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Re: Is the range of the integers 4, 7, x, 6, 5, y greater than 9 [#permalink]
01 Sep 2013, 04:57
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Is the range of the integers 4, 7, x, 6, 5, y greater than 9 ?
The range of a set is the difference between the largest and smallest elements of the set.
(1) y > x^2. Clearly insufficient. If y=4 and x=0, then the range is 7-0=7<9 but if y=100 and y=0, the the range is 100-0=100>9. Not sufficient.
(2) 3 < x < y. Also insufficient. Consider (x, y)=(4, 5) and (x, y)=(4, 100).
(1)+(2) Since x is an integer greater than 3, then the leas value of x is 4 (and the least value of x^2 is 16). From (1) we have that y > x^2, so the least value of y is 17, which mean that the least value of the range is 17-4=13>9. Sufficient.
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