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On the number line shown, the tick marks are equally spaced and the

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Bunuel
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On the number line shown, the tick marks are equally spaced and the [#permalink] New post   05 Aug 2023, 03:00
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On the number line shown, the tick marks are equally spaced and the coordinates of points F and G are 3^11 and 3^12, respectively. Which of the following points has the coordinate -(3^12) ?

A. A
B. B
C. C
D. D
E. E

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JeffTargetTestPrep
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Re: On the number line shown, the tick marks are equally spaced and the [#permalink] New post   07 Aug 2023, 08:02
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Bunuel wrote:

On the number line shown, the tick marks are equally spaced and the coordinates of points F and G are 3^11 and 3^12, respectively. Which of the following points has the coordinate -(3^12) ?

A. A
B. B
C. C
D. D
E. E


We see that G is three times as great as F. If F = x, then G = 3x and the distance between two consecutive tick marks is 2x.

We need to identify the point that has the coordinate –(3^12), which is the opposite of the coordinate of point G and can be denoted by –3x.

Now, we have everything in simple terms to quickly identify the point in question.

E = F – 2x = x – 2x = –x [This is not the point we are looking for.]

D = E – 2x = –x – 2x = –3x [This is the point we are looking for.]

Answer: D
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On the number line shown, the tick marks are equally spaced and the [#permalink] New post   26 Nov 2023, 01:11
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averagedude23 wrote:
I still don't understand this problem even with the explanations above. Does anyone have a better explanation?


Here's how I did it, which I think is a much simpler way.

First of all you need to determine the units between the two datapoints 3^11 and 3^12, which gives us the units between each tick mark.

You can do this by the equation:
3^12 - 3^11
= 3x3^11 - 3^11
= 3^11(3-1)
= (3^11)(2) which is our tick mark units

Then, we need to determine how many tick marks -(3^12) is away from 3^11 (since it must be one of the 5 possible tick marks to the left of F). We can do this by determining the distance between the two points, then dividing by the tick mark units (which will tell us how many tick marks to the left of our reference point).

We can do this with the equation:
(3^11 - (-3^12)) / (3^11)(2)
= (3^11 + 3^12)) / (3^11)(2)
= (3^11 + 3x3^11)) / (3^11)(2)
= (3^11(1 + 3)) / (3^11)(2)
= (3^11)(4) / (3^11)(2) - Then we can cancel out terms in the numerator and denominator
= 4/2 = 2

Therefore, the answer must be 2 tick marks left of 3^11 = D
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Re: On the number line shown, the tick marks are equally spaced and the [#permalink] New post   25 Feb 2024, 23:45
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Hope it helps.­­­
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gmatophobia
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On the number line shown, the tick marks are equally spaced and the [#permalink] New post   05 Aug 2023, 06:54
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Bunuel wrote:

On the number line shown, the tick marks are equally spaced and the coordinates of points F and Gare 3^11 and 3^12, respectively. Which of the following points has the coordinate -(3^12) ?

A. A
B. B
C. C
D. D
E. E

Show Spoiler
Attachment:
2023-07-27_15-03-34.png


As the tick marks are equally spaced, the numbers are in Arithmetic Progression

Common Difference = \( d = 3^{12} - 3^{11} = 3^{11}(3-1) = 2*3^{11}\)

\(a_n = a + (n-1)d\)

As we are finding the lower value (descending sequence), the difference is negative

\(-(3^{12}) = 3^{11} - (n-1)2*3^{11}\)

\(-(3^{12}) = 3^{11} (1 - (n-1)2\)

\(-(3^{12}) = 3^{11}(1 + 2 - 2n)\)

\(-3 = 3 - 2n\)

\(-6 = - 2n\)

\(n = 3\)

Therefore -(\(3^{12}\)), is the third term in the sequence. Hence, -(\(3^{12}\)) is two units on the left w.r.t to \(3^{11}\) i.e. at point D.

Option D
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Re: On the number line shown, the tick marks are equally spaced and the [#permalink] New post   06 Aug 2023, 21:33
I just wanted to ask how come 3rd from the left is D?
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On the number line shown, the tick marks are equally spaced and the [#permalink] New post   06 Aug 2023, 21:52
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Anki111 wrote:
I just wanted to ask how come 3rd from the left is D?


Anki111 - We have found that\( -(3^{12})\) is the third term in the sequence (as \(n = 3\)), also our calculations were based on considering \(3^{11}\) as the first term.

Hence, in the sequence -(\(3^{12}\)) is at the third position on the left. The number lies on the left side as its value, \(-(3^{12})\) is lower than \(3^{11}\).

You can also visualize this way

n = 1, represents the first term in the sequence → Value = \(3^{11}\) ; indicated by point F

n = 2, represents the second term in the sequence → Value = \(3^{11} - (2*3^{11}) = -(3^{11})\) ; indicated by point E

n = 3, represents the third term in the sequence → Value = \(-(3^{12})\) ; indicated by point D
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Re: On the number line shown, the tick marks are equally spaced and the [#permalink] New post   25 Oct 2023, 03:35
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I am confused at one point here. My question is how come 3^11 is the first term in this sequence? Where is it indicated in the question? Please help me understand if I am missing any concept here.
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Re: On the number line shown, the tick marks are equally spaced and the [#permalink] New post   25 Oct 2023, 13:47
ShubhamDadhe wrote:
I am confused at one point here. My question is how come 3^11 is the first term in this sequence? Where is it indicated in the question? Please help me understand if I am missing any concept here.



