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Bunuel
In the morning, Chris drives from Toronto to Oakville and in the evening he drives back from Oakville to Toronto on the same road. Was his average speed for the entire round trip less than 100 miles per hour?

(1) In the morning, Chris drove at an average speed of at least 10 miles per hour while travelling from Toronto to Oakville.
(2) In the evening, Chris drove at an average speed which was no more than 50 miles per hour while travelling from Oakville to Toronto.


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IMO the answer is E, because
Statement 1 Not evening speed is given ==> Insuffient
Statement 2 No morning speed is given ==> Insuffient

Combined
Evening speed max is 49.9 and morning speed can be any thing greater than 10 which drives the avg speed either sides of inequality. Hence E
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Bunuel
In the morning, Chris drives from Toronto to Oakville and in the evening he drives back from Oakville to Toronto on the same road. Was his average speed for the entire round trip less than 100 miles per hour?

(1) In the morning, Chris drove at an average speed of at least 10 miles per hour while travelling from Toronto to Oakville.
(2) In the evening, Chris drove at an average speed which was no more than 50 miles per hour while travelling from Oakville to Toronto.


Kudos for a correct solution.


+1 for E.
Statement 1:Avg speed =Atleast 10 miles per hour(can be 1000 or 50 or 100). Insufficient
Statement 2: Avg speed from O to T is <=50 miles per hour. Insufficient. No info about anything else.
Even combining both, we can't solve
Answer E
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IMO E,
seconds statement is out.
1st statement says at least 10, hence actual speed can be anything above 10, which can change the answer to below 100 miles or above 100miles
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IMO C
Statement 1 not sufficient since no information about the evening trip is given. Statement 2 not sufficient since no information about morning trip is given.
But combining both we have formula
Avg speed=2(s1*s2)/(s1+s2)
It can be determined. Hence C
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the problem seems complex but the solution is easy, just solve the inequality.
Now, the average speed should be 2/ (1/ v1 + 1 / v2 ) < 100?
From each st, we can see that change the sign every time we use reciprocal, then we should find the answer
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The way I solved this is this:

Average Speed for total trip= 2D/(T1+T2) where D is trip from T to O and T1 and T2 are the times taken for each way.

The question can be simplified to arrive at D>50(T1+T2)?

Statement 1 implies that D>=10T1. This is insufficient

Statement 2 implies that D<=50T2. This is sufficient since this means that D<50(T1+T2) and hence answer is no.

B
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Hi,

Answer is B.

Let V1 be velocity from toronto to oakvilee, V2 be velocity from oakville to toronto.

Average Velocity = 2(v1 * v2)/(v1+v2),
Question is => 2(v1 * v2)/(v1+v2) < 100?

Statement1
given v1 >= 10, so if both v1 = v2 = 102, the average velocity > 100,
if both v1 = v2 = 98, the average velocity < 100. -> InSuff

Statement2
given v2 <= 50,

Let v2 = 50,
let us assume that average velocity < 100
2 * (50 v1) / (50 + v1) < 100,
rearranging,
100 v1 < 5000 + 100 v1,
0 < 5000 => which is definitely true, so our assumption average velocity < 100 is true.

even if v1 were less than 50 (say, 40)
then above eqn becomes -20v1 < 4000, which is definitely true, as v1 will be positive,
So no matter whatever v1 be, as long as v2 <= 50, average velocity for entire trip is < 100.

Suff

Hence B
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Bunuel
In the morning, Chris drives from Toronto to Oakville and in the evening he drives back from Oakville to Toronto on the same road. Was his average speed for the entire round trip less than 100 miles per hour?

(1) In the morning, Chris drove at an average speed of at least 10 miles per hour while travelling from Toronto to Oakville.
(2) In the evening, Chris drove at an average speed which was no more than 50 miles per hour while travelling from Oakville to Toronto.


Kudos for a correct solution.

IMO : B

Let the distance between Toronto and Oakville be 100miles

Avg Speed = \(\frac{Total Distance traveled}{Total time taken}\)

Thus total distance covered will be 200 miles (from Toronto to Oakville 100+ 100 and from Oakville to Toronto )

Was his average speed for the entire round trip less than 100 miles per hour?

