If pqr = 1 then 1/(1 + p + q^(1)) + 1/(1 + q + r^( 1)) + 1/(1 + r +

Question

If  pqr = 1  then  \frac{1}{1 + p + q^{−1}} + \frac{1}{1 + q + r^{− 1}} + \frac{1}{1 + r + p^{−1}}  is equivalent to

A.  p + q + r

B.  \frac{1}{p + q + r}

C.  p^{− 1} + q^{− 1} + r^{− 1}

D. 1

E. 2

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MartyTargetTestPrep · Accepted Answer

Here's the question:

If  pqr = 1  then  \frac{1}{1 + p + q^{−1}} + \frac{1}{1 + q + r^{− 1}} + \frac{1}{1 + r + p^{−1}}  is equivalent to

Notice that, in a question that works like this one, with the variables defined in one expression and then used in an expression that generates the correct answer, it must the case that  all sets of values that fit the first expression must, when used in the second expression, generate the same result.

This principle is super valuable in GMAT quant, and it can be applied to many types of questions. Another example is a question in which the correct answer is based on a triangle with certain parameters.  All triangles with those parameters must generate the same result.  So, if the easiest way to solve the question is, for instance, to use a right triangle with those parameters, then you can use a right triangle.

Thus, in this case, all values for for p, q, and r such that  pqr = 1  will generate the same result when they are placed in the second expression.

So, one way you could answer this question is to choose any set of values such that  pqr = 1 .

So, let's see what happens if we make p, q, and r all 1, since 1 x 1 x 1 = 1.

\frac{1}{1 + 1 + 1} + \frac{1}{1 + 1 + 1} + \frac{1}{1 + 1 + 1}  =

\frac{1}{3} + \frac{1}{3} + \frac{1}{3}  = 1

The correct answer is (D).

CareerGeek · Answer

pqr = 1 
-->  r = \frac{1}{pq}  
Also,  \frac{1}{r} = pq  -->  r^{-1} = pq

\frac{1}{1 + p + q^{−1}} + \frac{1}{1 + q + r^{− 1}} + \frac{1}{1 + r + p^{−1}} 
=  \frac{1}{1 + p + 1/q} + \frac{1}{1 + q + pq} + \frac{1}{1 + 1/pq + 1/p} 
=  \frac{q}{q + pq + 1} + \frac{1}{1 + q + pq} + \frac{1}{(pq + 1 + q)/pq} 
=  \frac{q}{q + pq + 1} + \frac{1}{1 + q + pq} + \frac{pq}{pq + 1 + q} 
=  \frac{q + 1 + pq}{q + 1 + pq} = 1

Option D

TheNightKing · Answer

If you love Algebra then look how Dillesh4096 has solved about but if you don't then read below.

Let's say p=q=r=1. If we solve the given expression we get (1/3)+(1/3)+(1/3)=1

A.  p + q + r = 1+1+1=3   Nope

B.  \frac{1}{p + q + r}=1/3  Nope

C.  p^{− 1} + q^{− 1} + r^{− 1} =3   Nope

D. 1 Yes

E. 2 Nope

Answer D

chai9944 · Answer

https://gmatclub.com/forum/download/file.php?id=83338 Can some one explain how to deal with mods || ? GMAT-Club-Forum-1fecegxw.png

Bunuel · Answer

1. This question is discussed here: which-of-the-following-expressions-equals-0-when-x-0-and-equals-x-416985.html 2. Check the links below: Absolute Value Theory Math: Absolute value (Modulus) Absolute Value: Tips and hints Properties of Absolute Values on the GMAT Absolute modulus : A better understanding GMAT Question Patterns: Abolute Value The Reason Behind Absolute Value Questions on the GMAT Questions Inequality and absolute value questions from my collection The E-GMAT Question Series on ABSOLUTE VALUE DS Questions PS Questions For more check Ultimate GMAT Quantitative Megathread Hope it helps. GMAT-Club-Forum-f709cgnu.png

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If pqr = 1 then 1/(1 + p + q^(1)) + 1/(1 + q + r^( 1)) + 1/(1 + r +

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If pqr = 1 then 1/(1 + p + q^(1)) + 1/(1 + q + r^( 1)) + 1/(1 + r +

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