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# For all positive numbers p, the operation ♦ is defined by pv

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For all positive numbers p, the operation ♦ is defined by pv [#permalink]  05 Mar 2017, 08:39
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00:00

Question Stats:

77% (00:44) correct 22% (01:42) wrong based on 36 sessions

For all positive numbers p, the operation $$\blacktriangledown$$ is defined by $$p^\blacktriangledown$$ $$= p + \frac{1}{P}$$

 Quantity A Quantity B $$(\frac{2}{7})^\blacktriangledown)^\blacktriangledown$$ $$3.5$$

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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GRE 1: Q167 V156
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Re: For all positive numbers p, the operation ♦ is defined by pv [#permalink]  11 Mar 2017, 05:11
Expert's post
Explanation

We know that $$p^\Diamond = p + \frac{1}{P}$$. So putting $$p = \frac{2}{7}$$ we get

$$\frac{2}{7}^\Diamond = \frac{2}{7} + \frac{7}{2} \approx 3.79$$.

Now the question asks the value of $$(p^\Diamond)^\Diamond$$ so putting p = 3.79 into the expression we get

$$(3.79)^\Diamond \approx 4.05$$.

Se we can write $$(\frac{2}{7}^\Diamond)^\Diamond \approx 4.05$$.

Hence Quantity A is greater.
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Sandy
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Re: For all positive numbers p, the operation ♦ is defined by pv [#permalink]  27 Feb 2018, 12:52
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Good explanantion @sandy, but I believe we could have done this question with less calculation, since 3.79 is already greater than 3.5, and the operation defined always increases the value of p (by 1/p).
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Re: For all positive numbers p, the operation ♦ is defined by pv [#permalink]  28 Feb 2018, 12:27
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Expert's post
Carcass wrote:

For all positive numbers p, the operation is defined by $$p^\spades$$ $$= p + \frac{1}{P}$$

 Quantity A Quantity B $$(\frac{2}{7})^\spades)^\spades$$ $$3.5$$

KEY PROPERTY: 1/(a/b) = b/a

$$\frac{2}{7}^\spades$$ = 2/7 + 7/2
= 4/14 + 49/14
= 53/14

$$\frac{53}{14}^\spades$$ = 53/14 + 14/53
This is wayyy too much work! So, let's estimate

53/14 + 14/53 = 3 11/14 + 14/53
≈ 3.8 + 0.2
≈ 4

So, we have:
Quantity A: ≈ 4
Quantity B: 3.5

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com

Re: For all positive numbers p, the operation ♦ is defined by pv   [#permalink] 28 Feb 2018, 12:27
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