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28 Jul 2020, 13:19
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deepakrobi
Given: Reiko drove from point A to point B at a constant speed, and then returned to A along the same route at a different constant speed.
Target question: Did Reiko travel from A to B at a speed greater than 40 miles per hour?
This is a good candidate for rephrasing the target question.
Let d = the DISTANCE from A to B
Let t = the TIME to travel from A to B
Let u = the TIME to travel from B to A
Speed = distance/time
So, Reiko's speed from A to B = d/t
REPHRASED target question: Is d/t < 40?
Aside: the video below has tips on rephrasing the target question
Statement 1: Reiko's average speed for the entire round trip, excluding the time spent at point B, was 80 miles per hour.
Average speed = (TOTAL distance traveled)/(TOTAL travel time)
We know that the TOTAL distance traveled = d + d = 2d
The TOTAL travel time = t + u
So, when we plug in the values to get: 2d/(t + u) = 80
Multiply both sides of the equation by (t + u) to get: 2d = 80t + 80u
Divide both sides of the equation by 2 to get: d = 40t + 40u
Now take the REPHRASED target question, Is d/t < 40?, and replace d to get: Is (40t + 40u)/t < 40?
Rewrite as: Is 40t/t + 40u/t < 40?
Simplify: Is 40 + 40u/t < 40?
Subtract 40 from both sides of the inequality: Is 40u/t < 0?
Since u and t must be POSITIVE numbers, 40u/t is POSITIVE, which means the answer to the REPHRASED target question is NO!
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT
Statement 2: It took Reiko 20 more minutes to drive from A to B than to make the return trip.
Clearly not sufficient
Answer: A
Cheers,
Brent
VIDEO ON REPHRASING THE TARGET QUESTION:
28 Jul 2020, 13:36
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deepakrobi
Did Reiko travel from A to B at a speed greater than 40 miles per hour?
Statement 1:
Test whether it is possible that the speed from A to B = 40 mph.
Let the distance from A to B = 80 miles, implying that the entire round trip = 160 miles.
Since the average speed for the entire 160-mile round trip = 80 mph, the time for the entire trip = d/r = 160/80 = 2 hours.
If the speed for the 80-mile trip from A to B = 40 mph, the time from A to B = d/r = 80/40 = 2 hours.
Not possible.
Since the total time for the entire round trip = 2 hours, the time from A to B must be LESS THAN 2 HOURS.
Implication:
For the time from A to B to DECREASE, the speed from A to B must INCREASE.
Thus, the speed from A to B must be GREATER THAN 40 MPH.
SUFFICIENT
Statement 2:
Here, the speed from A to B can be any positive value.
INSUFFICIENT
03 Jul 2023, 23:34
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Reiko drove from point A to point B at a constant speed, and then returned to A along the same route at a different constant speed. Did Reiko travel from A to B at a speed greater than 40 miles per hour?
(1) Reiko's average speed for the entire round trip, excluding the time spent at point B, was 80 miles per hour.
Suppose,
D = distance between A and B
s1 = speed from A to B
s2 = speed from A to B
then, Avg Speed = 2D / (D/s1 + D/s2)
80 = 2D / D ((s1 + s2) / s1s2)
40 = (s1 x s2) / (s1 + s2)
Solving, s1 = 40 (s1 +s2) / s2
= 40 (s1/s2 + 1) > 40 (since, s1/s2 can't be negative)
YES is the answer..........SUFFICIENT
(2) It took Reiko 20 more minutes to drive from A to B than to make the return trip.
D/s1 = D/s2 + 1/3
s1 and s2 values can't be compared/calculated..............INSUFFICIENT
(A) is the correct option
(1) Reiko's average speed for the entire round trip, excluding the time spent at point B, was 80 miles per hour.
Suppose,
D = distance between A and B
s1 = speed from A to B
s2 = speed from A to B
then, Avg Speed = 2D / (D/s1 + D/s2)
80 = 2D / D ((s1 + s2) / s1s2)
40 = (s1 x s2) / (s1 + s2)
Solving, s1 = 40 (s1 +s2) / s2
= 40 (s1/s2 + 1) > 40 (since, s1/s2 can't be negative)
YES is the answer..........SUFFICIENT
(2) It took Reiko 20 more minutes to drive from A to B than to make the return trip.
D/s1 = D/s2 + 1/3
s1 and s2 values can't be compared/calculated..............INSUFFICIENT
(A) is the correct option
