Railroad Towns

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Railroad Towns

by sumit.sinha » Fri Sep 17, 2010 3:02 pm
This is a question from Manhattan Word Translations Bonus Question area:

QUESTION

Trains A and B travel at the same constant rate in opposite directions along the same route between Town G and Town H. If, after traveling for 2 hours, Train A passes Train B, how long does it take Train B to travel the entire distance between Town G and Town H?

(1) Train B started traveling between Town G and Town H 1 hour after Train A started traveling between Town H and Town G.

(2) Train B travels at the rate of 150 miles per hour.


ANSWER

We are asked to find the time that it takes Train B to travel the entire distance between the two towns.

(1) SUFFICIENT: This tells us that B started traveling 1 hour after Train A started traveling. From the question we know that Train A had been traveling for 2 hours when the trains passed each other. Thus, train B, which started 1 hour later, must have been traveling for 2 - 1 = 1 hour when the trains passed each other.

Let's call the point at which the two trains pass each other Point P. Train A travels from Town H to Point P in 2 hours, while Train B travels from Town G to Point P in 1 hour. Adding up these distances and times, we have it that the two trains covered the entire distance between the towns in 3 (i.e. 2 + 1) hours of combined travel time. Since both trains travel at the same rate, it will take 3 hours for either train to cover the entire distance alone. Thus, from Statement (1) we know that it will take Train B 3 hours to travel between Town G and Town H.

(2) INSUFFICIENT: This provides the rate for Train B. Since both trains travel at the same rate, this is also the rate for Train A. However, we have no information about when Train B started traveling (relative to when Train A started traveling) and we have no information about the distance between Town G and Town H. Thus, we cannot calculate any information about time.
[spoiler]
The correct answer is A.[/spoiler]



I think the question is flawed.
I have no issues against the Statement (1) explanation, its perfectly fine. time taken = 3 hours. It is sufficient.
But for Statement (2) explanation - it says "we have no information about when Train B started traveling (relative to when Train A started traveling)". My question is why do we even need this information? There is no mention of any relative delay in the main question, so why are we referring to Statement (1) for solving Statement (2). Isn't each of the statements are to be solved in isolation from one another??
Statement (2) also in isolation from Statement (1) is sufficient. Because time taken will come up to 4 hours.

Answer should be (D). But again as the two statements cannot conflict each other (time taken = 3 or 4) so this question itself is flawed.

Guys, please throw in your views.
Last edited by sumit.sinha on Sat Sep 18, 2010 2:04 pm, edited 1 time in total.
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by sanju09 » Sat Sep 18, 2010 1:22 am
sumit.sinha wrote:This is a question from Manhattan Word Translations Bonus Question area:

QUESTION

Trains A and B travel at the same constant rate in opposite directions along the same route between Town G and Town H. If, after traveling for 2 hours, Train A passes Train B, how long does it take Train B to travel the entire distance between Town G and Town H?

(1) Train B started traveling between Town G and Town H 1 hour after Train A started traveling between Town H and Town G.

(2) Train B travels at the rate of 150 miles per hour.


ANSWER

We are asked to find the time that it takes Train B to travel the entire distance between the two towns.

(1) SUFFICIENT: This tells us that B started traveling 1 hour after Train A started traveling. From the question we know that Train A had been traveling for 2 hours when the trains passed each other. Thus, train B, which started 1 hour later, must have been traveling for 2 - 1 = 1 hour when the trains passed each other.

Let's call the point at which the two trains pass each other Point P. Train A travels from Town H to Point P in 2 hours, while Train B travels from Town G to Point P in 1 hour. Adding up these distances and times, we have it that the two trains covered the entire distance between the towns in 3 (i.e. 2 + 1) hours of combined travel time. Since both trains travel at the same rate, it will take 3 hours for either train to cover the entire distance alone. Thus, from Statement (1) we know that it will take Train B 3 hours to travel between Town G and Town H.

(2) INSUFFICIENT: This provides the rate for Train B. Since both trains travel at the same rate, this is also the rate for Train A. However, we have no information about when Train B started traveling (relative to when Train A started traveling) and we have no information about the distance between Town G and Town H. Thus, we cannot calculate any information about time.

