Bunuel wrote:
On a certain nonstop trip, Marta averaged x miles per hour for 2 hours and y miles per hour for the remaining 3 hours. What was her average speed, in miles per hour, for the entire trip?
(1) 2x + 3y = 280
(2) y = x + 10
Kudos for a correct solution.
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 milesSo, her average speed = (
2x + 3y)/(
2 hours + 3 hours)
= (
2x + 3y)/
5So, 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 = 56Perfect!! 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 = 11Case b: x = 10 and y = 20. In this case
(2x + 3y)/5 = [2(10) + 3(20)]/5 = 16Since we cannot answer the
REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT
Answer =
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