Carcass wrote:
Suppose \(x_1 = (2)\)\((10^5)\), \(x_2 =\) \((2^5)(5^5)\), \(y_1 = 200\), and \(y_2 = 400\) and \(x_1\) and \(x_2\) represent the value of \(x\) in years 1 and 2, respectively, and \(y_1\) and \(y_2\) represent the value of \(y\) in years 1 and 2, respectively.
Quantity A |
Quantity B |
The percent decrease in x from year 1 to year 2 |
The percent increase in y from year 1 to year 2 |
Percent change = 100(new - old)/oldPercent decrease in x \(= \frac{100(2^5)(5^5) - (2)(10^5)}{(2)(10^5)}\)
Notice that \(10^5 = [(2)(5)]^5 = (2^5)(5^5)\)
So, we get: \(= \frac{100(2^5)(5^5) - (2^1)(2^5)(5^5)}{(2^1)(2^5)(5^5)}\)
Simplify to get: \(= \frac{100(2^5)(5^5) - (2^6)(5^5)}{(2^6)(5^5)}\)
Factor the numerator to get: \(= \frac{(100)(2^5)(5^5)[1 - 2]}{(2^6)(5^5)}\)
Simplify to get: \(= \frac{(100)[1 - 2]}{2}\)
Simplify to get: \(= \frac{-100}{2}\)
\(= -50\)
So, x
decreased by
50%-----------------------------------
Percent decrease in y \(= \frac{100(400 - 200)}{200}\)
Simplify to get: \(= \frac{100(200)}{200}\)
= 100So, y
increased by
100%-----------------------------------
We get:
QUANTITY A:
50QUANTITY B:
100Answer: B
Cheers,
Brent
_________________
Brent Hanneson – Creator of greenlighttestprep.com
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