lheiannie07 wrote:Each of the integers from 0 to 9, inclusive, is written on a separate slip of blank paper and the ten slips are dropped into hat. If the slips are then drawn one at a time without replacement, how many must be drawn to ensure that the numbers on two of the slips drawn will have a sum of 10?
A. 3
B. 4
C. 5
D. 6
E. 7
To guarantee that a pair of drawn numbers will have a sum of 10, we must consider the WORST-CASE SCENARIO: the greatest number of slips that can be drawn such that NO TWO NUMBERS HAVE A SUM OF 10.
If the numbers 0, 1, 2, 3, 4, and 5 are drawn -- for a total of 6 numbers -- no two numbers will have a sum of 10.
Thus, to GUARANTEE that a pair of numbers will have a sum of 10, we must draw at AT LEAST ONE MORE NUMBER -- for a total of 7 numbers -- as follows:
0, 1, 2, 3, 4, 5, and 6.
Here, one pair -- 4 and 6 -- has a sum of 10.
Thus, to ensure that a pair of drawn numbers will have a sum of 10, at least 7 slips must be drawn.
The correct answer is
E.
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