rahulvsd wrote:A certain airline's fleet consisted of 60 type A planes at the beginning of 1980. At the end of each year, starting with 1980, the airline retired 3 of the TYPE A planes and acquired 4 new type B plans. How many years did it take before the number of type A planes left in the airline's fleet was less than 50 percent of the fleet?
A. 6
B. 7
C. 8
D. 9
E. 10
Hi! You could solve this question very quickly by brute force - just make a chart and keep track of what happens each year. Remember, on the GMAT you get points for picking the right answer, not for HOW you arrive at that answer. Sometimes brute force is quicker than algebra.
Year A planes B planes
1980 60 0
+1 57 4
+2 54 8
+3 51 12
+4 48 16
+5 45 20
+6 42 24
+7 39 28
+8 36 32
+9 33 36 DING DING DING! Choose D!
Now, the really smart test taker would have saved a bunch of time by using the answer choices to our advantage. We know that the smallest choice is 6, so let's jump right to +6 and ignore the first 5 years.
Even better, a great GMAT strategist would have backsolved - plugged in the answers to see which one gave us slighty more Bs than As. When you backsolve, generally start with B or D. Here we want the first time the Bs outnumbered the As, so let's start with the smaller choice.
B) 7
After 7 years, we have -21 A and +28B, giving us a 39/28 split - too many As. Eliminate choices (A) and (B).
D) 9
After 9 years, we have -27A and +36 B, giving us a 33/36 split - more than 50% Bs! Further, since the difference is less than 7 (-3As and +4Bs means B gains 7/year), we know that this is the smallest number of years that will work. Choose D!
