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What is the distance from town A to town B?

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What is the distance from town A to town B?  [#permalink]

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New post 28 Oct 2015, 14:31
3
10
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

64% (02:11) correct 36% (02:15) wrong based on 247 sessions

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What is the distance from town A to town B, in miles?

(1) If Steve had traveled from town A to town B at an average speed that was 10 miles per hour faster, he would have traveled for 5 fewer hours

(2) If Steve had traveled from town A to town B at an average speed that was 50% greater, the amount of time he traveled would have been the time it actually took reduced by 1/3.

Why cant we assume that an average speed that was 50% greater is equal to 10 miles and combine the two statements ? The answer would have been C.
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Re: What is the distance from town A to town B?  [#permalink]

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New post 28 Oct 2015, 15:15
1
manhattan187 wrote:
What is the distance from town A to town B, in miles?

(1) If steve had traveled from town A to town B at an average speed that was 10 miles per hour faster, he would have traveled for 5 fewer hours

(2) If steve had traveled from town A to town B at an average speed that was 50% greater, the amount of time he traveled would have been the time it actually took reduced by 1/3.

Why cant we assume that an average speed that was 50% greater is equal to 10 miles and combine the two statements ? The answer would have been C.



Manhattan187 -

I understand your confusion - because we are always told that the Statements provided are TRUE. However, if you notice, the two statements above are hypotheticals. We can assume that they give us true information, but they really do not give us enough information to answer the question. We cannot assume that 10 mph = 50% because, while these two Stmts are true, they might not be describing the same situation. That is, we have nothing that would tell us that a 10 mph increase in speed equates to a 50% increase. Further, if you re-write Stmt (2) in terms of fractions, you will see that it tells you nothing. D = rt ==> D = (3/2r) (2/3t) No matter what Steve's beginning speed was, going 50% faster would always result in the time being reduced by 1/3,
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What is the distance from town A to town B?  [#permalink]

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New post 10 Feb 2017, 09:18
We can calculate the distance if the information provided gives clear idea of either speed or time. But none of them can actually be known clearly form the two statements.
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Re: What is the distance from town A to town B?  [#permalink]

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New post 14 May 2017, 04:40
Why cant we use the two statements together and solve for x(x being distance suppose). Even if we are not assuming "average speed that was 50% greater is equal to 10 miles ", we can create two equations separately for each statement and solve them for distance.
From first statement, x/a=x/(a+10) +5 ...
From second statement, x/1.5a=x/a - 1/3..

x=distance
a=average speed
Can anyone throw more light on this? What am I doing wrong here?
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Re: What is the distance from town A to town B?  [#permalink]

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New post 24 May 2017, 12:09
Hi,

Could someone please explain why Option 'C' isn't possible?

Since, we have two variables and have two equations (1 from each statement). We can use these two equations to solve for the variable values:

Statement 1 gives us:
Actual scenario: x (avg speed), y - time and xy - distance
==>(x+10) * (y-5) = xy
==> xy = xy+10y - 5x - 50
==> 5x + 50 = 10y
==> x = 2y - 10

Statement 2:
1.5x * (y-1/3) = xy
==> 5xy = 3y-1 ---- substitution x in terms of y

Shouldn't the two options be sufficient to solve? Experts! please help!
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Re: What is the distance from town A to town B?  [#permalink]

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New post 24 May 2017, 12:54
PMZ21 wrote:
Hi,

Could someone please explain why Option 'C' isn't possible?

Since, we have two variables and have two equations (1 from each statement). We can use these two equations to solve for the variable values:

Statement 1 gives us:
Actual scenario: x (avg speed), y - time and xy - distance
==>(x+10) * (y-5) = xy
==> xy = xy+10y - 5x - 50
==> 5x + 50 = 10y
==> x = 2y - 10

Statement 2:
1.5x * (y-1/3) = xy
==> 5xy = 3y-1 ---- substitution x in terms of y

Shouldn't the two options be sufficient to solve? Experts! please help!


Have you read this: https://gmatclub.com/forum/what-is-the- ... l#p1593590
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Re: What is the distance from town A to town B?  [#permalink]

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New post 24 May 2017, 13:04
Yup, I did. I was still confused about the reasoning.

Thanks anyway!

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Re: What is the distance from town A to town B?  [#permalink]

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New post 25 May 2017, 02:30
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Good question, below is my method (taking initial average speed as 's', initial time as 't' and distance as 'd' which is constant)

Statement 1: When s changes to s+10, t changes to t-5. No we know, initially for steve, d=s*t. with the given info, it will be, d=(s+10)*(t-5). so, s*t = s*t+10t-5s-50 => 2t-s=10. Two variables, one equation. Insufficient.

Statement 2: When s changes to (s+1/2s) and t changes to (t-1/3t). Again the initial equation for distance is, d=s*t. with given info it becomes, d=(s+1/2s)*(t-1/3t) => s*t = 3/2s*2/3t => 1=1. This gives us nothing but tells us that the relation between s and t is, s increased by 50% results in time reduced by 1/3 ans s and t can be anything which satisfies this relation. Insufficient.

If you combine both statement then also you have two variables and one equation. Insufficient.

So answer will be E.

Let me know if I am making any mistakes :)
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Re: What is the distance from town A to town B?  [#permalink]

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New post 15 Sep 2018, 21:35
Statement 1:
(r+10)(t-5)=rt
There's not enough info to find distance= rate * time
Insufficient

Statement 2:
(1.5r)(2/3t)=rt
This information is redundant as it results in 1=1
Insufficient

Answer E
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Re: What is the distance from town A to town B?  [#permalink]

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New post 20 Sep 2018, 03:50
utkarshthapak wrote:
Good question, below is my method (taking initial average speed as 's', initial time as 't' and distance as 'd' which is constant)

Statement 1: When s changes to s+10, t changes to t-5. No we know, initially for steve, d=s*t. with the given info, it will be, d=(s+10)*(t-5). so, s*t = s*t+10t-5s-50 => 2t-s=10. Two variables, one equation. Insufficient.

Statement 2: When s changes to (s+1/2s) and t changes to (t-1/3t). Again the initial equation for distance is, d=s*t. with given info it becomes, d=(s+1/2s)*(t-1/3t) => s*t = 3/2s*2/3t => 1=1. This gives us nothing but tells us that the relation between s and t is, s increased by 50% results in time reduced by 1/3 ans s and t can be anything which satisfies this relation. Insufficient.

If you combine both statement then also you have two variables and one equation. Insufficient.

So answer will be E.

Let me know if I am making any mistakes :)


if we combine both:
In Statement 1 , we are give (s+10)(t-5)=d
In statement 2, we are given (s+1/2s)(t-1/3t)=d

so we can compare values,
1/2s=10 => s=20
1/3t=5 =>t=15
distance d= 20*15 =300

So the answer should be C.

Please tell me if there is any error.
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Re: What is the distance from town A to town B? &nbs [#permalink] 20 Sep 2018, 03:50
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