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

Question

https://gmatclub.com/forum/download/file.php?id=13753 
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

Bunuel · Accepted Answer

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.

whiplash2411 · Answer

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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venugopis · Answer

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) ?

gettinit · Answer

thanks for clearing it up.

pacifist85 · Answer

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..?

EMPOWERgmatRichC · Answer

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:  D

GMAT assassins aren't born, they're made,
Rich

Rk91 · Answer

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 )

ENGRTOMBA2018 · Answer

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.

abani · Answer

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).

ada453 · Answer

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?

EMPOWERgmatRichC · Answer

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)

GMAT assassins aren't born, they're made,
Rich

mvictor · Answer

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

onamarif · Answer

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

Nunuboy1994 · Answer

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

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