It's not the first term in the sequence A through G, it's the 6th, as you can see.

Don't let references to "first" term or "third" in the prior responses confuse you, because people are defining them arbitrarily.

All that matters is finding the point that satisfies the question, and that is relative to F and G.

Posted from my mobile device
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Re: On the number line shown, the tick marks are equally spaced and the [#permalink] New post   30 Oct 2023, 08:07
I still don't understand this problem even with the explanations above. Does anyone have a better explanation?
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Re: On the number line shown, the tick marks are equally spaced and the [#permalink] New post   13 Dec 2023, 11:59
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averagedude23 wrote:
I still don't understand this problem even with the explanations above. Does anyone have a better explanation?


You do not have to think of 3^11 and 3^12 as 3^11*3. Think of 3^12 as 3^11+3^11+3^11 (3^11 * 2). Perhaps this helps you. It certainly did help me.
Now the problem states that in the line shown, the tick marks are equally spaced. Let´s see the space bt 3^11 and 3^12
3^11- (3^11+3^11+3^11)= 2 (3^11 + 3^11).
So, all ticks are spaced by 2 (hence, by 3^11 + 3^11).
Point E is the -(3^11) and point D is 2*-(3^11) which is the opposite of 3^12.
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On the number line shown, the tick marks are equally spaced and the [#permalink] New post   Updated on: 03 Feb 2024, 03:50
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ShubhamDadhe wrote:
I am confused at one point here. My question is how come 3^11 is the first term in this sequence? Where is it indicated in the question? Please help me understand if I am missing any concept here.

i didnt took it as a sequence, what i did was calculate de diference betwen the 2 given numbers then substract that from the \(3^{11}\) then substract it again (as many times till i get the value they ask for, like this:
1.- Calculate the distance between 2 points (wich we will call X):
\(X = 3^{12}-3^{11}\\
X = 3^{11}*(3-1)\\
X = 2*3^{11}\)
2.- Calculate what point E was:
\(E = F - X\\
E = 3^{11}-2*3^{11}\\
E = -3^{11}\)
3.- Calculate what point D was:
\(D = E - X\\
D = -3^{11}-2*3^{11}\\
D = -3*3^{11}\\
D = -3^{12}\)


then we know\( -3^{12}\) is 2 points away from F, so its D.



Hope it helps

Originally posted by MrChalo on 12 Jan 2024, 06:28.
Last edited by MrChalo on 03 Feb 2024, 03:50, edited 2 times in total.
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Re: On the number line shown, the tick marks are equally spaced and the [#permalink] New post   29 Jan 2024, 16:53
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Bunuel wrote:

On the number line shown, the tick marks are equally spaced and the coordinates of points F and G are 3^11 and 3^12, respectively. Which of the following points has the coordinate -(3^12) ?

A. A
B. B
C. C
D. D
E. E


We can PLUG IN THE ANSWERS, which represent the point equal to \(-(3^{12})\).

The answer choices are in ascending order, with A the smallest and E the greatest.
Thus, we can determine the correct answer by testing at most two answer choices:
D and B
If D is too small, the correct answer is E.
If D is too big and B too small, the correct answer is C.
If D is too big and B still too big, the correct answer is A.

The distance between one tick mark and the next = G-F = \(3^{12} - 3^{11} = 3^{11}(3-1) = 2*3^{11}\)

Answer choice D --> 2 tick marks below \(3^{11}\) (point F):
\(3^{11} - 2(2*3^{11}) = 3^{11} - 4*3^{11} = 3^{11}(1-4) = 3^{11}(-3) = -(3^{12})\)
Success!

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D
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Re: On the number line shown, the tick marks are equally spaced and the [#permalink] New post   01 Mar 2024, 09:30
Find the difference between \(3^{11}\) and \(3^{12}\). You get \(2 \times 3^{11}\).

Then you need to find how many segments away \(3^{11}\) (or you can choose \(3^{12}\), it doesn't matter) is from the desired \(-3^{12}\).

Set up the equation:

\[3^{11} - x \times 2 \times 3^{11} = -3^{12},\] where \(x\) will tell us the number of spaces away \(3^{11}\) is from the desired \(-3^{12}\).

Simplify, and you get \(x = 2\). So, move 2 spaces to the left from \(3^{11}\), which you'll end up on D.
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On the number line shown, the tick marks are equally spaced and the [#permalink] New post   08 Apr 2024, 06:48
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Bunuel wrote:

On the number line shown, the tick marks are equally spaced and the coordinates of points F and G are 3^11 and 3^12, respectively. Which of the following points has the coordinate -(3^12) ?

A. A
B. B
C. C
D. D
E. E

Show Spoiler
Attachment:
The attachment 2023-07-27_15-03-34.png is no longer available

­
Solving this question is a matter of observation. 

\(3^{12} = 3 * 3^{11} \)

So 3^12 is 3 times as far away from 0 as is 3^11. So we know now that 0 is between E and F. Both positive and negative numbers are symmetric about 0. So E will be 3^11 and F will be 3^12

 ­
Attachment:
Screenshot 2024-04-08 at 7.13.08 PM.png
Screenshot 2024-04-08 at 7.13.08 PM.png [ 28.66 KiB | Viewed 1549 times ]


Answer (D)

I have explained exponents on the number line here:
https://youtu.be/0rpppnnJNRs
 ­
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