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

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Intern
Joined: 14 Feb 2018
Posts: 1
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:

45% (medium)

Question Stats:

50% (01:38) correct 50% (01:52) wrong based on 46 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) $$5r$$
[Reveal] Spoiler: OA

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.
Math Expert
Joined: 02 Aug 2009
Posts: 5774
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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Intern
Joined: 12 Apr 2018
Posts: 2
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: 1
Don't understand Challenge Question in my Princeton Review book. [#permalink]

### Show Tags

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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Don't understand Challenge Question in my Princeton Review book.   [#permalink] 12 Apr 2018, 20:09
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