On a certain nonstop trip, Marta averaged x miles per hour for 2 hours

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: https://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.

Video solution from Quant Reasoning:
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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

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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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.

Solution:

Question Stem Analysis:

We need to determine the average speed, in miles per hour, for Marta’s entire trip. Notice that the total miles Marta drove is 2x + 3y, and the total number of hours driven is 2 + 3 = 5 hours. Therefore, the average speed of her entire trip is (2x + 3y) / 5 mph.

Statement One Alone:

Since we know 2x + 3y = 280, the average speed of her entire trip is 280/5 = 56 mph. Statement one alone is sufficient.

Statement Two Alone:

Since y = x + 10, in terms of x, the average speed of her entire trip is

[2x + 3(x + 10)] / 5 = (5x + 30) / 5 = x + 6 mph.

As we can see, a different value of x will yield a different average speed. Therefore, statement two alone is not sufficient

Answer: A
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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

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__
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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

Answer: Option A

Video solution by GMATinsight



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1 minute 41 seconds.

First distance = 2x
Second distance = 3y
total distance 2x + 3y
total time = 5.

Need to find out what 2x + 3y is to get total distance.

A) Tells you the value. Suff.

B) y = x + 10.

1 equation and 2 unknowns. Cannot find the value. Insuff.

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