For All Positive Numbers P

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Are positive numbers p, q and r equal? [#permalink] Updated on: 21 Jan 2018, 06:22

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Question Stats:

54% (00:47) correct 46% (00:xl) incorrect based on 326 sessions

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Are positive numbers p, q and r equal?

(ane) p = q
(two) q^2 = r^2

GMAT Social club Tests m03q25

Originally posted by karthiksms on 31 May 2012, 18:45.
Last edited by Bunuel on 21 Jan 2018, 06:22, edited iii times in total.

Edited the question

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Re: Are positive numbers p, q and r equal? [#permalink] 31 May 2012, 19:08

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

Combining , p=q=r , Hence sufficient

karthiksms wrote:

Are positive numbers p, q and r equal?

a) p = q
b) q^2 = r^2

What if p=two, q=2, r=sqroot4

then wouldn't it be Eastward?

OA is C

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Re: Are positive numbers p, q and r equal? [#permalink] 31 May 2012, xix:11

Why tin can't sq root iv be considered for r? It'south a positive number. So the ans would be E..

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Re: Are positive numbers p, q and r equal? [#permalink] 31 May 2012, 19:38

Karthik,
Lets stick our line of reasoning according to statements given.
Now, p,q,r are all positive nos.

Both individually can exist eliminated. At present the example of combining the 2.
For Stmt - 1
p=2
q=2

For Stmt 2,
q^2 = 2^2 =4.
For r, r^2 should exist iv. There tin be two values for r.
ii or -2. Only as r is positive no., hence r = 2. (r cannot exist -2)

Delight let me know if this helps.

karthiksms wrote:

Why tin can't sq root 4 exist considered for r? It'due south a positive number. So the ans would be E..

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Re: Are positive numbers p, q and r equal? [#permalink] 31 May 2012, 19:39

I got to respond (C).

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

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

*Note if the question did not land "positive numbers" the answer will be (Eastward) equally foursquare-rooting it can either exist + or - for statement (2).

Too I think you need to be aware that the statements given are "true". Practice not plug-in numbers trying to dis-testify the statement as that tin can easily confuse you.

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Re: Are positive numbers p, q and r equal? [#permalink] 31 May 2012, 19:44

Makes sense now, cool. thanks !

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Re: Are positive numbers p, q and r equal? [#permalink] 01 Jun 2012, 00:26

karthiksms wrote:

Are positive numbers p, q and r equal?

(1) p = q
(ii) q^2 = r^ii

What if p=2, q=2, r=sqroot4

then wouldn't it be East?

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 \(p\).

(i)+(2) Equally \(p = q\) and \(q=r\) then \(p=q=r\). Sufficient.

Answer: C.

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

Promise information technology'due south clear.
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Re: Are positive numbers p, q and r equal? [#permalink] 18 October 2013, 03:41

I am getting confused at statement 2:

Since p^2=r^two, so nosotros accept |p|=|r|, whereas two of the possible solutions are
p = r
p = -r

At present, if p=q=2 and -r = -2, then p=q=r
But if p = -r and p = 2, so r = -2, and then p=q=r doesn't hold, hence E.

What'southward incorrect with my concept?

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Re: Are positive numbers p, q and r equal? [#permalink] 18 October 2013, 04:00

Skag55 wrote:

I am getting confused at argument 2:

Since p^2=r^ii, then nosotros accept |p|=|r|, whereas two of the possible solutions are
p = r
p = -r

Now, if p=q=2 and -r = -ii, so p=q=r
But if p = -r and p = ii, so r = -ii, then p=q=r doesn't hold, hence E.

What'southward incorrect with my concept?

Notice that we are given that both p and r are positive numbers. Therefore from |p|=|r| we tin write p=r.

Hope it'due south clear.
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Re: Are positive numbers p, q and r equal? [#permalink] 18 Oct 2013, 04:06

Bunuel wrote:

Skag55 wrote:

I am getting dislocated at statement two:

Since p^2=r^2, and so we have |p|=|r|, whereas ii of the possible solutions are
p = r
p = -r

Now, if p=q=ii and -r = -two, so p=q=r
But if p = -r and p = 2, then r = -ii, then p=q=r doesn't hold, hence E.

What's incorrect with my concept?

Observe that nosotros are given that both p and r are positive numbers. Therefore from |p|=|r| we tin can write p=r.

Promise it's clear.

Yes, simply r volition be a positive integer but it's value negative. I'm non sure if what I'grand proverb is valid.

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Re: Are positive numbers p, q and r equal? [#permalink] eighteen Oct 2013, 04:10

Skag55 wrote:

Bunuel wrote:

Skag55 wrote:

I am getting dislocated at argument 2:

Since p^2=r^two, then we have |p|=|r|, whereas ii of the possible solutions are
p = r
p = -r

Now, if p=q=2 and -r = -two, and then p=q=r
Just if p = -r and p = ii, then r = -two, then p=q=r doesn't hold, hence Due east.

What's wrong with my concept?

Find that we are given that both p and r are positive numbers. Therefore from |p|=|r| we tin write p=r.

Hope it's clear.

Yep, merely r volition exist a positive integer only it's value negative. I'g not sure if what I'm saying is valid.

I don't understand what you mean.
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Re: Are positive numbers p, q and r equal? [#permalink] xviii Oct 2013, 04:21

Bunuel wrote:

I don't sympathise what y'all hateful.

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

If we say that r is a positive number, that means that it'due south non -r. Though it'due south value might notwithstanding be two or -2, nosotros don't know. Hence p=q=2 and r might be -two.
Post-obit my concept, it would be clearer if the question said that the values of the positive integers are also positive.

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

Skag55 wrote:

Bunuel wrote:

I don't understand what yous 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 = ii.

If we say that r is a positive number, that ways that it'southward non -r. Though it'southward value might withal be 2 or -2, we don't know. Hence p=q=2 and r might be -two.
Following my concept, it would be clearer if the question said that the values of the positive integers are too positive.

Sorry, just this does not make sense.

r is positive, it cannot exist -two, because -ii is negative.
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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 and so r might be -ii or 2.
And |r| might be +r or -r.
In case that r = 2 so -r = -two.
In case that r = -2 then -r = ii.

If we say that r is a positive number, that means that it's not -r. Though it's value might withal be 2 or -2, we don't know. Hence p=q=ii and r might exist -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 information technology.
p,q and r are not variables, are numbers.
Software evolution failed me.

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Re: Are positive numbers p, q and r equal? [#permalink] 21 Jun 2016, 09:41

karthiksms wrote:

Are positive numbers p, q and r equal?

(1) p = q
(2) q^2 = r^2

What if p=two, q=ii, r=sqroot4

so wouldn't it be E?

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(1) p = q

Cypher most r. Non sufficient.

(2) q^ii = r^2

Goose egg about p. Non sufficient.

Combining both statement=

p^2=q^2 = r^2

And so the numbers tin either be +ve or -ve. Only it is given in the question that numbers are +ve.

Hence Sufficient.

C is the answer
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Re: Are positive numbers p, q and r equal? [#permalink] 11 Dec 2019, twenty:38

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Re: Are positive numbers p, q and r equal? [#permalink]

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