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A device calculates the worth of gem stones based on quality such that

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Joined: 14 Feb 2018
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A device calculates the worth of gem stones based on quality such that  [#permalink]

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Updated on: 17 Feb 2018, 07:56
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Difficulty:

65% (hard)

Question Stats:

50% (02:10) correct 50% (02:21) wrong based on 60 sessions

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A device calculates the worth of gem stones based on quality such that a gem with a quality rating of q - 1 is worth 5 times more than a gem with a quality rating of q. According to this device, the worth of a gem with a quality rating of p - r is how many times greater than that of a gem with a rating of p?

(A) $$p^5-r^5$$
(B) $$r^5$$
(C) $$(p-r)^5$$
(D) $$5^{(p-r)}$$
(E) $$5r$$

Originally posted by itsmek80 on 14 Feb 2018, 18:12.
Last edited by chetan2u on 17 Feb 2018, 07:56, edited 1 time in total.
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Joined: 02 Aug 2009
Posts: 7415
A device calculates the worth of gem stones based on quality such that  [#permalink]

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17 Feb 2018, 07:56
itsmek80 wrote:
A device calculates the worth of gem stones based on quality such that a gem with a quality rating of q - 1 is worth 5 times more than a gem with a quality rating of q. According to this device, the worth of a gem with a quality rating of p - r is how many times greater than that of a gem with a rating of p?

(A) $$p^5-r^5$$
(B) $$r^5$$
(C) $$(p-r)^5$$
(D) $$5^{(p-r)}$$
(E) $$5r$$

q - 1 is worth 5 times more than a gem with a quality rating of q
the relation could be..
1) 5*1
2) 5^1

so for p-r. it can be
1) 5*r
2) 5^r

only 5r is there, so the answer is E

Otherwise
also substitute p as q and r as 1 and the ANSWER should be 5
lets see the choices
(A) $$p^5-r^5........q^5-1^5=q^5-1$$...NO
(B) $$r^5........1^5$$.... NO
(C) $$(p-r)^5.......(q-1)^5$$...NO
(D) $$5^{(p-r)}.....5^{q-1}$$...NO
(E) $$5r.....5*1=5$$....YES

E
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Joined: 12 Apr 2018
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Don't understand Challenge Question in my Princeton Review book.  [#permalink]

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12 Apr 2018, 19:30
Hi everyone,

I don't understand the following challenge question in my Princeton Review Cracking the GMAT book. I looked at the solution in the back, but the explanation is vague or not quite step by step. I personally felt like this question was missing some information in order for me to actually solve it. Please let me know your thoughts.

A device calculates the worth of gem stones based on quality such that a gem with a quality rating of q-1 is worth 5 times more than a gem with a quality rating of q. According to this device, the worth of a gem with a quality rating of p-r is how many times greater than that of a gem with a rating of p?

(A) p^5 - r^5
(B) r^5
(C) (p-r)^5
(D) 5^(p-r)
(E) 5r

The correct answer is D, but not sure how I would start to establish a pattern in order to even solve the question. I know I'm given that
q-1 = 5q
and I'm supposed to use solely that information?

Intern
Joined: 28 Feb 2017
Posts: 12
Don't understand Challenge Question in my Princeton Review book.  [#permalink]

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12 Apr 2018, 20:09
Hi everyone,

I don't understand the following challenge question in my Princeton Review Cracking the GMAT book. I looked at the solution in the back, but the explanation is vague or not quite step by step. I personally felt like this question was missing some information in order for me to actually solve it. Please let me know your thoughts.

A device calculates the worth of gem stones based on quality such that a gem with a quality rating of q-1 is worth 5 times more than a gem with a quality rating of q. According to this device, the worth of a gem with a quality rating of p-r is how many times greater than that of a gem with a rating of p?

(A) p^5 - r^5
(B) r^5
(C) (p-r)^5
(D) 5^(p-r)
(E) 5r

The correct answer is D, but not sure how I would start to establish a pattern in order to even solve the question. I know I'm given that
q-1 = 5q
and I'm supposed to use solely that information?

Consider 3 gems p p-1 p-2. Now using information you will see than P-2 is costlier than P-1 by 5 times P-1 is costlier than P by 5 times. So that makes P-2 costlier by 25 times compared to P. And only D satisfies.

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Joined: 05 Feb 2018
Posts: 120
Re: A device calculates the worth of gem stones based on quality such that  [#permalink]

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12 Mar 2019, 17:17
Official explanation:

The question asks for the factor by which the value of a gem with a rating of p would have to be multiplied to equal the value of a gem with a rating of p – r. According to the rating system described by the question stem, the value of a gem with a rating of q – 1 is 5 times greater than the value of a gem with a rating of q. Subtracting 1 from the rating corresponds to a 5-fold increase in value. Following the pattern suggested by the question stem, the value of a gem with a q – 2 rating is greater than the value of a gem with a q rating by a factor of 25, or 5^2 . Similarly, the value of a gem with a q – 3 rating is greater than the value of a gem with a q rating by a factor of 125, or 5^3.

Apply this pattern to gems rated p – r and p. The easiest way to do this is to Plug In values of p and r. Let p = 5 and r = 2. In this case, the gems to be compared are rated ‘5 –2’ and ‘5’. Based on the pattern above, the value of the gem rated ‘5 – 2’ is greater than the value of the gem rated ‘5’ by a factor of 25. Substitute p = 5 and r = 2 into the answer choices, looking for the answer that equals 25.

Choice (A) is (5) 5 – (2) 5 , a number much greater than 25. Eliminate (A).
Choice (B) is (2) 5 , or 32. Eliminate (B).
Choice (C) is (5 – 2) 5 , or 243. Eliminate (C).
Choice (D) is 5^2 , or 25. Keep (D).
Choice (E) is 5^5×2 , or 5^10 , a number much greater than 25. The correct answer is (D).
Re: A device calculates the worth of gem stones based on quality such that   [#permalink] 12 Mar 2019, 17:17
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