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Six shipments

by massi2884 » Thu May 10, 2012 10:22 am
S1=1/4 S2=1/5 S3=1/6 S4=3/20 S5=2/15 S6=1/10

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

OA B Source: OG13
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by neelgandham » Thu May 10, 2012 1:29 pm
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?

S1=1/4
S2=1/5
S3=1/6
S4=3/20
S5=2/15
S6=1/10
1) S2 and S4 were shipped on the first truck.

S2 + S4 = 7/20. Since, the value of shipments on the first truck is greater than 1/2 of the total value of the six shipments, we get a lot of combinations. i.e. (S2,S4,S1) or (S2,S4,S3) or (S2,S4,S3,S1) and so on... might be sent on the first truck

S2 + S4 + S1 = 12/20 > 1/2 or
S2 + S4 + S3 = 13/15 > 1/2 or
S2 + S4 + S1 + S3 = 23/30 or....

We can't(for sure) say if S3 is shipped on the first truck or if it is shipped on the second truck. So, Statement I is insufficient to answer the question.
(2) S1 and S6 were shipped on the second truck
S1 + S6 = 7/20
Since, the value of shipments on the first truck is greater than 1/2 of the total value of the six shipments, the value of shipments on the second truck should be less than 1/2 the total value of the six shipments.

If S3 is sent on the second truck, Shipment load on the second truck = S1 + S6 + S3 = 7/20 + 1/6 = 62/120 > 1/2 which shouldn't be the case because the value of shipments on the second truck should be less than 1/2 the total value of the six shipments. We, now, know that S3 is not sent in the second truck and that it is sent on the first. So, statement II is sufficient to answer that S3 is shipped on the first truck.

B
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by Brent@GMATPrepNow » Fri May 11, 2012 6:41 am
massi2884 wrote:S1=1/4 S2=1/5 S3=1/6 S4=3/20 S5=2/15 S6=1/10

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
OA B
We might be able to solve this one faster by first converting the fractions to decimals.
S1=0.25
S2=0.2
S3=0.17 (approx)
S4=0.15
S5=0.13 (approx)
S6=0.1

Statement 1: S2 and S4 were shipped on the first truck.
First truck has 0.2 + 0.15 = 0.35
Since the first truck holds more than 0.5, S3 may or may not be on that truck. For example, consider these two possible cases:
case a: first truck holds S2, S3 and S4, and second truck holds S1, S5 and S6,
case b: first truck holds S1, S2, and S4, and second truck holds S3, S5 and S6,

Statement 2: S1 and S6 were shipped on the second truck
Second truck has 0.25 + 0.1 = 0.35
Since the first truck holds more than 0.5, the second truck must have less than 0.5
Since S3 = 0.17, S3 cannot be on the second truck, otherwise the second truck would have more than 0.5
Since S3 cannot be on the second truck, we can be certain that it's on the first truck, in which case statement 2 is sufficient and the answer is B

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by hellother » Sat Jun 30, 2012 8:55 am
Hi,
I have understood the solution. But I have a small doubt , regarding the question .
I often approach GMAT questions by assuming that all the information that you need to know will be given in the question ( in any statement of the question ) and that there is no need to assume anything .

In the above question , nowhere does it say that 3 shipments are taken in each truck, though we assume it while solving. I mean , why could it not be 2 shipments in 1 truck and 4 in the other etc ?
Can anybody please clarify ?
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by Brent@GMATPrepNow » Sat Jun 30, 2012 10:31 am
hellother wrote:Hi,
I have understood the solution. But I have a small doubt , regarding the question .
I often approach GMAT questions by assuming that all the information that you need to know will be given in the question ( in any statement of the question ) and that there is no need to assume anything .

In the above question , nowhere does it say that 3 shipments are taken in each truck, though we assume it while solving. I mean , why could it not be 2 shipments in 1 truck and 4 in the other etc ?
Can anybody please clarify ?
There's nothing in the question that suggests that each truck must take 3 shipments each. Also, in the solution, we aren't assuming that each truck takes 3 shipments. However, we are told that shipments on the first truck had a value greater than 1/2 of the total value of the six shipments. So, even though statement 1 suggests that S2 and S4 were shipped on the first truck, we need to add at least one more shipment to the first truck to meet that condition (that shipments on the first truck had a value greater than 1/2 of the total value of the six shipments).

