

[RonPurewal]

the overhead cost changes in statement 1. no problem will ever be self-contradictory, so, that's enough to guarantee that the overhead cost can change.