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# The value of P if V = 20 and T = 32

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The value of P if V = 20 and T = 32 [#permalink]  13 Sep 2017, 12:38
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58% (00:59) correct 41% (01:15) wrong based on 24 sessions

For a certain quantity of a gas, pressure P, volume V, and temperature T are related according to the formula PV = kT, where k is a constant.

 Quantity A Quantity B The value of P if V = 20 and T = 32 The value of T if V = 10 and P = 78

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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Last edited by Carcass on 04 Oct 2017, 05:36, edited 2 times in total.
Edited by Carcass
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Re: The value of P if V = 20 and T = 32 [#permalink]  16 Sep 2017, 08:40
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I've put D because it seemed a nonsense question to me. Is it like that on purpose or is some formula missing? Otherwise, how can I know the value of a variable given two others without knowing their relationship?
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Re: The value of P if V = 20 and T = 32 [#permalink]  16 Sep 2017, 15:51
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Sorry. I do apologize. I should add the stimulus but internet related problems have been fighting against me.

Regards
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Re: The value of P if V = 20 and T = 32 [#permalink]  21 Sep 2017, 07:52
Using the formula, then we have that column A is equal to $$P=\frac{8}{5}k$$ and column B is equal to $$T=\frac{780}{k}$$. Comparing those two quantities and simplifying we finally reach a comparison between $$k^2$$ and 487.5. Given that k can be whatever constant, we can't say which one of the two is the greatest, thus answer is D!
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Re: The value of P if V = 20 and T = 32 [#permalink]  13 Nov 2018, 06:45
IlCreatore wrote:
Using the formula, then we have that column A is equal to $$P=\frac{8}{5}k$$ and column B is equal to $$T=\frac{780}{k}$$. Comparing those two quantities and simplifying we finally reach a comparison between $$k^2$$ and 487.5. Given that k can be whatever constant, we can't say which one of the two is the greatest, thus answer is D!

Just an example:
If k=0, a=0 b=undefined
k=1 makes a=1.6 b=780
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Re: The value of P if V = 20 and T = 32 [#permalink]  13 Nov 2018, 06:57
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Carcass wrote:

For a certain quantity of a gas, pressure P, volume V, and temperature T are related according to the formula PV = kT, where k is a constant.

 Quantity A Quantity B The value of P if V = 20 and T = 32 The value of T if V = 10 and P = 78

QUANTITY A: The value of P if V = 20 and T = 32
Take given formula, PV = kT, and plug in values to get: P(20) = k(32)
Divide both sides by 20 to get: P = 32k/20
Simplify to get: P = 8k/5

QUANTITY B: The value of T if V = 10 and P = 78
Take given formula, PV = kT, and plug in values to get: (78)(10) = kT
Divide both sides by k to get: (78)(10)/k = T
Simplify to get: T = 780/k

So, we have:
QUANTITY A: 8k/5
QUANTITY B:780/k

Let's TEST some possible values of k

Try k = 1
In this case, we get:
QUANTITY A: 8k/5 = (8)(1)/5 = 8/5
QUANTITY B:780/k = 780/1 = 780
In this case, QUANTITY B IS GREATER

Try k = 1000
In this case, we get:
QUANTITY A: 8k/5 = (8)(1000)/5 = some number greater than 1
QUANTITY B:780/k = 780/1000 = some number less than 1
In this case, QUANTITY A IS GREATER

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com

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Re: The value of P if V = 20 and T = 32 [#permalink]  13 Nov 2018, 08:34
In the first case it becomes P=1.6k whereas in the second case it becomes 780/k.

Since we don't know k we can't determine the answer.
Re: The value of P if V = 20 and T = 32   [#permalink] 13 Nov 2018, 08:34
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