lenagmat wrote:A person travels in a car with uniform speed. He observes a mile-stone,
which has 2 digits. After one hour he observes another mile-stone with same digits reversed. After another hour he observes another mile-stone with same 2 digits containing a 0. Find the speed of the car?
(for purposes of clarity, let me just add that mile-stones tell you how far you are from your destination OR how far one has travelled from the starting point)
A. 40 mph
B. 45 mph
C. 50 mph
D. 55 mph
E. 60 mph
When the tens digit and the units digit of the 1st milestone are reversed, the result must be a GREATER 2-digit integer -- 19 becoming 91, for example -- so that the 2nd milestone indicates a greater distance than the 1st milestone.
Thus, the tens digit must be LESS than the units digit.
If the tens digit is greater than 1, then the 3rd milestone will be a 3-digit integer greater than 200, yielding too great a distance between the 2nd milestone and the 3rd milestone.
Thus, the tens digit = 1.
Let U = the units digit.
1st milestone = 10 + U.
2nd milestone = 10U + 1.
3rd milestone (which contains 0):
The HUNDREDS digit must be 1; otherwise, the distance between the 2nd milestone and the 3rd milestone will be too great.
The TENS digit must be 0, implying a distance between 100 and 109; if the units digit is 0, then the distance between the 2nd milestone and the 3rd milestone will be too great.
Since the hundreds digit = 1 and the tens digit = 0, the UNITS digit = U (the units digit in the 1st milestone).
Thus, the 3rd milestone = 100 + U.
Since the car is traveling at a uniform speed, 3rd - 2nd = 2nd - 1st:
(100+U) - (10U+1) = (10U+1) - (10+U)
99 - 9U = 9U - 9
9(11-U) = 9(U-1)
11-U = U-1
12 = 2U
U=6.
Thus:
1st milestone = 16.
2nd milestone = 61.
3rd milestone = 106.
3rd - 2nd = 2nd - 1st = 45.
The correct answer is
B.
Last edited by
GMATGuruNY on Mon Oct 17, 2011 8:03 am, edited 3 times in total.
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