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The integers A, B, C, and D shown on the number line above a

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The integers A, B, C, and D shown on the number line above a  [#permalink]

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New post 27 Dec 2010, 03:41
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A
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The integers A, B, C, and D shown on the number line above are all equally spaced. If C and D are equal to 5^12 and 5^13, respectively, what is the value of A?

A. 5^11
B. 5^10
C. -5^12
D. (-7)5^12
E. (-12)5^13
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Re: Number Line problem  [#permalink]

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New post 27 Dec 2010, 07:32
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venugopis wrote:
Ok well, i will put the number line as below , hope you understand ( A,B,C,D are eully spaced).

__A_____B_____C_____D__

The integers A, B, C, and D shown on the number line above are all equally spaced. If C and D are equal to 512 and 513, respectively, what is the value of A?
A. 511
B. 510
C. -512
D. (-7)512
E. (-12)513

Answer is D.

The distance between C and D is 513 - 512. The distance between any two consecutive points is constant, so the distance between A and D will be 3 times the distance between C and D, or 3(513 – 512).
The value of A, therefore, will be equal to the value of D minus the distance from A to D:
513 – 3(513 – 512) .

Here, i guess my question is- how is the 513 converted to 512(5) ?


venugopis please read and follow: how-to-improve-the-forum-search-function-for-others-99451.html So please: Make sure you type the question in exactly as it was stated from the source.

Also check this: writing-mathematical-symbols-in-posts-72468.html and this: questions-about-posting-84537.html

Also note that you can easily attach an image file (or any other file) directly to the post it's not hard at all.

As for the question, as noted by whiplash2411 there should be 5^12 and 5^13 instead of 512 and 513, so the correct question is:
Attachment:
untitled.PNG
untitled.PNG [ 1.42 KiB | Viewed 22005 times ]
The integers A, B, C, and D shown on the number line above are all equally spaced. If C and D are equal to 5^12 and 5^13, respectively, what is the value of A?
A. 5^11
B. 5^10
C. -5^12
D. (-7)5^12
E. (-12)5^13

The distance between D and C is \(5^{13}-5^{12}=5^{12}*(5-1)=4*5^{12}\);

As A, B, C, and D on the number line are all equally spaced then \(A=C-2*(4*5^{12})=5^{12}-8*5^{12}=-7*5^{12}\).

Answer: D.

Hope it's clear.
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Re: Number Line problem  [#permalink]

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New post 27 Dec 2010, 03:53
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Yeah, the original question was 5^12 and 5^13, not 512 and 513 as you posted. Please check for validity of questions before you post.

So distance between the two points is 5^13 - 5^12 = 5^12 (5 - 1) = 5^12 (4).

So point B = 5^12 - 5^12 (4) = 5^12 (-3) and point A is: 5^12 (-3) - 5^12 (4) = 5^12 (-3-4) = 5^12 (-7) which is the OA

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Re: Number Line problem  [#permalink]

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New post 27 Dec 2010, 04:38
Ok well, i will put the number line as below , hope you understand ( A,B,C,D are eully spaced).

__A_____B_____C_____D__

The integers A, B, C, and D shown on the number line above are all equally spaced. If C and D are equal to 512 and 513, respectively, what is the value of A?
A. 511
B. 510
C. -512
D. (-7)512
E. (-12)513

Answer is D.

The distance between C and D is 513 - 512. The distance between any two consecutive points is constant, so the distance between A and D will be 3 times the distance between C and D, or 3(513 – 512).
The value of A, therefore, will be equal to the value of D minus the distance from A to D:
513 – 3(513 – 512) .

Here, i guess my question is- how is the 513 converted to 512(5) ?
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Re: Number Line problem  [#permalink]

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New post 27 Dec 2010, 11:01
thanks for clearing it up.
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The integers A, B, C, and D shown on the number line above a  [#permalink]

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New post 13 Feb 2015, 14:13
Hi all,

I got the answer. I tried it another way, but with my result I couldn't figure out the solution.

What I did was that I gave A a value of x. Then, since the distance is the same, B became 2x, C became 3x and D bacame 4x. Then, we know that 4x = 5^13. From there, I got to x = 5^13/4. And I couldn't do anything after that...

Is this way also correct and if yes can someone finish it for me..?
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Re: The integers A, B, C, and D shown on the number line above a  [#permalink]

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New post 13 Feb 2015, 14:38
Hi pacifist85,

From a 'concept' standpoint, you can call each of the DISTANCES between any 2 adjacent letters X, but you CANNOT create the following equations....

