Bunuel wrote:
Tough and Tricky questions: Exponents.
If x, y, and z are integers and (2^x)*(5^y)*z = 0.00064, what is the value of xy?
(1) z = 20
(2) x = –1
Kudos for a correct solution. Given: x, y, and z are integers and (2^x)*(5^y)*z = 0.00064 0.00064 = (64)(1/100,000) = (64)(10^-5)
= (2^6)(5^-5)(2^-5)
So, ONE possibility is that x = 6, y = -5 and z = 2^-5
However, we could also take (2^6)(5^-5)(2^-5) and combine the powers of 2 to get: (2^1)(5^-5)(1)
So, ANOTHER possibility is that x = 1, y = -5 and z = 1
As you can see, there are several possible outcomes.
Target question: What is the value of xy? Statement 1: z = 20So, we have: (2^x)(5^y)(20)= 0.00064
Divide both sides by 20 to get: (2^x)(5^y)= 0.00064/20
Simplify to get: (2^x)(5^y)= 0.00064/2
= 0.000032
= (32)(1/1,000,000)
= (2^5)(10^-6)
= (2^5)(2^-6)(5^-6)
= (2^-1)(5^-6)
If (2^x)(5^y) = (2^-1)(5^-6), then x = -1 and y = -6, which means
xy = (-1)(-6) = 6Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: x = –1Given: (2^x)(5^y)(z) = 0.00064
If x = -1, we get: (2^-1)(5^y)(z) = 0.00064
Simplify to get: (1/2)(5^y)(z) = 0.00064
Multiply both sides by 2 to get: (5^y)(z) = 0.00128
0.00128 = (128)(1/100,000)
= (2^7)(10^-5)
= (2^7)(2^-5)(5^-5)
= (2^2)(5^-5)
= (5^-5)(2^2)
In other words, (5^y)(z) = (5^-5)(2^2)
So, we COULD say that x = -1, y = -5 and z = 2^2, which means
xy = (-1)(-5) = 5HOWEVER, we could also take (5^-5)(2^2) and rewrite it as: (5^-6)(5^1)(2^2)
Then evaluate parts to get: (5^-6)(5)(4), which equals (5^-6)(20)
In other words, (5^y)(z) = (5^-6)(20)
So, we could ALSO say that x = -1, y = -6 and z = 20, which means
xy = (-1)(-6) = 6Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Answer: A
Cheers,
Brent
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