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If the distances between each pair of consecutive ticks are equal, wha

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Math Revolution GMAT Instructor
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If the distances between each pair of consecutive ticks are equal, wha  [#permalink]

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New post 30 May 2018, 01:29
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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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Re: If the distances between each pair of consecutive ticks are equal, wha  [#permalink]

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New post 30 May 2018, 01:45
B
X-2^11=2^11-2^10
X = 2^10(2+2-1)
X = 3(2^10)

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Re: If the distances between each pair of consecutive ticks are equal, wha  [#permalink]

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New post 30 May 2018, 07:06
Top Contributor
MathRevolution wrote:
[GMAT math practice question]

Attachment:
5.30.png


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

Cheers,
Brent
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Re: If the distances between each pair of consecutive ticks are equal, wha  [#permalink]

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New post 31 May 2018, 16:18
MathRevolution wrote:
[GMAT math practice question]

Attachment:
5.30.png


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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Math Revolution GMAT Instructor
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Re: If the distances between each pair of consecutive ticks are equal, wha  [#permalink]

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New post 01 Jun 2018, 02:35
=>

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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Re: If the distances between each pair of consecutive ticks are equal, wha &nbs [#permalink] 01 Jun 2018, 02:35
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