A device calculates the worth of gemstones based on quality...

BTGmoderatorLU wrote: ↑

Sun Jan 26, 2020 5:48 am

Source: Princeton Review

A device calculates the worth of gemstones 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 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 OA is E

Given that the worth of rating of q - 1 is worth 5 times more than a gem with a quality rating of q, we have the following.

Say the worth of the rating of p = V; thus,
the worth of the rating of p – 1= 5*V = 5V;
the worth of the rating of p – 2= 5*5V = 5^2*V;
the worth of the rating of p – 3= 5*5^2*V = 5^3*V;
.
.
.
the worth of the rating of p – r= 5^r*V;

Thus, the correct answer must be 5^r.

Unfortunately, there is no option as 5^r.

Hope this helps!

-Jay
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BTGmoderatorLU wrote: ↑

Sun Jan 26, 2020 5:48 am

Source: Princeton Review

A device calculates the worth of gemstones 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 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 OA is E

Since a gem with a quality rating of q - 1 is worth 5 times as much as a gem with a quality rating of q, then a gem with a rating of p - 1 is also worth 5 times as much as a gem with a quality rating of p. Furthermore, a gem with a rating of p - 2 will be worth 5 x 5 = 5^2 times as much, one with a rating of p - 3 will be worth 5 x 5 x 5 = 5^3 times as much, and so on. Therefore, one with a rating p - r will be worth 5^r times as much as one with a rating of p.

Answer: 5^r