Avg Speed < 100
\(\frac{200}{Total Time}\) <100

Total Time > 2hrs

Statement 1: In the morning, Chris drove at an average speed of at least 10 miles per hour while travelling from Toronto to Oakville.

If Chris travels at 10 mph in the mrng he will take 10 hrs to reach Oakville. Thus Total time > 2hrs Satisfies
If Chris travels at 200mph then he will take 30 mins to reach. We don't have evening data to confirm the condition.
Hence not sufficient

Statement 2: In the evening, Chris drove at an average speed which was no more than 50 miles per hour while travelling from Oakville to Toronto.

If Chris travels @ 50mph in the evening then he will take 2hrs to reach Toronto.
Thus minimum time taken will always be 2hrs
Thus total time always will be > 2hrs.
Hence Sufficient

But in statement 2, isn't it required that time be greater than 2? it's equal to 2 here...how is B correct then? can someone please help me out?
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Bunuel
In the morning, Chris drives from Toronto to Oakville and in the evening he drives back from Oakville to Toronto on the same road. Was his average speed for the entire round trip less than 100 miles per hour?

(1) In the morning, Chris drove at an average speed of at least 10 miles per hour while travelling from Toronto to Oakville.
(2) In the evening, Chris drove at an average speed which was no more than 50 miles per hour while travelling from Oakville to Toronto.


Kudos for a correct solution.

IMO : B

Let the distance between Toronto and Oakville be 100miles

Avg Speed = \(\frac{Total Distance traveled}{Total time taken}\)

Thus total distance covered will be 200 miles (from Toronto to Oakville 100+ 100 and from Oakville to Toronto )

Was his average speed for the entire round trip less than 100 miles per hour?

Avg Speed < 100
\(\frac{200}{Total Time}\) <100

Total Time > 2hrs

Statement 1: In the morning, Chris drove at an average speed of at least 10 miles per hour while travelling from Toronto to Oakville.

If Chris travels at 10 mph in the mrng he will take 10 hrs to reach Oakville. Thus Total time > 2hrs Satisfies
If Chris travels at 200mph then he will take 30 mins to reach. We don't have evening data to confirm the condition.
Hence not sufficient

Statement 2: In the evening, Chris drove at an average speed which was no more than 50 miles per hour while travelling from Oakville to Toronto.

If Chris travels @ 50mph in the evening then he will take 2hrs to reach Toronto.
Thus minimum time taken will always be 2hrs
Thus total time always will be > 2hrs.
Hence Sufficient

But in statement 2, isn't it required that time be greater than 2? it's equal to 2 here...how is B correct then? can someone please help me out?

It is implied that the morning trip will take time more than zero units of time... (unless teleportation is considered) so Total time will be 2+More than zero which is grater than 2.
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Bunuel
In the morning, Chris drives from Toronto to Oakville and in the evening he drives back from Oakville to Toronto on the same road. Was his average speed for the entire round trip less than 100 miles per hour?

(1) In the morning, Chris drove at an average speed of at least 10 miles per hour while travelling from Toronto to Oakville.
(2) In the evening, Chris drove at an average speed which was no more than 50 miles per hour while travelling from Oakville to Toronto.

Say, using Statement 2, that Chris drives as fast as possible, i.e. at 50 mph, from O to T. So 50 = d/t, where d is the distance from O to T, and t the time it takes. Say Chris drove the other half of the trip infinitely quickly, so covered the other d miles in 0 seconds. Then overall, Chris would cover 2d miles in t hours, and his average speed for the entire trip would be 2d/t = 2(d/t) = 2(50) = 100 mph (i.e. if we double the distance traveled, without changing the time, speed naturally doubles). That's the only way Chris can travel as fast as 100 mph for the whole trip -- he must travel at 50 mph from O to T, and must travel infinitely quickly from T to O. Since it's impossible to travel at an infinite speed, using Statement 2 alone, his average speed thus must have been less than 100 mph.

Statement 1 is clearly insufficient so the answer is B.
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max average speed<2*lower speed

1. staement 1 doesnt give us the lower speed. it could 10 or 100 insufficient
2. statement 2 gives the max lower speed as 50 therefore max avg speed<2*50 max avg speed<100 sufficient
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