Data Sufficiency

If it took a bus 4 hours to get from Town A to town B, what was the average speed of the bus for the trip?
1. In the first 2 hours the bus covered 100 miles
2. The average speed of the bus for the first half of the distance was twice its speed for the second half.


Source: GMAT Club App

Hi,
Let the distance between A and B be 'd'. so, avg speed is d/4
From(1): bus traveled 100 miles in first 2 hours. We don not know the distance it traveled in the next 2 hours.
Not sufficient
From(2): (d/2)/t1 = 2.(d/2)/t2 =>t2 = 2t1. But, t1+t2=4 =>t1=4/3, t2=8/3.We know nothing about 'd'
Not sufficient
From (1) & (2) we know nothing about 'd'
Not sufficient

Hence, E

Cheers!

time=4 hours. to find speed
a)avg speed for first 2 hours = 100/2 = 50 miles/hr
but no information about next 2 hours, thus insufficient.
b)let total distance=d
for first d/2 miles, speed = 2s and for next d/2 miles, speed=s
avg speed = d/4 (total distance/total time)
also total time = d/2*(1/2s + 1/s) = 3d/(4s)=4
insufficient.
both together, 2s=50 or s=25
thus 3d/100=4 or d=400/3
thus avg speed = d/4 = 100/3 miles/hr
IMO C

cans wrote:time=4 hours. to find speed
a)avg speed for first 2 hours = 100/2 = 50 miles/hr
but no information about next 2 hours, thus insufficient.
b)let total distance=d
for first d/2 miles, speed = 2s and for next d/2 miles, speed=s
avg speed = d/4 (total distance/total time)
also total time = d/2*(1/2s + 1/s) = 3d/(4s)=4
insufficient.
both together, 2s=50 or s=25
thus 3d/100=4 or d=400/3
thus avg speed = d/4 = 100/3 miles/hr
IMO C

Hey cans
Both together 2s= 50 ?
I think it is not the case as 2 hrs does not mean the distance traveled is half.
So s is not equal to 50 (you actually can not get value of s )
Hence option E

cans wrote:time=4 hours. to find speed
a)avg speed for first 2 hours = 100/2 = 50 miles/hr
but no information about next 2 hours, thus insufficient.
b)let total distance=d
for first d/2 miles, speed = 2s and for next d/2 miles, speed=s
avg speed = d/4 (total distance/total time)
also total time = d/2*(1/2s + 1/s) = 3d/(4s)=4
insufficient.
both together, 2s=50 or s=25
thus 3d/100=4 or d=400/3
thus avg speed = d/4 = 100/3 miles/hr
IMO C

Hi,
In (1), avg speed is calculated for first 2 hours but in (2), '2s' is average speed for half distance and this half distance is not traveled in 2 hours. So, you can't equate them.

Cheers!

oops! thanks for correction

Hi guys what the OA??

Please correct me if my approach is wrong. I agree that both A and B are not sufficient but yeah when we combine both

eq 2 : d/2v + d/4v = 4 so from this d/2v = 8/3 and d/4v = 4/3

from the first eqn we know that 4/3(2v) + (2-4/3)v = 100 So from this we can solve for v

v = 60 2v = 120 so we have no unknowns isn't the answer C ?

i think the answer is E

Hi could you tell me what is wrong with the approach that I have used?

phanideepak wrote:Hi guys what the OA??

Please correct me if my approach is wrong. I agree that both A and B are not sufficient but yeah when we combine both

eq 2 : d/2v + d/4v = 4 so from this d/2v = 8/3 and d/4v = 4/3

from the first eqn we know that 4/3(2v) + (2-4/3)v = 200 So from this we can solve for v

v = 60 2v = 120 so we have no unknowns isn't the answer C ?

Hey phanideepak there is problem in your first equation 4/3(2v) + (2-4/3)v = 200.
Problem here is 200 is a value which is not correct.
In first 2 hours the bus covered 100 miles does not mean in 4 hours it covered 200 miles as speed of the bus changed in between.Yes this change occurred when bus had traveled half the distance but it does not mean the time was also half used. So we can not get value 200 or in fact any value using 1st line

sjmit4 wrote:

phanideepak wrote:Hi guys what the OA??

Please correct me if my approach is wrong. I agree that both A and B are not sufficient but yeah when we combine both

eq 2 : d/2v + d/4v = 4 so from this d/2v = 8/3 and d/4v = 4/3

from the first eqn we know that 4/3(2v) + (2-4/3)v = 200 So from this we can solve for v

v = 60 2v = 120 so we have no unknowns isn't the answer C ?

Hey phanideepak there is problem in your first equation 4/3(2v) + (2-4/3)v = 200.
Problem here is 200 is a value which is not correct.
In first 2 hours the bus covered 100 miles does not mean in 4 hours it covered 200 miles as speed of the bus changed in between.Yes this change occurred when bus had traveled half the distance but it does not mean the time was also half used. So we can not get value 200 or in fact any value using 1st line

@sjmit4

Hey that was a typo.

We do know that in the first two hours the bus travelled 100 kms and we know that the bus has travelled at 2v for 4/3 and v for 8/3

so I used this in the first eqn.

2v(4/3) + v(2-4/3) = 100

from this we can solve for v and also get total d all are known now so the answer can be C. Please correct me if I'm wrong.

IMO E

phanideepak wrote:

sjmit4 wrote:

phanideepak wrote:Hi guys what the OA??

Please correct me if my approach is wrong. I agree that both A and B are not sufficient but yeah when we combine both

eq 2 : d/2v + d/4v = 4 so from this d/2v = 8/3 and d/4v = 4/3

from the first eqn we know that 4/3(2v) + (2-4/3)v = 200 So from this we can solve for v

v = 60 2v = 120 so we have no unknowns isn't the answer C ?

Hey phanideepak there is problem in your first equation 4/3(2v) + (2-4/3)v = 200.
Problem here is 200 is a value which is not correct.
In first 2 hours the bus covered 100 miles does not mean in 4 hours it covered 200 miles as speed of the bus changed in between.Yes this change occurred when bus had traveled half the distance but it does not mean the time was also half used. So we can not get value 200 or in fact any value using 1st line

@sjmit4

Hey that was a typo.

We do know that in the first two hours the bus travelled 100 kms and we know that the bus has travelled at 2v for 4/3 and v for 8/3

so I used this in the first eqn.

2v(4/3) + v(2-4/3) = 100

from this we can solve for v and also get total d all are known now so the answer can be C. Please correct me if I'm wrong.

Its getting confused by every post.
we can create 2 equations here.
1st - 2hours - 100 miles. speed of the second half not known. Hence, insufficient
2nd - first half - 2x mph, 2nd half - x mph - not sufficient

Combining both the equations,
(D1/2x) + (D2/x) = 4
D1 = 100
hence,
(50 + D2) = 4x

One equation, 2 unknown. Hence, not sufficient.

Hope it's clear now

Krish i think you have understood the question wrong. There is no question of D1 and D2 as he says that first half and second half of the distance. so d1 = d2 = d/2.

phanideepak wrote:Krish i think you have understood the question wrong. There is no question of D1 and D2 as he says that first half and second half of the distance. so d1 = d2 = d/2.

sorry, my bad..missed one of d most imp factor in the question..
In this case, can v even put these equations together?

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.