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Updated on: 02 Feb 2024, 13:49
Originally posted by bwashburn15 on 02 Feb 2024, 13:14.
Last edited by Bunuel on 02 Feb 2024, 13:49, edited 1 time in total.
Last edited by Bunuel on 02 Feb 2024, 13:49, edited 1 time in total.
Renamed the topic and edited the question.
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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)!
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The tick marks on the number line shown are equally spaced. What is the value of n?
A. \(4^{11}\)
B. \(4^{13}\)
C. \(30(4^7)\)
D. \(31(4^7)\)
E. \(46(4^7)\)
Attachment:
Untitled.png [ 5.7 KiB | Viewed 34720 times ]
Attachment:
Screenshot 2024-02-02 151034.png [ 14.36 KiB | Viewed 23899 times ]
Updated on: 02 Feb 2024, 14:28
Originally posted by MartyMurray on 02 Feb 2024, 13:35.
Last edited by MartyMurray on 02 Feb 2024, 14:28, edited 6 times in total.
Last edited by MartyMurray on 02 Feb 2024, 14:28, edited 6 times in total.
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The tick marks on the number line shown are equally spaced. What is the value of n?
We see that there is one unit between \(4^7\) and \(4^9\) and two units between \(4^9\) and \(n\).
So, since we are given that "The tick marks on the number line shown are equally spaced," the difference between \(4^9\) and \(n\) will be twice the difference between \(4^7\) and \(4^9\).
Accordingly, the value of \(n\) will be \(4^7 +\) three times the difference between \(4^7\) and \(4^9\).
The difference between \(4^7\) and \(4^9\) is the following:
\(4^9 - 4^7 = (4^2)(4^7) - 4^7 = 16(4^7) - 4^7 = 15(4^7)\)
So, each unit between two tick marks is \(15(4^7)\).
Thus, \( n = 4^7 + 3(15(4^7)) = 4^7 + 45(4^7) = 46(4^7)\).
A. \(4^{11}\)
B. \(4^{13}\)
C. \(30(4^7)\)
D. \(31(4^7)\)
E. \(46(4^7)\)
Now, to get the question correct, we must be sure to answer the question asked.
(C) is a trap choice that is the difference between \(4^9\) and \(n\).
(D) is a trap choice that is \(4^7 +\) the difference between \(4^9\) and \(n\).
Correct answer:
02 Feb 2024, 13:35
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bwashburn15
The tick marks on the number line shown are equally spaced. What is the value of n?
A. \(4^{11}\)
B. \(4^{13}\)
C. \(30(4^7)\)
D. \(31(4^7)\)
E. \(46(4^7)\)
Attachment:
Untitled.png
Attachment:
Screenshot 2024-02-02 151034.png
Since the tick marks are equally spaced, the distance between each two consecutive tick marks is 4^9 - 4^7. The point n on the number line is two units from 4^9, thus its value is:
- \(4^9 + 2(4^9 - 4^7) = \)
\(= 4^9 + 2*4^9 - 2*4^7 =\)
\(= 3*4^9 - 2*4^7 =\)
\(= 4^7(3*4^2 - 2) =\)
\(= 46*4^7\)
Answer: E.
