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The tick marks on the number line shown are equally spaced. What is

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bwashburn15
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The tick marks on the number line shown are equally spaced. What is [#permalink] The tick marks on the number line shown are equally spaced. What is   Updated on: 02 Feb 2024, 13:49
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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. \(46(4^7)\)

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E

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.
Renamed the topic and edited the question.
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The tick marks on the number line shown are equally spaced. What is [#permalink] The tick marks on the number line shown are equally spaced. What is   Updated on: 02 Feb 2024, 14:28
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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:
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E

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.
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The tick marks on the number line shown are equally spaced. What is [#permalink] The tick marks on the number line shown are equally spaced. What is   02 Feb 2024, 13:35
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bwashburn15 wrote:


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. \(46(4^7)\)

Show Spoiler
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.
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The tick marks on the number line shown are equally spaced. What is [#permalink] The tick marks on the number line shown are equally spaced. What is   02 Feb 2024, 13:48
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Bunuel wrote:
bwashburn15 wrote:


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. \(46(4^7)\)

Show Spoiler
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, 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.


Similar questions to practice:


Hope it helps.­
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Re: The tick marks on the number line shown are equally spaced. What is [#permalink] The tick marks on the number line shown are equally spaced. What is   03 Feb 2024, 02:37
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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. \(46(4^7)\)

Good question to test your brain's void/s.
Equally spaced means that difference between first and second or second and third and so on.
\(4^{9}\) - \(4^{7}\) = \(4^{7}(4^2 - 1)\) = \(15 * 4^{7}\)
So, the difference between next number wrt \(4^{9}\) on the number line would be
\(15 * 4^{7}\) + \(15 * 4^{7}\) = \(30 * 4^{7}\)
And total difference between \(4^{7}\) and n would be
\(30 * 4^{7}\) + \(15 * 4^{7}\) = \(15 * 4^{7}(2 + 1)\) = \(45 * 4^{7}\)

The number n would be then \(4^{7} + 45 * 4^{7}\) = \(4^{7}(1 + 45)\) = \(46 * 4^{7}\)

Answer E.
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Re: The tick marks on the number line shown are equally spaced. What is [#permalink] The tick marks on the number line shown are equally spaced. What is   03 Feb 2024, 02:43


Given: The tick marks on the number line shown are equally spaced.
Asked: What is the value of n?

\(n - 4^9 = 2(4^9 - 4^7) = 2*4^7(4^2 - 1) = 2*15*4^7 = 30(4^7)\)
\(n = 4^9 + 30(4^7) = 4^7(4^2 + 30) = 46(4^7)\)

IMO E
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The tick marks on the number line shown are equally spaced. What is [#permalink] The tick marks on the number line shown are equally spaced. What is   08 Apr 2024, 06:57
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bwashburn15 wrote:


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. \(46(4^7)\)

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­
A question based on observation.

\(4^9 = 16 * 4^7\)
Hence distance between 2 ticks is simply 15*4^7 or we call it '15a'. Now n is another 30a away and hence will be 46a = 46*4^7.

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Attachment:
Screenshot 2024-04-08 at 7.23.19 PM.png
Screenshot 2024-04-08 at 7.23.19 PM.png [ 29.24 KiB | Viewed 3579 times ]


Answer (E)

Here is a discussion on exponents on the number line:
https://youtu.be/0rpppnnJNRs­
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Re: The tick marks on the number line shown are equally spaced. What is [#permalink] The tick marks on the number line shown are equally spaced. What is   08 Jun 2024, 09:01
Bunuel KarishmaB MartyMurray Hi, slightly silly question but just wanted to make sure I got my concept right. Why would it be wrong to assume the sequence is a GP and the difference between two ticks was simply 4^2? This way, n would be 4^13, which I can see is an option here (trap). Thanks!
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The tick marks on the number line shown are equally spaced. What is [#permalink] The tick marks on the number line shown are equally spaced. What is   08 Jun 2024, 19:50
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mollyweasley wrote:
Bunuel KarishmaB MartyMurray Hi, slightly silly question but just wanted to make sure I got my concept right. Why would it be wrong to assume the sequence is a GP and the difference between two ticks was simply 4^2? This way, n would be 4^13, which I can see is an option here (trap). Thanks!

­
Because the tick marks on the number line for an AP, not a GP. 

Place a GP on the number line and see what you get: 1, 4, 16, 64...
Now place an AP  on the number line: 4, 8, 12, 16, 20...
Where do you get ticks placed at equal intervals? In an AP because that is how we define an AP - each term is at a fixed distance from the previous term. ­

Here are some blog posts on Sequences:

https://anaprep.com/algebra-introducing-sequences/
https://anaprep.com/algebra-a-difficult ... sequences/
https://anaprep.com/algebra-benefits-of ... -concepts/­
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