If |a/b| and |x/y| are reciprocals and a/b*x/y

Question

If  |\frac{a}{b}|  and  |\frac{x}{y}|  are reciprocals and  \frac{a}{b}*\frac{x}{y} < 0 , which of the following must be true?

A.  ab < 0

B.  \frac{a}{b} (\frac{x}{y}) < -1

C.  \frac{a}{b} < 1

D.  \frac{a}{b} = \frac{-y}{x}

E.  \frac{y}{x} > \frac{a}{b}

chetan2u · Accepted Answer

|\frac{a}{b}|  and  |\frac{x}{y}|  are reciprocals, so  |\frac{a}{b}|*|\frac{x}{y}|=1

But as  \frac{a}{b}*\frac{x}{y} < 0 , one of the fraction is positive and other negative, that is the product of fractions is negative =>  (\frac{a}{b})*(\frac{x}{y})=-1

Thus  \frac{a}{b}=-(\frac{y}{x})

D

DaniyalAlwani · Answer

chetan2u

In you explanation you assumed product of both the reciprocals equals to 1. Why is that? Question doesn't mention it plus it could've also said a/b * b/a. Then it would've been fair for product to be 1. Kindly explain please

prathyushaR · Answer

the modulus fractions are reciprocals of each other :  |\frac{a}{b}|  *  |\frac{x}{y}|  =1
  \frac{a}{b}*\frac{x}{y} < 0  : the fractions have opposite signs (since product is negative)
thus  \frac{a}{b}*\frac{x}{y} =-1  
  \frac{a}{b} = \frac{-y}{x} 
D

rishab0507 · Answer

question mentions that a/b and x/y are reciprocals i.e reciprocals of each other, so product will be 1, As product is less than < 0, so a/b*x/y = -1.

Hope i am able to make it clear

pierjoejoe · Answer

my line of reasoning was pretty complex, but i guess it was ok.

we know abs(a/b) = 1/(abs(x/y))
and a/b * x/y <0

from the second condition we are sure either a/b is positive and x/y is negative or vice versa (in general there should be an odd number of negative signs to be distributed among a,b,x,y).

from the first equation we know that, by opening the absolute value:
a/b > 0 and 1/x/y > 0 --> a/b = 1/x/y --> a/b = y/x [EXCLUDE because of the second condition]
a/b < 0 and 1/x/y > 0 --> -a/b = 1/x/y --> -a/b = y/x
a/b > 0 and 1/x/y < 0 --> a/b = -1/x/y --> a/b = -y/x
a/b < 0 and 1/x/y < 0 --> -a/b = -1/x/y --> -a/b = -y/x [EXCLUDE because of the second condition]

we are left with either
-a/b = y/x
or
a/b = -y/x

therefore a/b must be equal to -y/x

joshuaa77 · Answer

why does it  have to be  –y/x? Couldn’t the negative just as easily be on the x (like y/–x)? Aren’t they algebraically the same? Just trying to understand why GMAT would pick one as “must be true” when other forms seem equivalent.

kayarat600 · Answer

This is not an og question.

If |a/b| and |x/y| are reciprocals and a/b*x/y < 0, which of the follo

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