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DS (Distance Time and Speed)

Expert replies
by rintoo22 » Sat Mar 23, 2013 8:39 am
Stations X and Y are connected by two separate, straight, parallel rail lines that are 250 miles long. Train P and train Q simultaneously left Station X and Station Y, respectively, and each train traveled to the other's point of departure. The two trains passed each other after traveling for 2 hours. When the two trains passed, which train was nearer to its destination?
(1) At the time when the two trains passed, train P had averaged a speed of 70 miles per hour.
(2) Train Q averaged a speed of 55 miles per hour for the entire trip.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

Distance = 250 miles
Passed each other after travelling for 2 hours

Statement 1 (At the time when the two trains passed, train P had averaged a speed of 70 miles per hour.)
Train P
Distance = 250 miles
Rate = 70 m/hr
Time = 2 hours
Distance already covered by train P = 140 miles
Distance covered by train by train Q = 110 miles

Therefore statement 1 should be sufficient.

Similary statement 2 is sufficient as the speed of Train Q is given when 2 trains pass each other.

Answer D.

However the answer given is C. Please assist.
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Source: — Data Sufficiency |

by Anju@Gurome » Sat Mar 23, 2013 8:51 am
rintoo22 wrote:Similary statement 2 is sufficient as the speed of Train Q is given when 2 trains pass each other.
No. Average speed of Q is given for the entire trip in statement 2.
Hence, we cannot say how much distance Q has covered in first two hours.

Other than that, your analysis for statement 1 is correct.
In my opinion, the correct answer should be A.
Anju Agarwal
Quant Expert, Gurome

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by rintoo22 » Sat Mar 23, 2013 11:46 am
Thanks for the explanation.
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by srcc25anu » Sat Mar 23, 2013 12:37 pm
A. Train P had avg speed of 70 mph so in 2 hrs Train P traveled 140 miles away from Station X. Since total distance to Station Y is 250 miles, so it is 110 miles away from its destination (Station X).
At this point, Train Q will also have traveled 110 miles and hence, it is 140 miles away from its destination (that is Station X).
Train X is closer to its destination.
A is sufficient.

B. Train Q has average speed of 55 mph for entire trip. Avg for first 2 hours could be different from avg for the entire trip. hence insufficient.

Ans should be A
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