The explanation from MGMAT is not making sense to me at all. Can someone please explain this in a different way.
Question: 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.
(2) It took Reiko 20 more minutes to drive from A to B than to make the return trip.
Explanation:
(1) SUFFICIENT: Say the trip is d miles long in each direction, so that the round-trip distance is 2d miles. According to this statement, Reiko took (2d miles)/(80 miles/hour) = d/40 hours to drive the entire round trip.
Reiko could not have driven from B to A in zero time, so it must have taken her less than d/40 hours to drive from A to B. Therefore, her speed on the trip from A to B must have been (d miles)/(LESS than d/40 hours) = 1/(LESS than 1/40 hours) = GREATER than 40 miles per hour.
(especially the statement above makes no sense to me)
(Note: when dividing by a "less than" number, flip the sign to "greater than." If we had been dividing by a "greater than" number, we would have flipped the sign to "less than.")
Alternatively, try the above with real numbers: say the trip is 80 miles long in each direction, so that the round-trip distance is 160 miles. According to this statement, Reiko took (160 miles / 80 miles/hour) = 2 hours to drive the entire round trip.
Reiko could not have driven from B to A in zero time, so it must have taken her less than 2 hours to drive from A to B. Therefore, her speed on the trip from A to B must have been (80 miles)/(LESS than 2 hours) = (40 miles)/(LESS than 1 hour) = GREATER than 40 miles per hour.
(2) INSUFFICIENT: This statement could be true at all kinds of speeds, from very low to very high, so it cannot be determined whether Reiko's speed from A to B was greater than 40 miles per hour.
Question: 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.
(2) It took Reiko 20 more minutes to drive from A to B than to make the return trip.
Explanation:
(1) SUFFICIENT: Say the trip is d miles long in each direction, so that the round-trip distance is 2d miles. According to this statement, Reiko took (2d miles)/(80 miles/hour) = d/40 hours to drive the entire round trip.
Reiko could not have driven from B to A in zero time, so it must have taken her less than d/40 hours to drive from A to B. Therefore, her speed on the trip from A to B must have been (d miles)/(LESS than d/40 hours) = 1/(LESS than 1/40 hours) = GREATER than 40 miles per hour.
(especially the statement above makes no sense to me)
(Note: when dividing by a "less than" number, flip the sign to "greater than." If we had been dividing by a "greater than" number, we would have flipped the sign to "less than.")
Alternatively, try the above with real numbers: say the trip is 80 miles long in each direction, so that the round-trip distance is 160 miles. According to this statement, Reiko took (160 miles / 80 miles/hour) = 2 hours to drive the entire round trip.
Reiko could not have driven from B to A in zero time, so it must have taken her less than 2 hours to drive from A to B. Therefore, her speed on the trip from A to B must have been (80 miles)/(LESS than 2 hours) = (40 miles)/(LESS than 1 hour) = GREATER than 40 miles per hour.
(2) INSUFFICIENT: This statement could be true at all kinds of speeds, from very low to very high, so it cannot be determined whether Reiko's speed from A to B was greater than 40 miles per hour.
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