In a certain lottery drawing, five balls are selected from a tumbler in which each ball is printed with a different two-digit positive integer. If the average (arithmetic mean) of the five numbers drawn is 56 and the median is 60, what is the greatest value that the lowest number selected could be?
A) 43
B) 48
C) 51
D) 53
E) 56
Answer: B
Source: Manhattan GMAT
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In a certain lottery drawing, five balls are selected from a tumbler in which each ball is printed with a different two
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regor60
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To maximize the lowest number we need to minimize the other 3 numbers in order that the total of all numbers equals 5x56=280.
We know 60 points are used by the median, leaving 220 left over.
Because 60 is the median, there must be two numbers greater than 60 that need to be minimized. Therefore they must be 61 and 62, so 220-123 =97 points left over for the smaller two numbers.
The greater of the smaller two numbers must be minimized. Lets call the smallest number X. So the other number must be X+1.
X + (X+1) therefore must equal 97.
2X+1=97
2X=96
X=48, B
We know 60 points are used by the median, leaving 220 left over.
Because 60 is the median, there must be two numbers greater than 60 that need to be minimized. Therefore they must be 61 and 62, so 220-123 =97 points left over for the smaller two numbers.
The greater of the smaller two numbers must be minimized. Lets call the smallest number X. So the other number must be X+1.
X + (X+1) therefore must equal 97.
2X+1=97
2X=96
X=48, B
