Six shipments of machine parts were shipped from a factory on two

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?

For simplicity, assume 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.

Also, note that we are 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 it is given that the value of the shipments on the first truck must be greater than 30, 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 since, 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, less than 30. Thus, S3 was shipped on the first truck. Sufficient.

Answer: B.
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2 min approach to this problem.
Remember the cardinal rule of decimals and fractions. Use decimals for addition and subtraction.
This question is testing if you know apprx decimal values of common fractions
so s1=25%, s2=20%, s3=16.66%, s4=15%, s5=13.33%, s6=10%. I guess almost all of these are given in most of the standard prep books except maybe for s5. Here is how I got s5: 1/5=20% -->1/15=6.66-->2/15=13.33.

1)s2+s4=35% on the 1st truck. So s1 or s3 could get us past 50%. NSuff
2)s1+s6=35% on the 2nd truck. s3 cant be on the second truck as it will take force the proportion on it past 50%. SUFF

Ans: B

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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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.

Target question: Was S3 shipped on the first truck?

Given: The shipments on the first truck had a value greater than 1/2 of the total value of the six shipments

It might help to first convert 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,
As we can see, it's possible for S3 to be on EITHER truck 1 OR truck 2
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

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 S3 is on the first truck.
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer:

Cheers,
Brent

Hi chetan2u, amanvermagmat

Can you please let me know if I am missing anything in my understanding.

Take S2: Isn't the Statement itself saying directly that except S1 & S6, all other Shipments were shipped in First Truck. Because, each shipment was entirely on one of the trucks. .. Its Direct B.

I think we dont even need to consider if first truck had a value greater than 1/2 or not.

Hi...
You do require the statement that first truck had mote than 1/2..
Even statement I tells you that first carries S2 and S4..

So statement II does not mean that the rest all are in first truck..
May be all except S2 are in second truck or may be just S1 and S6 are in second..
We can't say for sure if we don't have that relation of load of first truck and total load
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Hi Brent ,

I think you meant Option B is sufficnet to ans the question. Looks like there is a Typo error. Marked the same in Yellow


" 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 S3 is on the first truck.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer:

Spoiler: ::
B

I know this is Math problem but while solving, I realized that even GMAT paper setter can make a mistake of SC in Math problem
Each shipment was labeled either
S1, S2, S3, S4, S5, or S6.
Either and OR is used for only two entities and not for a list - Error= Idiom+Parallelism

How do we assume that the two trucks are in the same size and 3 shipments go to each truck?

LCM of the denominator is 60, the value of
S1= 15
S2=12
S3=10
S4=9
S5=8
S6=6

THE FIRST TRUCK TAKES (T1)>1/2 OR 60*1/2=30+

(1) T1 ALREADY TOOK 12+9=21
TO BECOME GREATER THAN 30 IT MAY TAKE S3=10 OR S1=15 SO THE ANSWER IS YES AND NO; INSUFFICIENT.

(2) S1+S6 = 15+6=21 ARE IN SECOND TRUCK NOW THIS TRUCK CAN ONLY TAKE S5 BECAUSE IT HAS to BE LESS THAN 30. IF IT TAKES ANY OTHER VALUE(S) THEN THE TOTAL WILL BE MORE THAN 30 WHICH IS NOT POSSIBLE.

SO, SURELY S3 IN FIRST TRUCK. OPTION 2 IS SUFFICIENT.

THE ANSWER IS B.

Video solution from Quant Reasoning starts at 22:36
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Solution:

Question Stem Analysis:

We need to determine whether S3 was shipped on the first truck, given that the shipments on the first truck had a value greater than 1/2 of the total value of the six shipments.

Statement One Alone:

Even though we know S2 and S4 were shipped on the first truck, we can’t determine whether S3 was shipped on the first truck since it might or might be shipped on the first truck. For example, S2, S3, and S4 could be on truck one (notice that 1/5 + 1/6 + 3/20 = 31/60 > 1/2) and the other three shipments were on truck two. In this case, S3 was on truck one. However, S1, S2, and S4 could be on truck one (notice that 1/4 + 1/5 + 1/6 = 37/60 > 1/2) and the other three shipments (which includes S3) were on truck two. In this case, S3 was not on truck one. Statement one alone is not sufficient.

Statement Two Alone:

Knowing S1 and S6 were shipped on the second truck is sufficient to determine that S3 must be shipped on the first truck. That is because if S3 were shipped on the second truck, then the second truck would have to have 1/4 + 1/10 + 1/6 = 31/60 of the total value of all 6 shipments. In other words, the second truck would have more than 1/2 of the total value of all 6 shipments. However, we are given that it’s the first truck that had more than 1/2 of the total value of all 6 shipments. This means S3 couldn’t be on truck two, so it must be on truck one. Statement two alone is sufficient.

Answer: B
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Lovely observation. Im not convinced its valid though.


Edit: Seems open to discussion.

https://english.stackexchange.com/quest ... 411#170411

Posted from my mobile device

How do we know only 3 shipments go on each truck?

Answer: Option B

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Hi zangelchen
No. There is no such condition.
Say with statement 1, 21 units are on first truck.
I can have all the other shipments too on the first truck and have 60 units on first truck and 0 on the other to get a answer of YES.

Devmitra Sen
GMAT Mentor
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