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If the distances between each pair of consecutive ticks are

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by Max@Math Revolution » Wed May 30, 2018 12:18 am
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[GMAT math practice question]

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If the distances between each pair of consecutive ticks are equal, what is the value of x?

A. 2^{12}
B. 3(2^{10})
C. 5(2^{10})
D. (2^{13})
E. 3(2^{12})
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by Brent@GMATPrepNow » Wed May 30, 2018 6:00 am
Max@Math Revolution wrote:[GMAT math practice question]

Image

If the distances between each pair of consecutive ticks are equal, what is the value of x?

A. 2^{12}
B. 3(2^{10})
C. 5(2^{10})
D. (2^{13})
E. 3(2^{12})
If the distances between each pair of consecutive ticks are equal, we can write: 2^11 - 2^10 = x - 2^11
We must solve this equation for x....

Add 2^11 to both sides: 2^11 + 2^11 - 2^10 = x
Combine the two 2^11's to get: 2(2^11) - 2^10 = x
Rewrite 2 as 2^1 to get: (2^1)(2^11) - 2^10 = x
Simplify to get: 2^12 - 2^10 = x
Factor our 2^10 to get: 2^10(2^2 - 1) = x
Evaluate to get: 2^10(4 - 1) = x
Simplify to get: 2^10(3) = x

Answer: B

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Brent
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by GMATGuruNY » Wed May 30, 2018 6:27 am
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Max@Math Revolution wrote:[GMAT math practice question]

Image

If the distances between each pair of consecutive ticks are equal, what is the value of x?

A. 2^{12}
B. 3(2^{10})
C. 5(2^{10})
D. (2^{13})
E. 3(2^{12})
Since the ticks are equally spaced, the difference between x and 2¹¹ is equal to the the difference between 2¹¹ and 2¹�:
x - 2¹¹ = 2¹¹ - 2¹�
x = 2¹¹ + 2¹¹ - 2¹�
x = 2¹�(2 + 2 - 1)
x = 2¹�(3).

The correct answer is B.
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by Jeff@TargetTestPrep » Thu May 31, 2018 3:18 pm
Max@Math Revolution wrote:
Image

If the distances between each pair of consecutive ticks are equal, what is the value of x?

A. 2^{12}
B. 3(2^{10})
C. 5(2^{10})
D. (2^{13})
E. 3(2^{12})
The space between each pair of consecutive ticks is 2^11 - 2^10, so x is:

[2^11 + (2^11 - 2^10)]

2^10(2 + 2 - 1) = 2^10 x 3

Answer: B

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by Max@Math Revolution » Fri Jun 01, 2018 1:22 am
=>

The distance between each pair of consecutive ticks is 2^11 – 2^10 = 2*2^10 – 2^10 = 2^10.
Thus, x = 2^11 + 2^10 = 2*2^10 + 2^10 = 3(2^10).

Therefore, the answer is B.
Answer: B
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