4X = 5^13
3X = 5^12

Using these two equations will NOT lead to any fixed value for X (and by extension, won't lead to a solution).

To calculate the DISTANCE between 2 adjacent letters on this number line, we can use the values that we're given though:

D = 5^13
C = 5^12

The distance between them is 5^13 - 5^12, which can be simplified (and it needs to be simplified if you want to answer the question)....

5^13 - 5^12 = (5^12)(5 - 1) = (5^12)(4)

So, each of those distances (between A and B, between B and C, and between C and D) = (5^12)(4).

The question asks for the number that is at point A, so we have to take either the value at C (and subtract 2 'distances' from it) or the value at D (and subtract 3 'distances' from it).

Since C is the 'simpler' option, I'll use that:

C = 5^12
each 'distance' = (5^12)(4)
two 'distances' = (2)(5^12)(4)

5^12 - (2)5^12)(4) =
5^12 - (8)(5^12)

From this, you should notice that value MUST be NEGATIVE (so you can eliminate Answers A and B).

Now we can factor out 5^12....

(5^12)(1 - 8)
(5^12)(-7)

Final Answer:

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distance from a to d  [#permalink]

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New post 31 Aug 2015, 07:27
In the figure above, points A, B, C, D, and E are evenly spaced along the number line. If E = 913 and C = 911, what is the distance from point A to point D?

9^3
9^9
(120)(9^9)
9^11
(120)(9^11)


( i thought that this was a geometric progression question. As the ratio between the two no. is 9 in the sequence 9^9, 9^10,9^11,9^12,9^13 . Please help me with this question. Thanks )
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The integers A, B, C, and D shown on the number line above a  [#permalink]

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New post 31 Aug 2015, 07:33
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Rk91 wrote:
In the figure above, points A, B, C, D, and E are evenly spaced along the number line. If E = 913 and C = 911, what is the distance from point A to point D?

9^3
9^9
(120)(9^9)
9^11
(120)(9^11)


( i thought that this was a geometric progression question. As the ratio between the two no. is 9 in the sequence 9^9, 9^10,9^11,9^12,9^13 . Please help me with this question. Thanks )


Search for a question before posting a new one.

Follow posting guidelines (mentioned in my signatures).


Similar question with solution is mentioned above.

Format your formulae properly. C = \(9^{11}\)and NOT 911 and E = \(9^{13}\)and NOT 913.

As the spacing is constant between the letters, we have an arithmetic progression of the form: \(a_n\) = a+(n-1)d with a = A (or the 1st term) and n = number of terms = 5, d = constant distance between the letters.

Thus A = a
B= a+d
C=a+2d
D=a+3d
E=a+4d

As per the given information, C=a+2d=\(9^{11}\) and E = a+4d = \(9^{13}\)

Solving the above 2 equations we get, d = 40*\(9^{11}\)

Thus, distance between A and D = |D-A| = a+3d - a = 3d = 3*40*\(9^{11}\) = 120*\(9^{11}\). E is the correct answer.

FYI, a geometric progression needs to be have ratio of consecutive terms as a constant. The way the question is worded , the sequence has to be arithmetic progression and not a gemetric progression!

Hope this helps.
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Re: The integers A, B, C, and D shown on the number line above a  [#permalink]

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New post 21 Sep 2015, 02:58
venugopis wrote:
Image
The integers A, B, C, and D shown on the number line above are all equally spaced. If C and D are equal to 5^12 and 5^13, respectively, what is the value of A?

A. 5^11
B. 5^10
C. -5^12
D. (-7)5^12
E. (-12)5^13


My ans: D

Distance between C and D = 5^13 – 5^12 = 5^12(5-1) = 4 * 5^12
Value of A = Value of C - Distance between A and C = 5^12 – (2*4* 5^12)= 5^12 (1-8) = -7* 5^12 (ans).
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Re: The integers A, B, C, and D shown on the number line above a  [#permalink]

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New post 17 Oct 2015, 18:34
Pardon my lack of basic understanding here.

Could someone please explain why multiplying the quantity (4*5^12) by 2 is 8*5^12? Shouldn't the two multiply both values in the parentheses?
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Re: The integers A, B, C, and D shown on the number line above a  [#permalink]

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New post 17 Oct 2015, 23:20
2
Hi ada453,

To re-iterate how the rules of math work, I'm going to use some examples that get progressively more 'layered'...

