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Machine X and machine Y are the only two machines used
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Updated on: 28 Dec 2019, 07:20
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Machine X and machine Y are the only two machines used to fill bottles of Zap Cola for a certain shipment. X fills each bottle in the shipment with 584 milliliters of cola. Y fills each bottle in a shipment with 594 milliliters of cola. Bottles of Zap Cola in the shipment contain an average of 590 milliliters of cola.
Quantity A
Quantity B
The number of bottles in the shipment filled by machine Y
The number of bottles in the shipment filled by machine X
A.Quantity A is greater B.Quantity B is greater C.The two quantities are equal. D.The relationship cannot be determined from the information given.
Re: Machine X and machine Y are the only two machines used
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28 Dec 2019, 07:10
3
This is a weighted average problem. While it is not possible to know precisely how many bottles each machine fills, it is possible to determine the ratio between them. Consider first what would happen if X fills only one bottle and Y fills only one bottle as well. So the average for the shipment would simply be an average of 584 to 594. On the other hand, if X filled all of the bottles, then the average of the shipment would be 584; if Y filled all of the bottles, the average would be 594.
This simple thought experiment shows that as a machine makes more of a contribution to the shipment, the overall average is pulled closer to that machine. Since the average is closer to the average of Y than it is to the average of X, machine Y must have contributed more to the shipment than X, and thus must have filled more bottles.
In addition, we can get even more definite with this. Since there is a difference of 10 between the average of X and Y, and since the overall average is 6 greater than the average of X (or 4 less than the average of Y), Y must fill 6/10ths of the bottles, and X must fill 4/10ths.
Re: Machine X and machine Y are the only two machines used
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22 Apr 2020, 08:37
2
Carcass wrote:
584 ---------- X ------------- 590 ------ Y ------ 594
X is 6 and Y is 4
In the average X has a more specific weight
B is the answer
B - wrong answer!
if y = 4 means that the weight of Y should be higher. Suppose - we have 10X and 10Y - the mean is (10*584 + 10*594)/20 = 589 The mean = 590 requires that Y should be higher than X. In our case, if X=10, Y=15 that makes mean 590. If Y < X - the mean will always be less than 589.
Re: Machine X and machine Y are the only two machines used
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22 Apr 2020, 09:00
2
gulsam wrote:
Machine X and machine Y are the only two machines used to fill bottles of Zap Cola for a certain shipment. X fills each bottle in the shipment with 584 milliliters of cola. Y fills each bottle in a shipment with 594 milliliters of cola. Bottles of Zap Cola in the shipment contain an average of 590 milliliters of cola.
Quantity A
Quantity B
The number of bottles in the shipment filled by machine Y
The number of bottles in the shipment filled by machine X
ASIDE-------------------- Key concept: If we combine EQUAL amounts of two populations, then the average of those two populations COMBINED will equal the AVERAGE of those two populations For example, let's say solution A is 30% salt, and solution B is 40% salt. If we combine EQUAL amounts of solution A and solution B, the concentration of the resulting mixture = (30 + 40)/2 = 35 So the resulting mixture is 35% salt. ------------------------
GIVEN: Machine X bottles contain (on average) 584 ml Machine Y bottles contain (on average) 594 ml
If we were to combine an EQUAL number of bottles from each machine, then the average volume of the COMBINED population = (584 + 594)/2 = 589 ml
GIVEN: The COMBINED shipment has an average volume of 590 ml Since 590 is closer to Machine Y's average volume (of 594 ml) than it is to Machine X's average volume (of 584 ml), we know that the COMBINED shipment must contain more bottles from Machine Y.
Answer: A
The above concepts are described in greater detail in the following video:
Re: Machine X and machine Y are the only two machines used
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09 Jul 2022, 03:06
Can someone say what is wrong with this calculation.
Total volume in shipment if n is number of bottles= 590n. Number of bottles filled by X = 590n/584= 1.010273573n Number of bottles filled by Y = 590n/594= 0.993265993n Since n must be a positive integer B is greater.
Re: Machine X and machine Y are the only two machines used
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09 Jul 2022, 06:41
1
Adewale wrote:
Can someone say what is wrong with this calculation.
Total volume in shipment if n is number of bottles= 590n. Number of bottles filled by X = 590n/584= 1.010273573n Number of bottles filled by Y = 590n/594= 0.993265993n Since n must be a positive integer B is greater.
Presumably, n is the TOTAL number of bottles in the shipment (including bottles filled by machine X and bottles filled by machine Y). So, 590n = the TOTAL volume of cola in the entire shipment.
Now you need to ask yourself, "What does it mean when I write: X = 590n/584= 1.010273573n?" Hint: Notice that 1.010273573n is greater than n. So, what does 1.010273573n mean?
Re: Machine X and machine Y are the only two machines used
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14 Aug 2022, 15:55
1
First of all, we can just see that 590 is close to the amount 594 than it is of 584, so without any calculations, the answer is clearly machine Y (A). However, I didn't see this at first, so here is the calculation I did:
X = fraction of bottles filled by machine X Y = fraction of bottles filled by machine Y = 1-X
584X + 594Y = 590 --> 584X + 594(1-X) = 590 584X - 594X + 594 = 590 -10X = -4 X = 4/10 (meaning 4/10 bottles are filled by machine X), which means Y = 6/10 So more bottles are filled by machine Y --> answer A