Data Sufficiency

phanideepak wrote:Yep please look at my previous post. from the second question we can calculate the times for which the average velocities are v and 2v respectively and accordingly we can substitute in equation 1 and solve for v and d. Please verify my approach.

Hi,

you can't use that approach on this question, since it involves assuming facts that aren't in evidence.

From (1) we can conclude that for the first half of the time, the average rate is 50 mph.
From (2) we can conclude that the rate for the first half of the distance is two times the rate for the second half of the distance.

However, we have no link between the first half of the time and the first half of the distance, so there's no way to combine the info to solve.

For example, just because the average rate for the first 2 hours is 50mph doesn't mean that the bus travelled at exactly 50mph the entire time; it could have travelled at 98mph for the first hour and 2mph for the second; or it could have travelled at 20mph for the first and 80mph for the second. Choosing different rates within that first two hours will give you different answers to the question, as will choosing different total distances.

S (total distance) = v (speed) x t (time)
v1, t1, S1: speed, time and distance of first half of distance
v2, t2, S2: speed, time and distance of second half of distance

(1), (2) each is not sufficient.


From (2)S1= S2 => v1 x t1 = v2 x t2. As v1 = 2v2 => t2 = 2t1
We have t1+t2 = t = 4 hrs (the question gave out)
So, from the above 2 equations, we have t1=4/3 and t2=8/3

From (1)and (2), we see that in first 2 hours:
4/3 x v1 + 2/3 x (1/2 x v1) = 100 (as 4/3 + 2/3 = 2, the bus traveled first half in 4/3 hours at v1 so in the next 2/3 hours, it must travel at v2 = v1/2)

So, we could easily get solution based on the above equation. IMO, C is correct

Hope this help!

nubu wrote:S (total distance) = v (speed) x t (time)
v1, t1, S1: speed, time and distance of first half of distance
v2, t2, S2: speed, time and distance of second half of distance

(1), (2) each is not sufficient.


From (2)S1= S2 => v1 x t1 = v2 x t2. As v1 = 2v2 => t2 = 2t1
We have t1+t2 = t = 4 hrs (the question gave out)
So, from the above 2 equations, we have t1=4/3 and t2=8/3

From (1)and (2), we see that in first 2 hours:
4/3 x v1 + 2/3 x (1/2 x v1) = 100 (as 4/3 + 2/3 = 2, the bus traveled first half in 4/3 hours at v1 so in the next 2/3 hours, it must travel at v2 = v1/2)

So, we could easily get solution based on the above equation. IMO, C is correct

Hope this help!

I did the same mistake but asked Stuart to verify and as he pointed out our assumption is wrong. Please look at his explanation.

IMO E