A factory worker produced one lot of connecting clips, and initial qua

Question

A factory worker produced one lot of connecting clips, and initial quality control found that 5/7 of clips in the lot could be used. An assembly plant purchased this lot of clips valuing the lot at $3 per each usable clip. During assembly, it became known that only 3/5 of the clips in the lot were usable. What was price per usable clip that the assembly plant paid for the lot?

A. $$2*\frac{1}{7 }$

B. $$3*\frac{4}{7 }$

C. $$5*\frac{1}{4 }$

D. $$5$

E. $$6*\frac{3}{8}$

A.  $2*\frac{1}{7 } 
 
B.  $3*\frac{4}{7 } 
 
C.  $5*\frac{1}{4 } 
 
D.  $5 
 
E.  $6*\frac{3}{8}

prikh · Answer

Let the total number of clips be 70.

Usable clips = 5/7*70 = 50 clips.

50 clips were bought @ $3/clip. Total amount paid = $150.

During the assembly line, the company realised that only 3/5 of the 50 were actually usable i.e 30 clips were usable.

Therefore, the company ended up paying $150/30 = $5/clip.

Answer - D

CrackverbalGMAT · Answer

There are 2 fractions whose denominators are 7 and 5. LCM = 35

Let us assume that there were 35 clips initially of which  \frac{5}{7} * 35 = 25  were thought to be useful by the factory.

The assembly plant purchases these 25 clips at $3 each.

Total price paid - 25 * 3 = $75

It is found that  \frac{3}{5} * 25 = 15  clips were useful

Therefore actual price/useful clip =  \frac{75}{15} = $5

Option D
 
Arun Kumar

chrisbender · Answer

If you look at the wording of the question, the entire lot was purchased not simply the ones confirmed to be initially usable IMO. That would lead to answer B.

IanStewart · Answer

I think there are typos in most of the answer choices -- they should be sums, not products.

If there were 35 clips in total, quality control first determined that 5/7 of these, or 25, were usable. The question does not make clear that the company paid $3 for each clip that quality control decreed usable (rather than $3 per actual usable clip), but that must be what the question intends (since otherwise the answer would just be $3). So the company paid $75 for the 25 allegedly usable clips. But only 3/5 of the lot of 35 clips turn out to be usable, so only 21 clips are usable. So the company paid $75/21 per clip, or $25/7 per clip, which is 3 + 4/7 dollars per clip, which I assume is what B is meant to say.

You could also pick the answer just by estimation. The company originally paid $3 per usable clip. They then found out a fairly small fraction (3/5 and 5/7 are not far apart) were unusable. That will raise their cost per clip slightly. Only answer B makes sense.

prikh · Answer

Wouldn't the usable lot be calculated from the lot that the company paid for? Why are we taking the 3/5th of the total number? imo the 3/5th would be of the 25 the company paid for, which is 15.

Company paid $75 for 25 allegedly usable. 15 were ACTUALLY really usable from the 25 purchased. Thus 75/15 = $5.

Just my opinion. Please correct if wrong. Thanks.

chrisbender · Answer

It's says that 5/7 of the lot were usable. It then says the company bought the lot, implying they bought the unusable ones as well. Otherwise why would they even put a value on the lot for the usable clips?

IanStewart · Answer

I agree with chrisbender's interpretation - the part of the question that I take to confirm that this is what the question means I've highlighted below:

As I mentioned in my post though, I think some of the wording is problematic.

prikh · Answer

A factory worker produced one lot of connecting clips, and initial quality control found that 5/7 of clips in the lot could be used. An assembly plant purchased this lot of clips valuing the lot at $3 per each usable clip.

My assumption is "this lot of clips" is referring to the usable ones.

ScottTargetTestPrep MartyTargetTestPrep Bunuel inputs please

IanStewart · Answer

Yes, it could honestly be an SC question - when it says "this lot" later in the question, it needs to be clear what that refers back to. I took it to mean the same lot they mention at the beginning of the question, but I don't think it's totally unreasonable to take it to mean just the lot of usable clips first identified by quality control, since why would they buy the 2/7 of clips that are unusable too? Still if a question defines a "lot" at the outset, then just because of how math questions are supposed to be written, I'd always take every subsequent mention of "lot" to refer to that same "lot" the question initially defined. If the question means something else here, there's a profound problem with the way it's written.

ataman · Answer

IMO it is D.

Let me explain it. It said “ initial quality control found that 5/7 of clips in the lot could be used. An assembly plant purchased this lot of clips valuing the lot at $3 per each usable clip. During assembly, it became known that only 3/5 of the clips in the lot were usable.”

Ok. We have 7x Clips. But only 5x is usable according to initial QC. It said valuing the lot for $3 per each usable clip. So 7x lot is valued $15x

During assembly, only 3/5 of 5x usable are really usable. So only 3x can be used.

So we have 3x usable clips with $15x value. It makes $5 each usable clip.

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MartyTargetTestPrep · Answer

My call is that "this lot of clips" refers to all the clips, usable or not usable. The point seems to be that the plant assigned a value to the entire lot, usable and not usable, that was calculated by multiplying the number of usable clips by $3.

However, whether "this lot of clips" is all the clips or just the usable ones, the plant still paid $3 per supposedly usable clip. That fact is all you need.

Furthermore, the question is misworded.

Notice what it asks.

What was the  price per usable clip  that the assembly plant paid  for the lot ?

A price would be either a price per usable clip or a price for the lot. It would not be both.

The only question you need to answer is "What was the price per usable clip that the assembly plant paid?"

You can and should ignore "for the lot" in the question. It's meaningless.

msing454 · Answer

It's not exactly meaningless I feel. What is meant by "price per lot" is in effective/average sense here. They purchased the entire lot for one total price, but later found out that the price per usable clips of the "entire lot" is different than what they initially purchased for. We're talking about implied unit costs in terms of what they paid for the whole lot and what they got in return as usable output.

A factory worker produced one lot of connecting clips, and initial qua

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