2(10) = 20

2(2x5) = 4(5) = 20

2(4X) = 8X

2(4X)(Y) = 8XY

2(4)(5^12) = 8(5^12)

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Re: The integers A, B, C, and D shown on the number line above a  [#permalink]

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New post 30 Sep 2016, 07:18
venugopis wrote:
Image
The integers A, B, C, and D shown on the number line above are all equally spaced. If C and D are equal to 5^12 and 5^13, respectively, what is the value of A?

A. 5^11
B. 5^10
C. -5^12
D. (-7)5^12
E. (-12)5^13


5^13 - 5^12 = 5^12 *(5-1) = 5^12 *(4) - difference between C and D.
multiply by 3, and get difference between D and A. we get 12*5^12.
now, to find A, subtract from D - 5^13 - the difference - 12*5^12.


factor out a 5^12.
(5-12)*5^12
(-7)*5^12.

D
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Re: The integers A, B, C, and D shown on the number line above a  [#permalink]

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New post 11 Feb 2017, 01:04
Distance between C and D = \(5^1^3 - 5^1^2 = 5^1^2(5-1) = 4*5^1^2\)
Since the points are equally spaced AB=BC=CD. So, BC= \(4*5^1^2\)
For value of B => BC = C - B => \(4*5^1^2= 5^1^2\) - B => B = \(5^1^2 - 4*5^1^2\) = \(5^1^2 (1-4)\) = \(-3*5^1^2\)
Now for value of A => AB = B - A => \(4*5^1^2 = -3*5^1^2\) - A => A = \(-3*5^1^2 - 4*5^1^2 = 5^1^2 (-3 -4)\)
So, the value of A is \((-7)5^1^2\)
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Re: The integers A, B, C, and D shown on the number line above a  [#permalink]

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New post 17 May 2017, 03:01
venugopis wrote:
Image
The integers A, B, C, and D shown on the number line above are all equally spaced. If C and D are equal to 5^12 and 5^13, respectively, what is the value of A?

A. 5^11
B. 5^10
C. -5^12
D. (-7)5^12
E. (-12)5^13


The trap in this question is just getting the test taker to think lines A-D are a consistently increasing /decreasing series of exponents ( example 5^12 5^13 5^14 5^15) - actually if you did lines a-d with 5^3 as c and 5^2 as b then the distance between those two points would be 100- therefore line A cannot be 5^1 because 25-100= -125 - realizing we must apply what we know about subtracting exponents in order to calculate the answer

The distance between 5^13 and 5^12 is (4) 5^12 so we just subtract 5^12 by (4) 5^12 and then subtract the answer again by (4) 5^12

Therefore

D (-7) 5^12
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Re: The integers A, B, C, and D shown on the number line above a  [#permalink]

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New post 30 Jul 2017, 08:12
Bunuel wrote:
venugopis wrote:
Ok well, i will put the number line as below , hope you understand ( A,B,C,D are eully spaced).

__A_____B_____C_____D__

The integers A, B, C, and D shown on the number line above are all equally spaced. If C and D are equal to 512 and 513, respectively, what is the value of A?
A. 511
B. 510
C. -512
D. (-7)512
E. (-12)513

Answer is D.

The distance between C and D is 513 - 512. The distance between any two consecutive points is constant, so the distance between A and D will be 3 times the distance between C and D, or 3(513 – 512).
The value of A, therefore, will be equal to the value of D minus the distance from A to D:
513 – 3(513 – 512) .

Here, i guess my question is- how is the 513 converted to 512(5) ?


venugopis please read and follow: http://gmatclub.com/forum/how-to-improv ... 99451.html So please: Make sure you type the question in exactly as it was stated from the source.

Also check this: http://gmatclub.com/forum/writing-mathe ... 72468.html and this: http://gmatclub.com/forum/questions-abo ... 84537.html

Also note that you can easily attach an image file (or any other file) directly to the post it's not hard at all.

As for the question, as noted by whiplash2411 there should be 5^12 and 5^13 instead of 512 and 513, so the correct question is:
Attachment:
untitled.PNG
The integers A, B, C, and D shown on the number line above are all equally spaced. If C and D are equal to 5^12 and 5^13, respectively, what is the value of A?
A. 5^11
B. 5^10
C. -5^12
D. (-7)5^12
E. (-12)5^13

The distance between D and C is \(5^{13}-5^{12}=5^{12}*(5-1)=4*5^{12}\);

As A, B, C, and D on the number line are all equally spaced then \(A=C-2*(4*5^{12})=5^{12}-8*5^{12}=-7*5^{12}\).

Answer: D.

Hope it's clear.

Hi Bunuel,
I didn't get your solution. Can you please explain in more detail? How you write equation in terms of A?

Thanks.

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