What is the distance from town A to town B?

Question

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.

VeritasPrepDennis · Answer

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,

onamarif · Answer

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.

kkrrsshh · Answer

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?

PMZ21 · Answer

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!

Bunuel · Answer

Have you read this: https://gmatclub.com/forum/what-is-the- ... l#p1593590

PMZ21 · Answer

Yup, I did. I was still confused about the reasoning.

Thanks anyway!

Posted from my mobile device

utkarshthapak · Answer

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

gmatzpractice · Answer

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

ayush93 · Answer

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.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

What is the distance from town A to town B?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

What is the distance from town A to town B?

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards