Target question: What was Marta's average speed for the entire trip?

This is a great candidate for rephrasing the target question.
Aside: Here’s a video with tips on rephrasing the target question: http://www.gmatprepnow.com/module/gmat-data-sufficiency?id=1100

Given: Marta averaged x miles per hour for 2 hours and y miles per hour for the remaining 3 hours
Average speed = (total distance)/(total time)
- Travelling at x miles per hour for 2 hours, Marta travels 2x miles
- Travelling at y miles per hour for 3 hours, Marta travels 3y miles
So, her average speed = (2x + 3y)/(2 hours + 3 hours)
= (2x + 3y)/5
So, we can REPHRASE our target question....
REPHRASED target question: What is the value of (2x + 3y)/5?

Statement 1: 2x + 3y = 280
This looks VERY SIMILAR to our REPHRASED target question.
If we divide both sides by 5, we get: (2x + 3y)/5 = 56
Perfect!! Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: y = x + 10
This information cannot help us determine the value of (2x + 3y)/5.
Here's why:
There are several values of x and y that satisfy statement 2. Here are two:
Case a: x = 5 and y = 15. In this case (2x + 3y)/5 = [2(5) + 3(15)]/5 = 11
Case b: x = 10 and y = 20. In this case (2x + 3y)/5 = [2(10) + 3(20)]/5 = 16
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Answer =

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Average speed = Total distance/Total time ;
Total distance = Avg speed * Total time

Marta averaged x miles per hour for 2 hours = 2x
y miles per hour for the remaining 3 hours = 3y
Total distance = 2x+3y

Total time = 2+3 = 5 hrs

Avg speed = 2x+3y/5

St 1: 2x+3y=280

Avg speed = 280/5 = 56m/h. Sufficient.

St 2: y = x + 10, Not sufficient.

Ans A.

An easy question.
The average speed can be taken out by adding Marta's speed per hour for each hour divided by the total no of hours she traveled. So, we are given that she travels with x miles per hour for 2 hours and y miles per hour for 3 hours, hence average speed would be = (2x+3y)/5.

Statement 1. 2x+3y=280, which can be written as (2x+3y)/5=56. {Sufficient}
Statement 2. y = x+10, 2 variables 1 eqn {Insufficient}

Answer: A

P.S. Don't forget Kudos. :D

do we not calculate total speed by sum of all distances/sum of all hours

(Average Speed) = (Total Distance Covered)/(Total Time Spent)
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How are you guys coming up with 2x and 3y. I see everyone skipping the step. please show the algebra to come up with 2x + 3y and please show the unit Hours (H)

We are looking for total distance divided by total time

We are told that Marta averaged X mph for 2 hours and Y mph for 3 hours. We know the total time is 5 hours. The distance, the numerator, is:

X(miles/hours)*2hours + Y(miles/hours)*3hours

The hours cancel and you have 2x miles + 3y miles for the numerator.

Bunuel, @pushpiktc chetan2u
Why answer is A and not C We have two unknowns in statement one , havent we ? and when we have two unknowns and one equation how can one get answer

The question asks: what is the value of (2x + 3y)/5?

Statement 1 says: 2x + 3y = 280. Could you answer the question what is the value of (2x + 3y)/5 knowing that 2x + 3y = 280?
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Testing.. Please ignore

Hi Bunuel

Just out of curiosity..

If S2 had given use the actual values of x miles /hr and y miles/ hr

Could we have calculated the average speed in that case ?

I think we could have have based on the teeter totter weighted averages method

Posted from my mobile device

Hello Experts,
EMPOWERgmatRichC, VeritasKarishma, IanStewart, chetan2u, ArvindCrackVerbal, GMATGuruNY, AaronPond, GMATinsight, ccooley, RonPurewal
Could you help me by explaining the statement 2 with weighted average style?
Thanks__

Hello Asad,

Statement II says y = x + 10. Therefore,

Total distance = 2 * x + 3 * (x+10).
Total time = 2 + 3 = 5 hours

Average Speed =\( \frac{2x + 3x + 30 }{ 5}\) = \(\frac{5x + 30 }{ 5}\) = x +6.

Since we do not know x, the average speed cannot be calculated. Hence, statement II alone is insufficient.

Hope that helps!
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Hi Asad,

When a question asks for AVERAGE SPEED over the course of an entire trip, you will almost certainly end up needing the TOTAL TIME and the TOTAL DISTANCE traveled. In this prompt, we know that the total time is 5 hours (since "Marta averaged X miles per hour for 2 HOURS and Y miles per hour for the remaining 3 HOURS"). Thus, to answer the question, we need some additional information that 'locks in' the total distance - otherwise the answer to the question will change.

At this point, total distance = 2X + 3Y

Fact 2 has no "limit" on the values of X and Y (other than the idea that X and Y must be positive, since they're speeds). With the equation Y = X + 10.... as X increases, Y will also increase... so there would be no limit to how high the total distance could become. As such, treating this as a Weighted Average isn't practical, since the total distance will just keep getting bigger and bigger as X and Y increase, so the answer to the question will change will every iteration of X and Y.

GMAT assassins aren't born, they're made,
Rich

When considering average speed, weight is "time taken".

Savg = (S1 * t1 + S2 * t2)/(t1 + t2) = (2x + 3y)/(2 + 3)

We need the value of this expression. If we know y = x + 10, we get

Savg = (2x + 3x + 30)/(5) = x + 6

But we don't know x. So we cannot get Savg. Not sufficient.
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The prompt is not giving to us any equalities.

We only know that Av speed= tod distance/ Tot time
Tot distance is 2x+3y
Tot time is 5h
So the question is how much is 2x+3y/5

1) gave to use the value of 2x+3y so we can use it to find the AvSpeed. Sufficient

2) gave to us the equality y=x+10.
Also if we would like to use this equality with 2x+3y/5 we will have x+6=Av Speed. Still not sufficient to have any value. So not sufficient.

Average speed = Total distance / Total time

To find the answer to this, we need to find the total distance and total time

To find total distance:
Given: x mph for 2 hours (Speed = Distance/ time; hence, Distance = Speed * Time)
Distance of 1st leg = 2x

Similarly y mph for 3 hours
Distance of 2nd leg = 3y

Total distance = 2x + 3y

Total time = 2hr + 3 hr = 5 hr

Hence to find:

Average speed = Total distance / total time
Average speed = 2x + 3y / 5.........(1)

Statement 1
2x+3y = 280

Directly substitute the value in Eq (1)
280 / 5 = 56
Hence sufficient

Statement 2
y = x + 10
Substitute the value of y in Eq (1)
2x + 3 (x +10)/5 = (5x + 30)/5 = Does not give a numeric value since we do not know the value of x... Hence not sufficient

Answer A..Statement 1 only solves

In 1 hour X miles, in 2 hours 2x miles, similarly
in 1 hour y miles, 3 hours 3y miles

Average Speed \(=\frac{(Tatal \ distance)}{Total \ time}\)

\(=\frac{(2x + 3y)}{5}\)

(1) \(2x + 3y = 280\)

\( \frac{280}{5 }= 56\)

Sufficient.

(2) x+y = -10, We don't get value of 2x +3x from here.

Insufficient.

Ans. A
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