Mo2men wrote:A certain fruit stand sold a total of 76 oranges to 19 customers. How many of them bought only one orange?
(1) None of the customers bought more than 4 oranges.
(2) The difference between the number of oranges bought by any two customers is even.
Statement 1:
Test the THRESHOLD.
Since no one may buy more than 4 oranges, the threshold here is 4.
Case 1: Each of the 19 customers buys exactly 4 oranges
Here, we get the following set:
{4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4}
Sum of the values = 19*4 = 76.
In Case 1, none of the customers buys exactly 1 orange.
Test whether Case 1 can be altered so that one of the customers buys exactly 1 orange.
Case 2:
{4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1}
Sum of the values = (18*4) + 1 = 73.
The sum is too small.
For the sum to increase to 76, at least one of the first 18 values must increase beyond the threshold of 4.
Not viable.
Implication:
Only Case 1 is possible.
Thus, none of the customers buys exactly 1 orange.
SUFFICIENT.
Statement 2:
For the difference between any two values in the set to be even, all of the values must be even or all of the values must be odd.
Consider the following case:
{4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
4, 7, 1}
Here, the difference between the two terms in red is odd, so the set is not viable.
The sum of 19 odd values will be odd.
Since it is not possible for 19 odd values to have a sum of 76, all of the values in the set cannot be odd.
Thus, all of the values in the set must be EVEN, with the result that none of the 19 customers buys exactly 1 orange.
SUFFICIENT.
The correct answer is
D.
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