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Algebra

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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Algebra

by SFtraveler » Wed Nov 24, 2010 11:41 pm
If x>1 and a/b=1-(1/x), then b/a= ?

a) x
b) x-1
c) (x-1)/x
d) x/((x-1)
e) (1/x)-1

Need step-by-step explanation of how to solve this question.
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by shovan85 » Thu Nov 25, 2010 1:17 am
a/b=1-(1/x)

Divide both sides by 1

=> (a/b) / 1 = [1-(1/x)] / 1

Using cross multiplication, (More Info: https://en.wikipedia.org/wiki/Cross-multiplication)

=> 1/(a/b) = 1/[1-(1/x)]

We need to solve each side individually.

Consider, LHS = 1/(a/b) = b/a .....(1)

Consider RHS. We need to solve The outermost bracket [] in the denominator of Right Hand Side of the equation.

[1-(1/x)] = (x-1)/x

Thus, RHS = 1/[1-(1/x)] = 1/ [(x-1)/x] = x / ( x - 1) ......(2)

Now, LHS = RHS

From Eqn (1) and (2) [Marked above]

=> b/a = x / ( x - 1)

IMO D
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by SFtraveler » Mon Dec 06, 2010 10:25 pm
I don't understand this part: [1-(1/x)] = (x-1)/x

What did you do to [1-(1/x)] to get (x-1)/x?
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by shovan85 » Mon Dec 06, 2010 11:09 pm
SFtraveler wrote:I don't understand this part: [1-(1/x)] = (x-1)/x

What did you do to [1-(1/x)] to get (x-1)/x?
This is just a simple math. Please see below.
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