Bunuel wrote:
A road crew painted two black lines across a road as shown in the figure above, to mark the start and end of a 1-mile stretch. Between the two black lines, they will paint across the road a red line at each third of a mile, a white line at each fifth of a mile, and a blue line at each eighth of a mile. What is the smallest distance (in miles) between any of the painted lines on this stretch of highway?
(A) 0
(B) 1/120
(C) 1/60
(D) 1/40
(E) 1/30
Attachment:
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MANHATTAN GMAT OFFICIAL SOLUTION:When comparing fractional pieces of a whole, we must find a common denominator. In this case, the 1-mile stretch is divided in thirds, fifths, and eighths. The smallest common denominator of 3, 5, and 8 is 120. If the 1-mile highway is divided into 120 equal increments, where will the red, white, and blue marks fall?
Red (thirds): 40, 80 (out of 120 increments)
White (fifths): 24, 48, 72, 96 (out of 120 increments)
Blue (eighths): 15, 30, 45, 60, 75, 90, 105 (out of 120 increments)
The smallest distance between two marks is 75 – 72 = 3 or 48 – 45 = 3. This equates to 3/120, or 1/40 miles.
The correct answer is D.