Is x/p(p 2 + q 2 + r 2 ) = x : GMAT Data Sufficiency (DS)
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# Is x/p(p 2 + q 2 + r 2 ) = x

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Is x/p(p 2 + q 2 + r 2 ) = x [#permalink]

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03 Feb 2013, 17:45
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Is $$\frac{x}{p}$$ $$(p^2 + q^2 + r^2 ) = xp + yq + zr$$?

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

(2) $$yq = zr$$
[Reveal] Spoiler: OA

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Re: Is x/p(p 2 + q 2 + r 2 ) = x [#permalink]

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03 Feb 2013, 21:46
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carcass wrote:
Is $$\frac{x}{p}$$ $$(p 2 + q 2 + r 2 ) = xp + yq + zr$$?

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

(2) $$yq = zr$$

There are too many variables here so let's focus on logic.

Is $$\frac{x}{p}$$ $$(p 2 + q 2 + r 2 ) = xp + yq + zr?$$
Is $$xp + \frac{x}{p}(q 2 + r 2 ) = xp + yq + zr?$$
Is $$\frac{x}{p}(q 2 + r 2 ) = yq + zr?$$

(1) $$q^2 = r^2$$
Even if q^2 = r^2, there are lots of other variables e.g. x, y and z which can take different values to make the two sides unequal. But if q = r = 0, the two sides become equal so not sufficient alone.

(2) $$yq = zr$$
Again, there are no constraints on x and p and they can take different values to make the two sides of the equation unequal. But if q = r = 0, the two sides become equal so not sufficient alone.

Using both together, there are still no constraints on the values x and p can take so the two sides needn't be equal. But if q = r = 0, the two sides become equal so not sufficient.

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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Moderator Joined: 01 Sep 2010 Posts: 3139 Followers: 808 Kudos [?]: 6788 [0], given: 1050 Re: Is x/p(p 2 + q 2 + r 2 ) = x [#permalink] ### Show Tags 04 Feb 2013, 03:59 i thought E as well but I wanted to be sure Thanks the question was a bit convoluted _________________ Moderator Joined: 10 May 2010 Posts: 825 Followers: 25 Kudos [?]: 403 [0], given: 192 Re: Is x/p(p 2 + q 2 + r 2 ) = x [#permalink] ### Show Tags 04 Feb 2013, 13:16 What additional condition must be present for the equation to be true ? [Reveal] Spoiler: $$xq = yp$$ _________________ The question is not can you rise up to iconic! The real question is will you ? GMAT Club Legend Joined: 09 Sep 2013 Posts: 13975 Followers: 591 Kudos [?]: 167 [0], given: 0 Re: Is x/p(p 2 + q 2 + r 2 ) = x [#permalink] ### Show Tags 13 Jan 2015, 12:39 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 8572 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: 340 Q170 V170 Followers: 400 Kudos [?]: 2564 [0], given: 166 Re: Is x/p(p 2 + q 2 + r 2 ) = x [#permalink] ### Show Tags 13 Jan 2015, 12:56 Hi All, DS questions rarely involve this many variables, but when a DS question is this "crazy looking" the solution can usually be found by TESTing VALUES and keeping everything really 'simple' Here, we're asked if (X/P)(P^2 + Q^2 + R^2) = XP + YQ + ZR. This is a YES/NO question. The first thing that you should notice is that the variables Y and Z only appear on the right side of the equation/question. Their respective values will have a great impact on whether the answer to the question is YES or NO. Fact 1: Q^2 = R^2 Let's TEST VALUES (and keep it simple!) IF.... EVERY variable = 0, then the answer to the question is YES. IF..... X, P, Q and R = 1 Y = Z = 2, then the answer to the question is NO. Fact 1 is INSUFFICIENT Fact 2: YQ = ZR Notice how BOTH TESTs from Fact 1 ALSO fit Fact 2.....This gives us a YES answer and a NO answer here as well. Fact 2 is INSUFFICIENT Combined, we have the same two TESTs that fit BOTH Facts and provide 2 different answers. Combined, INSUFFICIENT Final Answer: [Reveal] Spoiler: E GMAT assassins aren't born, they're made, Rich _________________ Contact Rich: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin # Special Offer: Save$75 + GMAT Club Tests

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Re: Is x/p(p 2 + q 2 + r 2 ) = x   [#permalink] 13 Jan 2015, 12:56
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