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B
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Difficulty:
75%
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Question Stats:
58% (02:41) correct
42%
(02:41)
wrong
based on 793
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On a particular trip, Jane drove x miles at 30 miles per hour and y miles at 40 miles per hour. Was her average speed for the trip greater than 35 miles per hour?
(1) y > x + 60
(2) y/x > 4/3
(1) y > x + 60
(2) y/x > 4/3
10 Jun 2015, 07:38
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dpo28
On a particular trip, Jane drove x miles at 30 miles per hour and y miles at 40 miles per hour. Was her average speed for the trip greater than 35 miles per hour?
(1) y > x + 60
(2) y/x > 4/3
(1) y > x + 60
(2) y/x > 4/3
On a particular trip, Jane drove x miles at 30 miles per hour and y miles at 40 miles per hour. Was her average speed for the trip greater than 35 miles per hour?
\(average \ speed = \frac{total \ distance}{total \ time}=\frac{x+y}{(\frac{x}{30}+\frac{y}{40})}=\frac{120(x+y)}{4x+3y}\)
Thus the question asks whether \(\frac{120(x+y)}{4x+3y}>35\).
After simplifying the question becomes: is \(\frac{y}{x}>\frac{4}{3}\).
(1) y > x + 60.
If x = 1 and y = 100, then y/x > 4/3.
If x = 1000 and y = 1200, then y/x < 4/3.
Not sufficient.
(2) y/x > 4/3. Directly gives an answer to our question. Sufficient.
Answer: B.
Hope it's clear.
Alternatively, notice that 35 miles per hour is halfway between 30 and 40 miles per hour. Now, for the average speed to be exactly 35 miles per hour, the amount of time spent to cover x miles (x/30 hours) must equal to the amount of time spent to cover y miles (y/40 hours). The average speed to be greater than 35 miles per hour, the amount of time spent to cover x miles at the slower speed (x/30 hours) must be less than the amount of time spent to cover y miles at the faster speed(y/40 hours):
x/30 < y/40.
Then continue as above.
10 Jun 2015, 07:37
Kudos
Bookmarks
dpo28
On a particular trip, Jane drove x miles at 30 miles per hour and y miles at 40 miles per hour. Was her average speed for the trip greater than 35 miles per hour?
(1) y > x + 60
(2) y/x > 4/3
(1) y > x + 60
(2) y/x > 4/3
35 miles this is average speed if both distance will take equal time.
For example x = 300 miles on the speed 30 mph - 10 hours
and y = 400 on the speed 40 mph - 10 hours
So for have average speed more than 35 miles Jane should spend more time on distance y than on distance x
time = distance / speed
\(\frac{y}{40}>\frac{x}{30}\) --> \(\frac{y}{x}>\frac{4}{3}\)
1) this statement insufficient because we can't find ratio of distances x and y from given information
2) This statement gives us direct answer on the question.
Sufficient
Answer is B
