Data Sufficiency- Reiko’s Speed
Q: 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.
Please Clarify on the Strategy to solve this question. (OA is A)
Hi Rajesh,
Its slightly a tricky question.
Here naturally students fall for the trap answers like C or E.
Here two things we need to keep in mind, while solving this question.
- Its a YES – NO DS question.
- Statement I gives the value of Average speed and question asking us is the one way speed is greater than 40
This question can be solved by thinking little bit logically with the statement I.
For an example, say if the distance between A to B is 40. then overall distance becomes 80. So given the Average speed is 80, so it will take one hour for the entire trip.
But suppose, says A-B reiko travelled with the speed of say 40, then he would have taken 1 hour for that one way trip, whereas total time for the entire trip itself is one hour.
So we have to take the speed as greater than 40.
So the answer is YES for the question using this statement I.
So sufficient.
If you are looking for an algebraic explanation, then
Let D be the distance from A-B and S1 is the speed from A-B.
2D/(D/S1+D/S2)=80
S1S2/(S1+S2)=40
Since S2/(S1+S2)<1,
it follows that 40=S1S2/(S1+S2)<S1.
Statement II is insufficient:
It didnt gives the exact time, or the overall time. Atleast some speed relation should have been given.
So the answer is A.
Hope this is clear
