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# M03-25

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Math Expert
Joined: 02 Sep 2009
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16 Sep 2014, 00:21
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Difficulty:

35% (medium)

Question Stats:

48% (00:30) correct 52% (00:19) wrong based on 209 sessions

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Are positive numbers $$p$$, $$q$$, and $$r$$ equal?

(1) $$p = q$$

(2) $$q^2 = r^2$$

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Joined: 02 Sep 2009
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16 Sep 2014, 00:21
Official Solution:

(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.

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11 Feb 2015, 12:01
1
Hi Bunuel,

Thanks for this question.

I agree with the solution provided. Concerning the old debate whether 0^2=1 or 0^2=0, could it be assumed that for the purposes of the GMAT 0^2=0. With regards to this question this could change the answer substantially, as if not, it could mean that in (2) p and q can b both 0 and 1, and so the sanswer would be (E).

Thank you!
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12 Feb 2015, 06:22
1
bgpower wrote:
Hi Bunuel,

Thanks for this question.

I agree with the solution provided. Concerning the old debate whether 0^2=1 or 0^2=0, could it be assumed that for the purposes of the GMAT 0^2=0. With regards to this question this could change the answer substantially, as if not, it could mean that in (2) p and q can b both 0 and 1, and so the sanswer would be (E).

Thank you!

There is no debate whatsoever:

0^(positive) = 0, for example, 0^2 = 0.

(anything but 0)^0 = 1, for example, 3^0 = 1.

0^0 is undefined and not tested on the GMAT.

For the question at hand none of the variables can be 0, because we are told that p, q, and r are positive numbers, while 0 is neither positive nor negative.

Hope it helps.
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12 Feb 2015, 06:28
Got it! Thanks so much! Seems I was wrong based on some other old discussions.

0^(any positive) = 0
3^0 = 1.
0^0 is undefined and not tested on the GMAT
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16 Nov 2015, 14:05
What if p = 2 q= 2 and r=$$\sqrt{2}$$, then these values are not equal?
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16 Nov 2015, 22:13
rhio wrote:
What if p = 2 q= 2 and r=$$\sqrt{2}$$, then these values are not equal?

(2) says that q^2 = r^2, which is violated with your example: $$(q^2 =4) \neq (2 = r^2)$$.
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21 Apr 2016, 14:05
I observed in another problem whose equation is as follows,
q^2 - r^2 = 0

In that problem, it was said q cannot be equal to r, since the equation can be further reduced to |q| - |r| = 0.

Does it apply here as well?
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21 Apr 2016, 14:12
atturhari wrote:
I observed in another problem whose equation is as follows,
q^2 - r^2 = 0

In that problem, it was said q cannot be equal to r, since the equation can be further reduced to |q| - |r| = 0.

Does it apply here as well?

Not sure I fully understand what you mean there but q^2 - r^2 = 0 can be written as |q| - |r| = 0:

q^2 - r^2 = 0
q^2 = r^2
|q| = |r| (by taking the square root from both sides, which we can safely do since both sides are non-negative).

If we knew that $$q \neq r$$, then we could further simply it to q = -r.
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13 Oct 2016, 11:40
THIS IS CRAZY . I CANNOT BELIEVE I DID NOT READ P,Q,R ARE POSITIVE. DAMN ****
Intern
Joined: 08 Oct 2017
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06 Nov 2017, 15:14
q2=r2 if
q = - 2 and
r = 2 than both are 4, but are not the same, or am I wrong?

Than the answer must be E
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06 Nov 2017, 20:42
nephews wrote:
q2=r2 if
q = - 2 and
r = 2 than both are 4, but are not the same, or am I wrong?

Than the answer must be E

Re-read the stem: "Are positive numbers p, q, and r equal?"
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Re: M03-25   [#permalink] 06 Nov 2017, 20:42
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# M03-25

Moderators: chetan2u, Bunuel

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