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22 Jul 2010, 00:49
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
20% (02:49) correct
80%
(02:53)
wrong
based on 6040
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Train A leaves New York for Boston at 3 PM and travels at the constant speed of 100 mph. An hour later, it passes Train B, which is making the trip from Boston to New York at a constant speed. If Train B left Boston at 3:50 PM and if the combined travel time of the two trains is 2 hours, what time did Train B arrive in New York?
(1) Train B arrived in New York before Train A arrived in Boston.
(2) The distance between New York and Boston is greater than 140 miles.
(1) Train B arrived in New York before Train A arrived in Boston.
(2) The distance between New York and Boston is greater than 140 miles.
Please help me know the difficulty level of this question. I was not able to solve it in even 5 mins 
22 Jul 2010, 03:34
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rohitgoel15
Let:
\(d\) be the distance between cities;
\(x\) be the rate of Train B.
"An hour later (so at 4:00PM), Train A passes Train B" --> before they pass each other A traveled 1 hour (4PM-3PM) and B traveled 1/6 hours (4PM-3:50PM).
"Combined travel time of the two trains is 2 hours" --> d/100(time to cover all distance for train A)+d/x(time to cover all distance for train B)=2 --> \(\frac{d}{100}+\frac{d}{x}=2\);
As before they pass A traveled 100 miles (1 hour at 100 miles per hour), then distance to cover for B after they pass is this 100 miles and as B traveled x*1/6 miles before they pass (1/6 hour at x miles per hour), then distance to cover for A after they pass is this x*1/6 miles --> \(100+\frac{x}{6}=d\);
So, we have:
\(\frac{d}{100}+\frac{d}{x}=2\) and \(100+\frac{x}{6}=d\).
Solving for \(d\) and \(x\)
\(d=150\) and \(x=300\);
OR:
\(d=\frac{800}{6}\approx{133.3}\) and \(x=200\).
(1) Says that train B arrived before A.
If \(x=200\) A arrives at 4:20, B at 4:30, not good;
If \(x=300\) A arrives at 4:30, B at 4:20, OK.
Sufficient
(2) Says that \(d>140\) --> \(d=150\) --> \(x=300\), arrival time for B 4:20. Sufficient
Answer D.
P.S. This is definitely a hard (700+) question.
Hope it's clear.
06 Mar 2011, 19:36
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Interesting question. I would like to share my thoughts on it. The first thing I notice is that the statements do not provide any concrete data. I cannot solve anything using them so most probably I will be able to get an answer from the data in the question stem but I will get multiple possible answers. The statements will probably help me choose one of them. (all a speculation based on the statements. The answer may be E) I know a quadratic gives me multiple answers.
Ques2.jpg [ 5.7 KiB | Viewed 184864 times ]
The diagram above incorporates the data given in the question stem. Let x be the distance from meeting point to Boston.
Speed of train A = 100 mph
Speed of train B = x/(10 min) = 6x mph (converted min to hr)
Total time taken by both is 2 hrs. Already accounted for is 1hr + (1/6) hr
The remaining (5/6) hrs is the time needed by both together to reach their respective destinations.
Time taken by train A to reach B + time taken by train B to reach NY = 5/6
x/100 + 100/6x = 5/6
3x^2 - 250x + 5000 = 0 (Painful part of the question)
x = 50, 33.33
(1) Train B arrived in New York before Train A arrived in Boston.
If x = 50, time taken by train A to reach B = 1/2 hr, time taken by train B to reach NY = 1/3 hr
If x = 33.33, time taken by train A to reach B = 1/3 hr, time taken by train B to reach NY = 1/2 hr
Since train B arrived first, x must be 50 and B must have arrived at 4:20. Sufficient.
(2) The distance between New York and Boston is greater than 140 miles.
x must be 50 to make total distance more than 140. Time taken by train B must be 1/3 hr and it must have arrived at 4:20. Sufficient.
Attachment:
Ques2.jpg [ 5.7 KiB | Viewed 184864 times ]
Speed of train A = 100 mph
Speed of train B = x/(10 min) = 6x mph (converted min to hr)
Total time taken by both is 2 hrs. Already accounted for is 1hr + (1/6) hr
The remaining (5/6) hrs is the time needed by both together to reach their respective destinations.
Time taken by train A to reach B + time taken by train B to reach NY = 5/6
x/100 + 100/6x = 5/6
3x^2 - 250x + 5000 = 0 (Painful part of the question)
x = 50, 33.33
(1) Train B arrived in New York before Train A arrived in Boston.
If x = 50, time taken by train A to reach B = 1/2 hr, time taken by train B to reach NY = 1/3 hr
If x = 33.33, time taken by train A to reach B = 1/3 hr, time taken by train B to reach NY = 1/2 hr
Since train B arrived first, x must be 50 and B must have arrived at 4:20. Sufficient.
(2) The distance between New York and Boston is greater than 140 miles.
x must be 50 to make total distance more than 140. Time taken by train B must be 1/3 hr and it must have arrived at 4:20. Sufficient.