Now, for statement 1, we could have met the criteria and had these two conflicting cases:
case a: first truck holds S1, S2, S3 and S4, and second truck holds S5 and S6,
case b: first truck holds S1, S2, and S4, and second truck holds S3, S5 and S6
The result is still the same: statement 1 is not sufficient.

Cheers,
Brent
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by GMATGuruNY » Sat Jun 30, 2012 11:55 am
massi2884 wrote:S1=1/4 S2=1/5 S3=1/6 S4=3/20 S5=2/15 S6=1/10

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

OA B Source: OG13
Let the total value of the shipments = 60 units.
Then:
S1 = (1/4)60 = 15.
S2 = (1/5)60 = 12.
S3 = (1/6)60 = 10.
S4 = (3/20)60 = 9.
S5 = (2/15)60 = 8.
S6 = (1/10)60 = 6.

Since the first truck must have more than 1/2 of the total shipment, the number of units on the first truck > 30.

Statement 1: S2 and S4 were shipped on the first truck.
S2 + S4 = 12+9 = 21.
For the total value to exceed 30 units, the first truck must carry at least 10 more units.
No way to determine whether these 10 more units include S3.
INSUFFICIENT.

Statement 2: S1 and S6 were shipped on the second truck.
S1 + S6 = 15+6 = 21.
If S3 is NOT on the first the truck, then the maximum number of units on the first truck = S2 + S4 + S5 = 12+9+8 = 29.
Since the total on the first truck must exceed 30 units, S3 must be on the first truck.
SUFFICIENT.

The correct answer is B.
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by Gaurav 2013-fall » Sun Jul 01, 2012 1:44 am
massi2884 wrote:S1=1/4 S2=1/5 S3=1/6 S4=3/20 S5=2/15 S6=1/10

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

OA B Source: OG13

Thanks! Interesting problem. True representative of 700+ problems.
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by sachindia » Fri Jan 04, 2013 9:10 pm
Brent@GMATPrepNow wrote:
hellother wrote:Hi,
I have understood the solution. But I have a small doubt , regarding the question .
I often approach GMAT questions by assuming that all the information that you need to know will be given in the question ( in any statement of the question ) and that there is no need to assume anything .

In the above question , nowhere does it say that 3 shipments are taken in each truck, though we assume it while solving. I mean , why could it not be 2 shipments in 1 truck and 4 in the other etc ?
Can anybody please clarify ?
There's nothing in the question that suggests that each truck must take 3 shipments each. Also, in the solution, we aren't assuming that each truck takes 3 shipments. However, we are told that shipments on the first truck had a value greater than 1/2 of the total value of the six shipments. So, even though statement 1 suggests that S2 and S4 were shipped on the first truck, we need to add at least one more shipment to the first truck to meet that condition (that shipments on the first truck had a value greater than 1/2 of the total value of the six shipments).

Now, for statement 1, we could have met the criteria and had these two conflicting cases:
case a: first truck holds S1, S2, S3 and S4, and second truck holds S5 and S6,
case b: first truck holds S1, S2, and S4, and second truck holds S3, S5 and S6
The result is still the same: statement 1 is not sufficient.

Cheers,
Brent
hi brent,

The questions where we need to test multiple cases, my brain finds it difficult to test different things. how do u do this?
by writing down the cases? and evaluating them one by one?
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?
Regards,
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by Brent@GMATPrepNow » Sat Jan 05, 2013 8:00 am
sachindia wrote: hi brent,

The questions where we need to test multiple cases, my brain finds it difficult to test different things. how do u do this?
by writing down the cases? and evaluating them one by one?
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?
Hi sachindia,

Testing cases is best applied when you suspect that a statement may be insufficient.
This is covered in greater detail in one of our many free Data Sufficiency videos: https://www.gmatprepnow.com/module/gmat- ... cy?id=1101

In general, testing cases is also a good idea when you have no idea where to begin since the results may indicate the sufficiency of a statement. For example, if you test 3 cases for a given statement, and you get the same answer to the target question each time, this suggests that the statement may be sufficient. Even better, if you get different answers to the target question, then you can be certain that the statement is not sufficient.

As far as how one goes about testing cases, it really depends on the nature of the question. For questions where you need to plug in numbers it's often best to use a cross section of numbers (e.g., 0, 1, -1, 1/2, -1/2, 10, -10). For other questions it may be best to test extreme values (whatever those may be).

Cheers,
Brent
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by vardhankirti » Mon Apr 27, 2015 11:09 am
Hi Folks,

Does each truk carry 3 shipments each.? If it does, i donot see that mentioned in the question.

Please assist

Regards
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