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If the hash marks above are equally spaced, what is the value of p?

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If the hash marks above are equally spaced, what is the value of p?  [#permalink]

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New post 26 Aug 2018, 05:26
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If the hash marks above are equally spaced, what is the value of p?


(A) \(\frac{3}{2}\)

(B) \(\frac{8}{5}\)

(C) \(\frac{24}{15}\)

(D) \(\frac{512}{125}\)

(E) \(\frac{625}{256}\)


Attachment:
Capture.PNG
Capture.PNG [ 23.87 KiB | Viewed 526 times ]

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Re: If the hash marks above are equally spaced, what is the value of p?  [#permalink]

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New post 26 Aug 2018, 05:44
D?

Let say each part = x : so 5x = 2 hence x = 2/5
\(p^1/3\) = 4x = 8/5
p = 8*8*8/125 = 512/125
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If the hash marks above are equally spaced, what is the value of p?  [#permalink]

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New post 26 Aug 2018, 08:52
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Bunuel wrote:
Image
If the hash marks above are equally spaced, what is the value of p?


(A) \(\frac{3}{2}\)

(B) \(\frac{8}{5}\)

(C) \(\frac{24}{15}\)

(D) \(\frac{512}{125}\)

(E) \(\frac{625}{256}\)


Attachment:
Capture.PNG


You may notice that 5nos. of hash marks add up to 2. Since the hash marks are equally spaced hence gap between consecutive hash marks is \(\frac{2}{5}\).

Now, \(\sqrt[3]{p}\) is situated after 4 gaps from the reference point(0).
So, \(\sqrt[3]{p}\)=\(4*\frac{2}{5}\)
Or, \(p=(\frac{8}{5})^3\) (Taking cube both sides)
Or, p=\(\frac{512}{125}\)

Ans. (D)
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Re: If the hash marks above are equally spaced, what is the value of p?  [#permalink]

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New post 26 Aug 2018, 09:48
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Bunuel wrote:
Image
If the hash marks above are equally spaced, what is the value of p?


(A) \(\frac{3}{2}\)

(B) \(\frac{8}{5}\)

(C) \(\frac{24}{15}\)

(D) \(\frac{512}{125}\)

(E) \(\frac{625}{256}\)

Attachment:
Capture.PNG


There are 5 spaces between 0 and 2
So, each space represents 2/5

∛p is 4 spaces from 0.
So: ∛p = 4(2/5)
Simplify right side: ∛p = 8/5
Cube both sides to get : (∛p)³ = (8/5)³
Simplify: p = (8/5)³ = 512/125

Answer: D

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Brent
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Re: If the hash marks above are equally spaced, what is the value of p? &nbs [#permalink] 26 Aug 2018, 09:48
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