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# In the figure, points A, B, C, D, and E are evenly spaced

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Manager
Joined: 26 May 2013
Posts: 99

Kudos [?]: 30 [0], given: 30

In the figure, points A, B, C, D, and E are evenly spaced [#permalink]

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21 Aug 2017, 19:08
ScottTargetTestPrep wrote:
pavan2185 wrote:
Attachment:
ABCDE.png
In the figure above, points A, B, C, D, and E are evenly spaced along the number line. If E = 9^13 and C = 9^11, what is the distance from point A to point D?

A. 9^3
B. 9^9
C. (120)(9^9)
D. 9^11
E. (120)(9^11)

We can let the space between each pair of consecutive points = n.

Thus, the space from C to E is n + n = 2n. So, we can create the following equation:

9^11 + 2n = 9^13

2n = 9^13 - 9^11

2n = 9^11(9^2 - 1)

2n = 9^11(80)

n = 9^11(40)

Since the distance from A to D = 3n:

3n = 3(9^11)(40) = 120(9^11)

if n = 9^11(40), how come C does not equal 2(n)?

Answering my own question here, would appreciate if you could chime in though: the distance between does not equal the distance from zero. C is 9^11 from 0, however we're just interested in calculating the distance between A --> D. The distance from A --> C indeed does equal 80*9^11, and this implies that A is a negative number since 9^11 < (9^11 * 80)

Last edited by ak1802 on 21 Aug 2017, 19:43, edited 1 time in total.

Kudos [?]: 30 [0], given: 30

Manager
Joined: 26 May 2013
Posts: 99

Kudos [?]: 30 [0], given: 30

In the figure, points A, B, C, D, and E are evenly spaced [#permalink]

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21 Aug 2017, 19:31
Bunuel wrote:

In the figure above, points A, B, C, D, and E are evenly spaced along the number line. If E = 9^13 and C = 9^11, what is the distance from point A to point D?

A. 9^3
B. 9^9
C. (120)(9^9)
D. 9^11
E. (120)(9^11)

The distance between E and C is $$9^{13}-9^{11}=9^{11}*(9^2-1)=80*9^{11}$$;

The distance between A and D is 1.5 times the distance between C and E, thus it equal to $$120*9^{11}$$

Similar question to practice:
Quote:

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

Discussed here: http://gmatclub.com/forum/the-integers- ... 06968.html

Hope it helps.

Hi - I have two questions on this problem.

1) how come C does not equal 3*(9^11)*40

2) why can't you just add C + "one distance" unit = 9^11 + (9^11)*40... to arrive at point D?

I'm unable to reconcile both 1 and 2 here...

Answering my own question here, would appreciate if you could chime in though: the distance between does not equal the distance from zero. C is 9^11 from 0, however we're just interested in calculating the distance between A --> D. The distance from A --> C indeed does equal 80*9^11, and this implies that A is a negative number since 9^11 < (9^11 * 80)

Kudos [?]: 30 [0], given: 30

In the figure, points A, B, C, D, and E are evenly spaced   [#permalink] 21 Aug 2017, 19:31

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