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Six shipments of machine parts were shipped from a factory [#permalink]
14 Dec 2012, 05:24

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Difficulty:

75% (hard)

Question Stats:

47% (03:28) correct
52% (02:45) wrong based on 275 sessions

Attachment:

Table.png [ 23.3 KiB | Viewed 3468 times ]

Six shipments of machine parts were shipped from a factory on two trucks, with each shipment entirely on one of the trucks. Each shipment was labeled either S1, S2, S3, S4, S5, or S6. The table shows the value of each shipment as a fraction of the total value of the six shipments. If the shipments on the first truck had a value greater than 1/2 of the total value of the six shipments, was S3 shipped on the first truck?

(1) S2 and S4 were shipped on the first truck. (2) S1 and S6 were shipped on the second truck.

Re: Six shipments of machine parts were shipped from a factory [#permalink]
14 Dec 2012, 05:36

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Expert's post

Six shipments of machine parts were shipped from a factory on two trucks, with each shipment entirely on one of the trucks. Each shipment was labeled either S1, S2, S3, S4, S5, or S6. The table shows the value of each shipment as a fraction of the total value of the six shipments. If the shipments on the first truck had a value greater than 1/2 of the total value of the six shipments, was S3 shipped on the first truck?

To simplify, let's assume that the total value of the shipments is 60 (LCM of 4, 5, 6, 20 15 and 10).

In this case: S1=15, S2=12, S3=10, S4=9, S5=8, and S6=6.

Given that the total value of the shipments on the first truck is greater than 1/2*60=30.

(1) S2 and S4 were shipped on the first truck. S2+S4=12+9=21. Since the value of the shipments on the first truck is greater than 30, then S3=10 may or may not be on the first truck. Not sufficient.

(2) S1 and S6 were shipped on the second truck. S1+S6=15+6=21. S3 cannot be on that truck sine in this case the value of the shipments on the second truck would be 31, which would mean that the value of the shipments on the first truck was 29<30. Thus S3 was shipped on the first truck. Sufficient.

Re: Six shipments of machine parts were shipped from a factory [#permalink]
14 Dec 2012, 06:58

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Expert's post

Walkabout wrote:

Attachment:

Table.png

Six shipments of machine parts were shipped from a factory on two trucks, with each shipment entirely on one of the trucks. Each shipment was labeled either S1, S2, S3, S4, S5, or S6. The table shows the value of each shipment as a fraction of the total value of the six shipments. If the shipments on the first truck had a value greater than 1/2 of the total value of the six shipments, was S3 shipped on the first truck?

(1) S2 and S4 were shipped on the first truck. (2) S1 and S6 were shipped on the second truck.

Total sum is 60/60.

Given fact: Value of shipments on first truck > 30/60. Question- was S3 shipped on first truck?

1)S2 and S4 were shipped on the first truck. Sum of S2 and S4-21/60. Anything that makes the sum more than 30/60 would counter. If S2 were also on first truck then also the value of shipment becomes more than 30/60 and if S3 were also on first truck then also the value of shipment becomes more than 30/60. Hence insufficient.

2) S1 and S6 were shipped on the second truck. Sum of S1 and S6-21/60. Now the key thing here is that the value of shipments on second truck has to be less than 30/60. So if we add S3 on second truck, the value of shipment becomes more than 30/60. Hence it clearly implies that S3 is on first ship only.
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Re: Six shipments of machine parts were shipped from a factory [#permalink]
04 Jan 2013, 21:09

Marcab wrote:

Walkabout wrote:

Attachment:

Table.png

Six shipments of machine parts were shipped from a factory on two trucks, with each shipment entirely on one of the trucks. Each shipment was labeled either S1, S2, S3, S4, S5, or S6. The table shows the value of each shipment as a fraction of the total value of the six shipments. If the shipments on the first truck had a value greater than 1/2 of the total value of the six shipments, was S3 shipped on the first truck?

(1) S2 and S4 were shipped on the first truck. (2) S1 and S6 were shipped on the second truck.

Total sum is 60/60.

Given fact: Value of shipments on first truck > 30/60. Question- was S3 shipped on first truck?

1)S2 and S4 were shipped on the first truck. Sum of S2 and S4-21/60. Anything that makes the sum more than 30/60 would counter. If S2 were also on first truck then also the value of shipment becomes more than 30/60 and if S3 were also on first truck then also the value of shipment becomes more than 30/60. Hence insufficient.

2) S1 and S6 were shipped on the second truck. Sum of S1 and S6-21/60. Now the key thing here is that the value of shipments on second truck has to be less than 30/60. So if we add S3 on second truck, the value of shipment becomes more than 30/60. Hence it clearly implies that S3 is on first ship only.

The questions where we need to test multiple things, my brain finds it difficult to test different things. how do u do this? by writing down the cases? Also, To read and understand and get the lcm and to make all the ratios to have 60 in denominator, it took around 2 mins 45 secs.. after which I had to guess to avoid over shooting the time limit.

how much time did u take to solve this one?
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hope is a good thing, maybe the best of things. And no good thing ever dies.

Re: Six shipments of machine parts were shipped from a factory [#permalink]
04 Jan 2013, 21:28

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Expert's post

Actually, I don't remember much about time but the LCM thing just comes intuitively not because I want to do this way but because I don't want to do much effort. Moreover I actually didn't take the LCM, I just looked for a common multiple and 60 seemed the best fit. Apart from 60, 120, 180 could have also been equally good. As you mentioned that it took about 2min 45 sec to do this question, I shall say don't worry because some questions from topics such as SD, Probability, Algebra with which you are very comfortable will defnitely come on the test day. You may be able to solve those questions under 50-55 seconds and hence compensate for the former. But for a piece for advice, just practice. Once you practice such questions, then you will become quite comfortable with the topic and the format of such questions. Hope that helps.
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