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x=1, y=3,z=5

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x=1, y=3,z=5 [#permalink] New post 11 Dec 2017, 03:02
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Question Stats:

95% (00:56) correct 5% (00:35) wrong based on 20 sessions
\(x=1, y=3,z=5\)

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.
[Reveal] Spoiler: OA

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Re: x=1, y=3,z=5 [#permalink] New post 11 Dec 2017, 03:50
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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
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Re: x=1, y=3,z=5 [#permalink] New post 11 Dec 2017, 12:59
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Expert's post
Carcass wrote:
\(x=1, y=3, z=5\)

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.

[Reveal] Spoiler: 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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Re: x=1, y=3,z=5   [#permalink] 11 Dec 2017, 12:59
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