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Difficulty:
65%
(hard)
Question Stats:
58% (02:09) correct
42%
(02:25)
wrong
based on 490
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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) \(5^r\)
(A) \(p^5-r^5\)
(B) \(r^5\)
(C) \((p-r)^5\)
(D) \(5^{(p-r)}\)
(E) \(5^r\)
12 Mar 2019, 17:17
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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).
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).
General Discussion
17 Feb 2018, 07:56
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itsmek80
please follow the rules..
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
