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
Answer: A
Source: official guide
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On a certain nonstop trip, Marta averaged x miles per hour for 2 hours and y miles per hour for the remaining 3 hours. W
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BTGModeratorVI
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Given that Marta averaged x miles per hour for 2 hours and y miles per hour for the remaining 3 hours $$Average\ speed\ =\ \frac{total\ dis\tan ce}{total\ time}$$
At x mph for 2 hours, Marta covers (x * 2) miles
At y mph for 3 hours, Marta covers (y * 3) miles
Target question => What was her average speed in miles per hour for the entire trip?
$$Average\ speed=\frac{2x+3y}{\left(2+3\right)hour}=\frac{2x+3y}{5}??$$
$$Statement\ 1\ =2x+3y=280$$
$$Average\ speed=\frac{280}{5}=56\ miles\ per\ hour$$
$$Statement\ 1\ is\ SUFFICIENT$$
$$Statement\ 2\ =>\ y=x+10$$
$$Averae\ speed\ =\frac{2x+3\left(x+10\right)}{5}=\frac{2x+3x+30}{5}=\frac{5x+30}{5}$$
$$The\ value\ of\ x\ is\ unknown\ so\ statement\ 2\ is\ NOT\ SUFFICIENT$$
$$Since\ only\ statement\ 1\ is\ SUFFICIENT,\ answer\ =\ A$$
At x mph for 2 hours, Marta covers (x * 2) miles
At y mph for 3 hours, Marta covers (y * 3) miles
Target question => What was her average speed in miles per hour for the entire trip?
$$Average\ speed=\frac{2x+3y}{\left(2+3\right)hour}=\frac{2x+3y}{5}??$$
$$Statement\ 1\ =2x+3y=280$$
$$Average\ speed=\frac{280}{5}=56\ miles\ per\ hour$$
$$Statement\ 1\ is\ SUFFICIENT$$
$$Statement\ 2\ =>\ y=x+10$$
$$Averae\ speed\ =\frac{2x+3\left(x+10\right)}{5}=\frac{2x+3x+30}{5}=\frac{5x+30}{5}$$
$$The\ value\ of\ x\ is\ unknown\ so\ statement\ 2\ is\ NOT\ SUFFICIENT$$
$$Since\ only\ statement\ 1\ is\ SUFFICIENT,\ answer\ =\ A$$
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Target question: What was Marta's average speed for the entire trip?BTGModeratorVI wrote: ↑Wed Jan 06, 2021 8:04 amOn 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
Answer: A
Source: official guide
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- ... cy?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 = A
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Solution:BTGModeratorVI wrote: ↑Wed Jan 06, 2021 8:04 amOn 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
Answer: A
Source: official guide
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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