Are positive numbers p, q and r equal? : GMAT Data Sufficiency (DS)
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# Are positive numbers p, q and r equal?

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

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31 May 2012, 18:45
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Are positive numbers p, q and r equal?

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

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

then wouldn't it be E?

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[Reveal] Spoiler: OA

Last edited by Bunuel on 01 Jun 2012, 00:27, edited 2 times in total.
Edited the question
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31 May 2012, 19:08
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

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=2, q=2, r=sqroot4

then wouldn't it be E?

OA is C

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31 May 2012, 19:11
Why can't sq root 4 be considered for r? It's a positive number. Then the ans would be E..
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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 be eliminated. Now the case of combining the 2.
For Stmt - 1
p=2
q=2

For Stmt 2,
q^2 = 2^2 =4.
For r, r^2 should be 4. There can be 2 values for r.
2 or -2. But as r is positive no., hence r = 2. (r cannot be -2)

Please let me know if this helps.

karthiksms wrote:
Why can't sq root 4 be considered for r? It's a positive number. Then the ans would be E..

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31 May 2012, 19:39

(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.
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31 May 2012, 19:44
Makes sense now, cool. thanks !
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01 Jun 2012, 00:26
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karthiksms wrote:
Are positive numbers p, q and r equal?

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

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

then wouldn't it be E?

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.

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

Hope it's clear.
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Re: Are positive numbers p, q and r equal? [#permalink]

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18 Oct 2013, 03:41
I am getting confused at statement 2:

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

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

What's wrong with my concept?
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Re: Are positive numbers p, q and r equal? [#permalink]

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18 Oct 2013, 04:00
Skag55 wrote:
I am getting confused at statement 2:

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

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

What's wrong with my concept?

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

Hope it's clear.
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Re: Are positive numbers p, q and r equal? [#permalink]

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18 Oct 2013, 04:06
Bunuel wrote:
Skag55 wrote:
I am getting confused at statement 2:

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

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

What's wrong with my concept?

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

Hope it's clear.

Yes, but r will be a positive integer but it's value negative. I'm not sure if what I'm saying is valid.
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Re: Are positive numbers p, q and r equal? [#permalink]

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18 Oct 2013, 04:10
Skag55 wrote:
Bunuel wrote:
Skag55 wrote:
I am getting confused at statement 2:

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

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

What's wrong with my concept?

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

Hope it's clear.

Yes, but r will be a positive integer but it's value negative. I'm 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]

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

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

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

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

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

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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=2, q=2, r=sqroot4

then wouldn't it be E?

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(1) p = q

(2) q^2 = r^2

Combining both statement=

p^2=q^2 = r^2

So the numbers can either be +ve or -ve. But it is given in the question that numbers are +ve.

Hence Sufficient.

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