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

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Math Expert
Joined: 02 Sep 2009
Posts: 58453
If the hash marks above are equally spaced, what is the value of p?  [#permalink]

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26 Aug 2018, 06:26
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Difficulty:

25% (medium)

Question Stats:

73% (01:39) correct 27% (01:56) wrong based on 71 sessions

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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) $$\frac{625}{256}$$

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Capture.PNG [ 23.87 KiB | Viewed 1085 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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26 Aug 2018, 06:44
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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26 Aug 2018, 09:52
1
Bunuel wrote:

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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26 Aug 2018, 10:48
Top Contributor
Bunuel wrote:

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

Cheers,
Brent
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Re: If the hash marks above are equally spaced, what is the value of p?   [#permalink] 26 Aug 2018, 10:48
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