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a) p = q Not Sufficient - as r can be any other positive number b) Again Not Sufficient.It denotes that q= r as only positive numbers are to be considered It cannot be 2^2 and (-2)^2

(1) P=Q Not sufficient - you don't know what R is (2) Q^2=R^2 Not sufficient - you don't know what P is

Together, you find that in statement (2) by square-rooting you get Q=R. From statement (1) you know P=Q thus by combining both statements you get P=Q=R.

*Note if the question did not state "positive numbers" the answer will be (E) as square-rooting it can either be + or - for statement (2).

Also I think you need to be aware that the statements given are "true". Do not plug-in numbers trying to dis-prove the statement as that can easily confuse you.

Are positive numbers \(p\), \(q\), and \(r\) equal?

(1) \(p = q\). Not sufficient, since no info about \(r\) (2) \(q^2 = r^2\) --> since given that \(p\) and \(q\) are positive numbers then \(q=r\). Not sufficient since no info about \(p\).

(1)+(2) As \(p = q\) and \(q=r\) then \(p=q=r\). Sufficient.

Answer: C.

As for your question: if \(p=q=2\) and \(r=\sqrt{4}\) --> \(\sqrt{4}=2\), so we have that \(p=q=r=2\).

Re: Are positive numbers p, q and r equal? [#permalink]
18 Oct 2013, 04:21

Bunuel wrote:

I don't understand what you mean.

I mean that a variable might be -ve or +ve so r might be -2 or 2. And |r| might be +r or -r. In case that r = 2 then -r = -2. In case that r = -2 then -r = 2.

If we say that r is a positive number, that means that it's not -r. Though it's value might still be 2 or -2, we don't know. Hence p=q=2 and r might be -2. Following my concept, it would be clearer if the question said that the values of the positive integers are also positive.

Re: Are positive numbers p, q and r equal? [#permalink]
18 Oct 2013, 04:23

Expert's post

Skag55 wrote:

Bunuel wrote:

I don't understand what you mean.

I mean that a variable might be -ve or +ve so r might be -2 or 2. And |r| might be +r or -r. In case that r = 2 then -r = -2. In case that r = -2 then -r = 2.

If we say that r is a positive number, that means that it's not -r. Though it's value might still be 2 or -2, we don't know. Hence p=q=2 and r might be -2. Following my concept, it would be clearer if the question said that the values of the positive integers are also positive.

Sorry, but this does not make sense.

r is positive, it cannot be -2, because -2 is negative. _________________

Re: Are positive numbers p, q and r equal? [#permalink]
18 Oct 2013, 04:25

Skag55 wrote:

Bunuel wrote:

I don't understand what you mean.

I mean that a variable might be -ve or +ve so r might be -2 or 2. And |r| might be +r or -r. In case that r = 2 then -r = -2. In case that r = -2 then -r = 2.

If we say that r is a positive number, that means that it's not -r. Though it's value might still be 2 or -2, we don't know. Hence p=q=2 and r might be -2. Following my concept, it would be clearer if the question said that the values of the positive integers are also positive.

On the other hand I'm overly thinking about it. p,q and r are not variables, are numbers. Software development failed me.

Re: Are positive numbers p, q and r equal? [#permalink]
15 Jan 2015, 19:59

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