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02 Feb 2017, 11:07
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
50% (00:54) correct
50%
(00:55)
wrong
based on 343
sessions
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Set N is populated with all numbers m, where |m| < 5. Which of the following is the closest to the value of the range of Set N?
A. 3
B. 4
C. 5
D. 8
E. 10
A. 3
B. 4
C. 5
D. 8
E. 10
04 Feb 2017, 00:00
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Given |m|<5 which means -5<m<5. Set N consists of all numbers between 5 and -5 (exclusive of 5 and -5)
We need to estimate the range, which is the difference between the largest and the smallest number in set N.
Lets say the largest number is \(m_1\)
\(m_1\)<5
Lets say the smallest number is \(m_2\)
\(m_2\)>-5 => -\(m_2\)<5
So we have
\(m_1\)<5
-\(m_2\)<5
Adding both equations, we get
\(m_1\)-\(m_2\)<10
That is the range of the set is less that 10.
The closest number to the range is therefore 10
There is another graphical way to look at this
Consider the number line below
--------------- -5 ---------------- 0 ------------------ 5 -----------
All the number in set N lie between 5 and -5 and the distance between 5 and -5 is 10.
Since the smallest number is a little greater that -5 ( -4.99 for e.g.) it will lie to the right of -5 on the number line and since the largest number is a little less than 5 (4.99 for example) will lie to the left of 5. So distance between the two numbers will be less than 10 (Range will be 4.99 - (-4.99) = 9.98 in our example).
As you can see, 10 is closest to the range.
Answer E
We need to estimate the range, which is the difference between the largest and the smallest number in set N.
Lets say the largest number is \(m_1\)
\(m_1\)<5
Lets say the smallest number is \(m_2\)
\(m_2\)>-5 => -\(m_2\)<5
So we have
\(m_1\)<5
-\(m_2\)<5
Adding both equations, we get
\(m_1\)-\(m_2\)<10
That is the range of the set is less that 10.
The closest number to the range is therefore 10
There is another graphical way to look at this
Consider the number line below
--------------- -5 ---------------- 0 ------------------ 5 -----------
All the number in set N lie between 5 and -5 and the distance between 5 and -5 is 10.
Since the smallest number is a little greater that -5 ( -4.99 for e.g.) it will lie to the right of -5 on the number line and since the largest number is a little less than 5 (4.99 for example) will lie to the left of 5. So distance between the two numbers will be less than 10 (Range will be 4.99 - (-4.99) = 9.98 in our example).
As you can see, 10 is closest to the range.
Answer E
04 Feb 2017, 08:51
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Bunuel
\(N = \{x \in R | -5 <x<5\}\)
The range of set \(N\) is the difference between the maximum element \(a\) and the minimum element \(b\) in that set.
We could have \(a \approx 5\) and \(b \approx -5\) so \(a-b \approx 10\)
The answer is E
