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x=1, y=3,z=5
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11 Dec 2017, 03:02
11 Dec 2017, 03:02
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\(x=1, y=3,z=5\)
A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal
D. The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
\(x^{-1}yz^{-2}\) |
\((\frac{xz}{y})^{-2}\) |
A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal
D. The relationship cannot be determined from the information given.
Re: x=1, y=3,z=5
[#permalink]
11 Dec 2017, 03:50
11 Dec 2017, 03:50
1
Hi
I hope my reasoning is fine.
Quantity A:
(X)^-1 which is 1/1 then 1
Y = 3
And Z^-2 which gives us 1/25
We have (1)(3)/25 = 3/25
Quantity B
(XZ/Y)^-2 (remember PEMDAS)
So (5/3)^-2
Reciproqual to erase the minus.
(3/5)^2 which gives us 9/25.
We can compare them since they have the same denominator.
Quantity B is greater !
I hope I did not make any mistake
I hope my reasoning is fine.
Quantity A:
(X)^-1 which is 1/1 then 1
Y = 3
And Z^-2 which gives us 1/25
We have (1)(3)/25 = 3/25
Quantity B
(XZ/Y)^-2 (remember PEMDAS)
So (5/3)^-2
Reciproqual to erase the minus.
(3/5)^2 which gives us 9/25.
We can compare them since they have the same denominator.
Quantity B is greater !
I hope I did not make any mistake
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: x=1, y=3,z=5
[#permalink]
11 Dec 2017, 12:59
11 Dec 2017, 12:59
1
Carcass wrote:
\(x=1, y=3, z=5\)
A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal
D. The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
\(x^{-1}yz^{-2}\) |
\((\frac{xz}{y})^{-2}\) |
A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal
D. The relationship cannot be determined from the information given.
Show: :: OA
OA in 24h
IMPORTANT CONCEPT #1: x^(-n) = 1/(x^n)
IMPORTANT CONCEPT #2: (x/y)^(-n) = (y/x)^n
Given:
Quantity A: [x^(-1)](y)[(z^(-2]
Quantity B: (xz/y)^(-2)
Apply rule #1 to Quantity A to get:
Quantity A: (1/x)(y)(1/z^2)
Quantity B: (xz/y)^(-2)
Apply rule #2 to Quantity B to get:
Quantity A: (1/x)(y)(1/z^2)
Quantity B: (y/xz)^2
Simplify to get:
Quantity A: y/(xz²)
Quantity B: y²/(x²z²)
Since z² is positive, we can multiply both quantities by z² to get:
Quantity A: y/x
Quantity B: y²/x²
Since x² is positive, we can multiply both quantities by x² to get:
Quantity A: xy
Quantity B: y²
Since y is positive, we can divide both quantities by y to get:
Quantity A: x
Quantity B: y
Since x=1 and y=3, the correct answer is B
Cheers,
Brent
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