ACME problem

[vkailash17]

The ACME company manufactured x brooms per month from January to April, inclusive. On the first of each month, during the following May to December, inclusive, it sold x/2 brooms. At the beginning of production on January 1st, the ACME company had no brooms in its inventory. If storage costs were $1 per month per broom, approximately how much, in terms of x, did the ACME company pay for storage from May 2nd to December 31st, inclusive?


$x
$3x
$4x
$5x
$14x

In the explanation storage costs were condisered from may to dec but the storage costs from Jan to may was not considered.If 4 brooms are produced in Jan then the storage cost for that month is 4 rt?

Am i missing something here????

Given Explanation:
Since this problem includes variables in both the question and the answer choices, we can try solving by plugging in smart numbers. For x, we want to choose a multiple of 2 because we will have to take x/2 later. Let's say that ACME produces 4 brooms per month from January to April, so x = 4. The total number of brooms produced was (4 brooms x 4 months), or 16 brooms.

ACME sold x/2 brooms per month, or 2 brooms per month (because we chose x = 4). Now we need to start figuring out the storage costs from May 2nd to December 31st. Since ACME sold 2 brooms on May 1st, it needed to store 14 brooms that month, at a cost of $14. Following the same logic, we see that ACME sold another two brooms June 1st and stored 12 brooms, which cost the company $12. We now see that the July storage costs were $10, August were $8, September $6, October $4, November $2, and for December there were no storage costs since the last 2 brooms were sold on December 1st.

So ACME's total storage costs were 14 + 12 + 10 + 8 + 6 + 4 + 2 = $56. Now we just need to find the answer choice that gives us $56 when we plug in the same value, x = 4, that we used in the question. Since 14 x 4 = 56, $14x must be the correct value.

The correct answer is E.

[RonPurewal]

hi - you're not reading the problem carefully enough.

viz.:
... approximately how much, in terms of x, did the ACME company pay for storage from May 2nd to December 31st, inclusive?

hope that helps

[NL]

Do you know by which way we just need to count 2 terms? The choices are created to support lazy or bad-calculating-skill people (like me). Is this the intent of the author or just an accident?

(The title of the question is so fun: broom boom boom! Come on :)

[RonPurewal]

Do you know by which way we just need to count 2 terms?

I don't understand what you are asking.

[NL]

Do you know by which way we just need to count 2 terms?

I don't understand what you are asking.

It's actually an introduction for the question following it.
The introduction is this: if you just count 2 terms:
(4x-x/2)+(4x-x) = 6.5x, then you see the result is bigger than the second biggest one among choices. So we're done.

The question is: whether the author wants test takers recognize this?
(I didn't see this after getting wet with doing long counting. So I wonder, whether I should look for a trick every time I encounter long calculation)

[RonPurewal]

The only lesson worth taking there is "Pay attention to the answer choices".
Simple advice, really"”and, in retrospect, obvious"”but many, many people essentially forget that the answer choices even exist. (This is the same reason why methods like backsolving and "plugging in" are underutilized.)

[ElijahS782]

Time to see if anybody is still monitoring this thread . I was solving the same question as posted by the original poster, but I got stuck because the question does not state on which day of the month rent is assessed. The leaves the month of May in question. If rent is paid on the 1st rent for May is free. If it is paid on the last day of the month May is not free. I took the phrasing of the prompt (rent starting on the 2nd of the May) to mean it was assessed on the first of the month (otherwise why exclude the 1st?), therefore didn't include May and got the wrong answer. The question assumes rent is paid on the last day of the month for the brooms in inventory on that day.

My question is this, is the prompt ambiguous or is there a tell there that I missed? Is there something that indicates rent is assessed on the last day of the month or excludes the first as an option?

[Sage Pearce-Higgins]

Yes, this thread is still being monitored

Sure, I agree that the question is a little ambiguous, but it's not too ambiguous. I.e. despite the ambiguity, you can still solve it. Actually, the correct answer is so far away from the other answers, that you could be pretty inaccurate and still get the right answer.

Following, for argument's sake, your logic, imagine if we missed off the month of May completely. Then the answer would come out as 10.5x. That's still closest to answer choice E.

However, I think you're making an error in your logic. You state that "the question does not state on which day of the month rent is assessed. The leaves the month of May in question. If rent is paid on the 1st rent for May is free. If it is paid on the last day of the month May is not free." I would argue that it doesn't matter at all which day of the month the rent is paid on, the company will still have to pay for storage for May. I mean, if you rent an apartment, it doesn't really matter what day of the month you pay your rent on, you still have to pay the same amount.

That said, perhaps you were confused by the wording "how much, in terms of x, did the ACME company pay for storage from May 2nd to December 31st, inclusive?". You might be interpreting this as "how much did the company actually pay during that time?", not "how much did the storage cost for that time?". Now, I would argue that the first interpretation is illogical. If we open the possibility that we're interested in the bills the company actually paid, then anything is possible - the company could be in arrears, or default on its payments, or could be paying extra rent for earlier unpaid bills. In this interpretation any answer is possible and the question doesn't make sense.

There's a wider point here that if we're reading a GMAT question and we've interpreted it so that the question makes no sense, then the logical thing to do is to reject that interpretation.

[ElijahS782]

Thank you for your reply Sage, glad y'all keep tabs on these old threads, wasn't expecting a response . I think you're (not surprisingly) spot on with your assessment. In hindsight I can see that I definitely overthought the problem. I also phrased my question incorrectly when I say May would be 'free', what I meant was that rent for May would have been paid before the 2nd and therefore excluded from the answer. You already picked up on that obviously, 10.5x was the erroneous answer I got the first time. I thought I'd share my lessons learned in case some fool 4 or 10 years from now has the same problem I did.

I should have noted at the beginning of the problem, when I was deciding which interpretation to solve for, that had rent been assessed at the end of the month the answer would have been larger than what I was calculating for. This would have allowed me to know with certainty that answer E (14x) was the answer even after I calculated for the wrong interpretation as it was the only answer higher than 10.5x.

As for how I got the wrong interpretation, I think you're describing the same (or at least a similar) flaw that I found in my initial logic when I revisited the problem a few days later. I interpreted "how much ... did the ACME company pay for storage from May 2nd to December 31st...?" to essentially mean how much was the company invoiced between those dates, as opposed to how much would services provided from May 2nd to December 31st cost. I applied the modifier "from May to December" to the company rather than than to the services. It's the difference between "how much did ACME company pay from May 2nd to December 31st" and "how much was storage from May to December". I should have realized that I had read the question incorrectly for few reasons though. First, the modifier is closer to 'storage' and the GMAT doesn't try to trick you with confusing sentence structure in Quant. Second, the way I read the problem lead left a lot of room for ambiguity, which the GMAT doesn't do in Quant problems. Lastly, the number of brooms in inventory was static for all but the 1st day of the month. It makes more sense for that value to be the one intended to calculate rent for that month.

So yeah, like you said, a little ambiguous but not too ambiguous.

Anyway, thanks for the help, and good luck to all you future GMATers!

[Sage Pearce-Higgins]

Excellent analysis of your thought process - well done! Good job too for spotting that the confusion came from interpreting a modifier. All the best with your studies.