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16 Sep 2014, 00:38
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Are all elements of set \(S\) less than 20?
(1) The smallest element of \(S\) is 0.
(2) The range of \(S\) is 20.
(1) The smallest element of \(S\) is 0.
(2) The range of \(S\) is 20.
16 Sep 2014, 00:38
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Official Solution:
Are all elements of set \(S\) less than 20?
(1) The smallest element of \(S\) is 0.
Clearly insufficient.
(2) The range of \(S\) is 20.
Also insufficient. For example, if the set is \(S = \{-5, 15\}\), the answer is YES. However, if the set is \(S = \{25, 45\}\), the answer is NO.
(1)+(2) The range of a set is the difference between its largest and smallest elements. Given the information, we have \(20 = \text{largest} - \text{smallest} = \text{largest} - 0\). This implies that \(\text{largest} = 20\). Hence, we can conclusively answer NO to the question, "Are ALL elements of set \(S\) less than 20?" because at least one element of the set, specifically 20, is not less than 20.
Answer: C
Are all elements of set \(S\) less than 20?
(1) The smallest element of \(S\) is 0.
Clearly insufficient.
(2) The range of \(S\) is 20.
Also insufficient. For example, if the set is \(S = \{-5, 15\}\), the answer is YES. However, if the set is \(S = \{25, 45\}\), the answer is NO.
(1)+(2) The range of a set is the difference between its largest and smallest elements. Given the information, we have \(20 = \text{largest} - \text{smallest} = \text{largest} - 0\). This implies that \(\text{largest} = 20\). Hence, we can conclusively answer NO to the question, "Are ALL elements of set \(S\) less than 20?" because at least one element of the set, specifically 20, is not less than 20.
Answer: C
08 Sep 2023, 06:39
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
