The total cost of producing item X is

[abhisheks901]

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? (CAT 1 Question 11)

(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.

My take: total cost (tc) = overhead cost(oc) + production cost(pc)
According to statement 2, oc=5(pc), (before changes made in january)

so, now, tc= oc+pc. let oc=5, pc=1, then,
tc=5+1=6.
if pc decreased by 5%, then new pc=0.95

new tc=5+0.95=5.95

and we can find % change in total cost. which is =(0.05/6)*100 = 0.833...%

and correct answer should be "Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient."

but this is not answer. the correct answer given is "Both statements TOGETHER are sufficient, but NEITHER one ALONE is sufficient."

please tell where i am wrong in my approach?

thanks in advance....

[Sage Pearce-Higgins]

Well done for writing your thinking out so clearly. Also, be sure to search before posting as this problem is discussed quite a lot elsewhere: https://www.manhattanprep.com/gmat/foru ... 20X#p89315

Translating this problem into Algebra, as you do, is a good method. However, you're making one error in your thinking.

According to statement 2, oc=5(pc), (before changes made in january)

so, now, tc= oc+pc. let oc=5, pc=1, then,
tc=5+1=6.
if pc decreased by 5%, then new pc=0.95

This is all good so far. However, there's a key phrase in Statement 2 "Before the changes in January..." We know that the production cost has decreased by 5%, but what about the overhead cost? How do we know that's stayed the same? We don't, and statement 1 reminds us that it might change. So we can't say that:

new tc=5+0.95=5.95