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Difficulty:
55%
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Question Stats:
72% (01:43) correct
28%
(02:24)
wrong
based on 53
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Robert walks along a straight track in a stadium at a constant speed and takes 80 seconds to walk from the start of the track to the finish. Along the track, tick marks of negligible width are painted at uniform intervals of 20 meters, with the first mark at the start of the track and the last mark at the finish. Are there more than 20 tick marks along the track?
(1) Robert’s walking speed is less than 5 meters per second.
(2) Robert’s walking speed is greater than 4 meters per second.
(1) Robert’s walking speed is less than 5 meters per second.
(2) Robert’s walking speed is greater than 4 meters per second.
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GMAT Club Official Solution:
Robert walks along a straight track in a stadium at a constant speed and takes 80 seconds to walk from the start of the track to the finish. Along the track, tick marks of negligible width are painted at uniform intervals of 20 meters, with the first mark at the start of the track and the last mark at the finish. Are there more than 20 tick marks along the track?
Let v be Robert’s walking speed in meters per second. Then the distance traveled in 80 seconds, which is the length of the track, is:
80v meters.
If n is the number of marks, there are n - 1 intervals from the first mark to the last, so the length of the track is:
20 * (n - 1) meters. Notice here that, since both 20 and n - 1 are integers, the length of the track must be a multiple of 20.
We must determine whether n > 20. Since the track length is 20 * (n - 1), this is equivalent to asking whether the track length is greater than 20 * 19 = 380 meters. Since the length of the track must be a multiple of 20, for the answer to be YES, it must be 400, 420, 440, and so on. If the length of the track is less than 400 meters, such as 380, 360, and so on, we get a NO answer.
(1) Robert’s walking speed is less than 5 meters per second.
This gives v < 5. At exactly 5 meters per second, the length of the track is 80v = 400 meters. Since v < 5, the length is less than 400 meters, and thus n, the number of marks, is NOT greater than 20. Sufficient.
(2) Robert’s walking speed is greater than 4 meters per second.
This gives v > 4. If v = 4.25, the length of the track is 80v = 340 meters, giving a NO answer to the question. However, if v = 5, the length of the track is 80v = 400 meters, giving a YES answer to the question. Not sufficient.
Answer: A.
Robert walks along a straight track in a stadium at a constant speed and takes 80 seconds to walk from the start of the track to the finish. Along the track, tick marks of negligible width are painted at uniform intervals of 20 meters, with the first mark at the start of the track and the last mark at the finish. Are there more than 20 tick marks along the track?
Let v be Robert’s walking speed in meters per second. Then the distance traveled in 80 seconds, which is the length of the track, is:
80v meters.
If n is the number of marks, there are n - 1 intervals from the first mark to the last, so the length of the track is:
20 * (n - 1) meters. Notice here that, since both 20 and n - 1 are integers, the length of the track must be a multiple of 20.
We must determine whether n > 20. Since the track length is 20 * (n - 1), this is equivalent to asking whether the track length is greater than 20 * 19 = 380 meters. Since the length of the track must be a multiple of 20, for the answer to be YES, it must be 400, 420, 440, and so on. If the length of the track is less than 400 meters, such as 380, 360, and so on, we get a NO answer.
(1) Robert’s walking speed is less than 5 meters per second.
This gives v < 5. At exactly 5 meters per second, the length of the track is 80v = 400 meters. Since v < 5, the length is less than 400 meters, and thus n, the number of marks, is NOT greater than 20. Sufficient.
(2) Robert’s walking speed is greater than 4 meters per second.
This gives v > 4. If v = 4.25, the length of the track is 80v = 340 meters, giving a NO answer to the question. However, if v = 5, the length of the track is 80v = 400 meters, giving a YES answer to the question. Not sufficient.
Answer: A.
General Discussion
05 Mar 2026, 07:59
Kudos
Bookmarks
Since the start and end has the mark I believe the value has to be a multiple of 20 only.
Statement 1:
Taking critical point 5:
We get 80*5=400
400/20=20+1=21 (Because the starting and ending has a tick mark, its like counting from 2 to 9 included we have 8 numbers)
But this value of speed is less than 5, thus
Ticks<21
So no.of ticks are NOT greater than 20
SUFFICIENT.
Statement 2:
Greater than 4 m/s:
Take critical point.
80*4=320
320/20 = 16+1=17
17<20 LESS than 20 and there is no upper bound so we will have values above 20 as well
INSUFFICIENT
Answer: Option A IMO
Statement 1:
Taking critical point 5:
We get 80*5=400
400/20=20+1=21 (Because the starting and ending has a tick mark, its like counting from 2 to 9 included we have 8 numbers)
But this value of speed is less than 5, thus
Ticks<21
So no.of ticks are NOT greater than 20
SUFFICIENT.
Statement 2:
Greater than 4 m/s:
Take critical point.
80*4=320
320/20 = 16+1=17
17<20 LESS than 20 and there is no upper bound so we will have values above 20 as well
INSUFFICIENT
Answer: Option A IMO
Bunuel
