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Distance

by seamaster1 » Mon Apr 29, 2013 7:20 am
Dear All!
How long did it take to travel 400km?
a. The car travelled the first 200km in 2.5hrs
b. If the car's average speed had been 20 km/h faster, it would have travelled the 400km in 1 hour less time.

Experts please help!
My understanding is:
A. In sufficient(obviously)
B. In sufficient
Because:
400 = ST = (S + 20)(T-1) = ST-S+20T-20
-->-S+20T -20 =0
Insufficient
Please explain why E is not correct choice because B seems insufficient.
Please teach me if I miss something.
OA: B
Many thanks
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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Mon Apr 29, 2013 7:51 am
seamaster1 wrote:Dear All!
How long did it take to travel 400km?
a. The car travelled the first 200km in 2.5hrs
b. If the car's average speed had been 20 km/h faster, it would have travelled the 400km in 1 hour less time.
Aside: When posting questions, please use the spoiler function to hide the correct answer. This will allow others to attempt the question without seeing the final answer.


Target question: How long did it take to travel 400km

To find the travel time, we need to know the average speed traveled.
Let x = the average speed traveled.

Rephrased target question: What is the value of x?

Statement 1: The car travelled the first 200km in 2.5hrs
No info about the 2nd half of the trip, so we can't determine the overall average speed.
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: If the car's average speed had been 20 km/h faster, it would have travelled the 400km in 1 hour less time.
Let's start with a word equation:
(travel time at x km/h) - 1 = (travel time at x+20 km/h)
Since time = distance/speed, we can now write:
(400/x) - 1 = 400/(x+20)

IMPORTANT: At this point, we need only determine whether or not this equation will yield 1 or 2 values of x. If it yields only 1 value, then statement 2 is sufficient. If it yields 2 values, then statement 2 is not sufficient.

Rewrite as: (400-x)/x = 400/(x+20)
Cross multiply: (400)(x) = (400-x)(x+20)
Simplify: 400x = 8000 + 380x - x^2
Rewrite: x^2 + 20x - 8000 = 0
Factor: (x + 100)(x - 80) = 0
So, x = -100 or 80
Since x cannot be negative, it must be the case that x = 80
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = B

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by seamaster1 » Mon Apr 29, 2013 8:23 am
Dear Brent!
Thank you so much for your explanation.
Now, I know what I miss.
Aside: I will pay attention to your recommend to hide correct answer.
Once again thank you a lot.
Cheer!
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by Anju@Gurome » Mon Apr 29, 2013 8:36 am
I think it'll be easier for you if I can point out your mistake.
seamaster1 wrote:400 = ST = (S + 20)(T-1) = ST-S+20T-20
-->-S+20T -20 =0
Insufficient
The part in blue is actually two equations : ST = 400 and (S + 20)(T - 1) = 400
By writing ST = (S + 20)(T - 1), you are discarding half of the information.

So, what you actually should've done is after getting (-S + 20T - 20) = 0, use the information you have earlier discarded, i.e. ST = 400 ---> S = 400/T and use this expression of S in your final equation.

So, (-S + 20T - 20) = 0
--> S - 20T + 20 = 0
--> 400/T - 20T + 20 = 0
--> Now we can solve this quadratic in T and check whether we have two possible answer or just one.

Hope that helps.
Anju Agarwal
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Backup Methods : General guide on plugging, estimation etc.
Wavy Curve Method : Solving complex inequalities in a matter of seconds.

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by Blue_Skies » Mon Apr 29, 2013 3:00 pm
Dear All!
How long did it take to travel 400km?
a. The car travelled the first 200km in 2.5hrs
b. If the car's average speed had been 20 km/h faster, it would have travelled the 400km in 1 hour less time.

Experts please help!
My understanding is:
A. In sufficient(obviously)
B. In sufficient
Because:
400 = ST = (S + 20)(T-1) = ST-S+20T-20
-->-S+20T -20 =0
Insufficient
Please explain why E is not correct choice because B seems insufficient.
Please teach me if I miss something.
OA: B
Many thanks

THis questions asks for application of speed = distance/time formula.
In case 2) t1=400/s1.-----------------A
From the 2nd condition :
t2=400/s2 -> t1-1 = 400/s1+ 20.--------B

From A and B , you can get the time.

Your Soln is also correct but you need to use S=400/T and reduce your equation to one variable to get the answer.
My advice is to take one step at a time.This will help to think clearly.
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by GMATGuruNY » Mon Apr 29, 2013 3:12 pm
seamaster1 wrote: How long did it take to travel 400km?
a. The car travelled the first 200km in 2.5hrs
b. If the car's average speed had been 20 km/h faster, it would have travelled the 400km in 1 hour less time.
Statement 1: The car travelled the first 200km in 2.5hrs
No information about the last 200km.
INSUFFICIENT.

Statement 2: If the car's average speed had been 20 km/h faster, it would have travelled the 400km in 1 hour less time.
Since the difference between the two speeds is 20km, each speed is almost certainly a multiple of 20.
20, 40, 60, 80, 100...
Since the difference between the two times is an integer value, each speed is almost certainly a factor of 400 -- the value of the total distance -- implying that the combinations in red are the most likely options.

Case 1: actual speed = 20kph, faster speed = 40kph
Actual time = 400/20 = 20 hours.
Faster time = 400/40 = 10 hours.
Time difference = 20-10 = 10 hours.
Doesn't work: the time difference must be 1 hour.

Case 2: actual speed = 80kph, faster speed = 100kph
Actual time = 400/80 = 5 hours.
Faster time = 400/100 = 4 hours.
Time difference = 5-4 = 1 hour.
Success!
Thus, the actual time = 5 hours.
SUFFICIENT.

The correct answer is B.
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by seamaster1 » Mon Apr 29, 2013 4:07 pm
Greeting Anju, Blue_Skies,Hunt
Thank you for your further explanation.
It really helps me.
To:Mr.Hunt
Your access to the problem is amazing.
Once again thank and best regards to all.
Cheer!
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