If x, y, and z are integers and (2^x)*(5^y)*z = 0.00064, what is the

2^x 5^y z = .00064

statement 1 -

z=20 clearly sufficient.

statement 2 -

x=-1

5^y * z = 128/10^5
5^y * z = 2^2 5^-5

y=-5 and x= -1

xy=5. sufficient.

OA is D.

Bunuel, please confirm.

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

Here is my version.
1) if z=20 ==> 2^(x)*5^(y)=(0.00064/20)=0.000032 ==> 2^(x)*5^(y)=32*10^(-6) ==> 2^(x)*5^(y)=2^(5)*(2*5)^(-6) ==>x=-1 and y=6 ==>xy=-6
2) We know x=-1 but nothing is said about z. Hence not sufficient. Hope it is clear

Hi navkaran:

Can you please elaborate how you go from "..if z=2^2*5" to "..then 2^x*5^y = 2^-1*5^4". My reason is that I am getting a different value for y only, just want to make sure my methods aren't incorrect. Thank you.

The statement asks 2^x . 5^y. z = 0.00064 which can be translated into prime factors as

Statement 1: 2^x . 5^y. z = 2^6 . 10^ -6 = 2^0 . 5^ -6
comparing both the parts we get x= 0 & y=-6 so xy= 0
sufficient.

Statement 2: 5^y . z = 0.000128 which means y & z can take any values. not sufficient.

Therefore A.

Posting solution for above problem.

(2^x)(5^y)z = 64 x 10^-5
St 1: z = 20. therefore
(2^x)(5^y) = 32 x 10^-6 = 2^5 x (5 x 2)^-6 = 2^-1 x 5^-6.
Hence, x = -1 and y = -6. xy = 6. ANSWER

St 2: x = 9. no idea about z. INSUFFICIENT.

Option A

Please someone explain Statement 2:

statement 2 -

x=-1
substitute x in the given equation.
2^-1 * 5^y * z = 64* 10^-5
5^y * z = 2^2 5^-5

y=-5 and x= -1

xy=5. sufficient.

why cannot the OA be D
Bunuel nightblade354

From \(5^y * z = 2^2 5^{-5}\) we cannot conclude that y = -5. What if say y = -6 and z = 20? Or y = -7 and z = 100? ...

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 = 20
So, 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) = 6
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: x = –1
Given: (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) = 5

HOWEVER, 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) = 6
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT


Answer: A

Cheers,
Brent