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time distance

by nakul17 » Mon Oct 14, 2013 11:02 am
Reiko drove from point A to point B at a constant speed, and then returned to A along the same route at a different constant speed. Did Reiko travel from A to B at a speed greater than 40 miles per hour?

(1) Reiko's average speed for the entire round trip, excluding the time spent at point B, was 80 miles per hour.

(2) It took Reiko 20 more minutes to drive from A to B than to make the return trip.


Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

Both statements TOGETHER are sufficient, but NEITHER one ALONE is sufficient.

EACH statement ALONE is sufficient.

Statements (1) and (2) TOGETHER are NOT sufficient
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by rakeshd347 » Mon Oct 14, 2013 3:31 pm
nakul17 wrote:Reiko drove from point A to point B at a constant speed, and then returned to A along the same route at a different constant speed. Did Reiko travel from A to B at a speed greater than 40 miles per hour?

(1) Reiko's average speed for the entire round trip, excluding the time spent at point B, was 80 miles per hour.

(2) It took Reiko 20 more minutes to drive from A to B than to make the return trip.


Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

Both statements TOGETHER are sufficient, but NEITHER one ALONE is sufficient.

EACH statement ALONE is sufficient.

Statements (1) and (2) TOGETHER are NOT sufficient
In this B is easy to eliminate so I would start with B.
B only tells us the time and not even the time but how much extra time it took reiko from A to B than the time from B to A.
So B is clearly insufficient. Eliminate B and D. Now answer is either A C or E.

Have a look at A.
Let us say the total distance for the entire trip from A to B and B to A is 400miles.
at 80miles/hour average speed is would take him 5 hours to cover the entire trip.
Now let us assume that reikos speed never exceeded more than 40miles/hour and was always either less than or equal to 40miles/hour.
If his speed was 40miles/hour or less for the entire tour then even at 40miles/hour it would take him 5 hours to travel from A to B only( 200 miles from A to B). now we just calculated that the total time for the entire trip was 5 hours. How can it be possible that reiko took 5 hours just from A and B. So his speed must have been more than 40miles/hour for sure.

So the answer is A
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by mevicks » Tue Oct 15, 2013 5:48 am
nakul17 wrote:Reiko drove from point A to point B at a constant speed, and then returned to A along the same route at a different constant speed. Did Reiko travel from A to B at a speed greater than 40 miles per hour?
(1) Reiko's average speed for the entire round trip, excluding the time spent at point B, was 80 miles per hour.
(2) It took Reiko 20 more minutes to drive from A to B than to make the return trip.
Let the speeds be S1 for A-B & S2 for B-A.

Q: Is S1 > 40

St1:
The average speed for a to and fro journey is given by : (2*S1*S2)/(S1+S2)

This is given as 80, thus
(2*S1*S2)/(S1+S2) = 80
(S1+S2) = (2*S1*S2)/80
(S1+S2) = (S1*S2)/40 ... (i)

Since speeds cant be negative, S2 < S1 + S2
S2 < (S1*S2)/40 ... From (i)
40*S2 < S1 * S2
S1 > 40
SUFFICIENT

St2:
S2 can be any positive number and S1 would change accordingly (by adding 20 more minutes to S2). Since we dont know the exact value of S2, this statement is INSUFFICIENT.

Answer A

Regards,
Vivek
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