The correct answer is A.



I think the question is flawed.
I have no issues against the Statement (1) explanation, its perfectly fine. time taken = 3 hours. It is sufficient.
But for Statement (2) explanation - it says "we have no information about when Train B started traveling (relative to when Train A started traveling)". My question is why do we even need this information? There is no mention of any relative delay in the main question, so why are we referring to Statement (1) for solving Statement (2). Isn't each of the statements are to be solved in isolation from one another??
Statement (2) also in isolation from Statement (1) is sufficient. Because time taken will come up to 4 hours.

Answer should be (D). But again as the two statements cannot conflict each other (time taken = 3 or 4) so this question itself is flawed.

Guys, please throw in your views.

What we are not free to conclude from the stem is that

"¢ Trains started at the same time

Things that we are free to conclude from the stem are

"¢ Trains' rates are equal to x mph each.
"¢ A started from G and B started from H.
"¢ Train A travels for 2 hours before seeing Train B.

Question is: What is the value of the distance between Town G and Town H divided by x?

[1] Since, Train B started traveling 1 hour after Train A started traveling, hence Train B would have traveled 1 hour less than the Train B when they pass. Train A took 2 hours for the pass, so Train B would have traveled for 1 hour for the same pass. Their rates are same, hence Train A traveled 2 x miles and Train B traveled x miles to prove the distance between Town G and Town H to be 3 x, which could be covered by either train in 3 hours.

Sufficient

[2] We have x = 150, but do we know the distance between Town G and Town H. If the trains were started at the same time, then both would have taken an equal time of 2 hours for the pass as their rates are same, and the question could have been answered uniquely; but as mentioned earlier, we cannot assume that from the stem. Can we?

Insufficient


[spoiler]A


Relative delay remains the question if not mentioned.
[/spoiler]
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by sumit.sinha » Sat Sep 18, 2010 2:25 am
Ok. I will keep it in mind next that "Relative delay remains the question if not mentioned".
But i have a couple of other questions which may seem to follow the same reasoning, but i still believe they are flawed :P

here are they:

(I)

On January 1st Thomas deposited $2,000 into an interest bearing checking account. If he made no withdrawals, what was the total amount Thomas had in the checking account on December 31st of the same year?

(1) Thomas deposited an additional $4,000 throughout the year.
(2) The checking account earned 7 percent simple annual interest.

Official Answer:
E. Simple interest means that our boy did not earn interest on his interest, but unless you know both the exact balance throughout the year and the interest rate, you can't calculate what interest he earned. Statement 1 doesn't give you the interest rate, so eliminate AD. Statement 2 doesn't tell you whether any deposits were made, so eliminate B. When you combine them, you still don't know when the deposits were made. If the deposits were all in January, the interest will be larger than if the deposits were all in December. Eliminate C.

My Question: Statement (1) - no mention of Interest rate - clearly INSUFFICIENT. But Statement (2) - Initial amount is given, interest rate is known then why are we concerned about the extra deposits?? Does the theory "Additional deposits remains in the question if not mentioned" apply here too??

(II)

If the average of 6 numbers is 20, how many of the numbers are equal to 21?

(1) Three of the numbers are equal to 19.
(2) Three of the numbers are less than 21.

Official Answer:
E. If the average of 6 numbers is 20, then the sum of the numbers is 6 × 20 = 120. From statement 1, the numbers could be 19, 19, 19, 21, 21, 21, giving you an answer of 3, or it could be 19, 19, 19, 20, 20, 23, giving you an answer of 0, so you should write down BCE. For statement 2, you could use the exact same numbers to again get an answer of 3 and an answer of 0. Since the statement does not say "exactly three of the numbers are less than 21", there could be three or there could be more. So you should eliminate B. Using both statements together, you could plug in the same numbers yet again, getting an answer of 3 and an answer of 0. The answer is E.

My Question: I am spellbound here. I don't even know how to ask my question here :P. Bottom line is either i assume too many things OR these questions are dicey ones.