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 Post subject: GMAT AlgebraPosted: Thu Aug 05, 2010 12:49 pm

Joined: Sun May 30, 2010 3:15 am
Posts: 424
If x / y = 3 / z, then 9y² =
A. x²/9
B. x²z
C. x²z²
D. 3x²
E. (1/9)x²z²

(C) This question is most easily solved by isolating y in the equation and substituting into the expression 9y²:
x/y = 3/z
x = 3y/z
3y = xz
y = xz/3.

If we substitute xz/3 into the expression for y, we get:
9(xz/3)² = 9(x²z²/9) = x²z².

The correct answer is choice (C).

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 Post subject: Re: math: algebraPosted: Thu Aug 05, 2010 1:59 pm

Joined: Sun May 30, 2010 2:23 am
Posts: 498
Remember that we can multiply or divide each side of any equality by the same non-zero number and get the equivalent equality. That simple rule creates even simpler one, the cross-multiplication rule.

If we have
a/b = c/d we can

multiply each side by b and get
a = bc/d

or divide each side by c and get
a/(bc) = 1/d

So, basically, we can move any number from denominator of one side to the numerator of another or from numerator to the denominator.
Take a look at these animations to strengthen your understanding:

When we use cross-multiplication rule to solve this question we can easily find y:

Then we can plug it in 9y² and simplify to get the answer.

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