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Is x/p(p 2 + q 2 + r 2 ) = x

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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.

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

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New post 04 Feb 2013, 14:16
What additional condition must be present for the equation to be true ?

[Reveal] Spoiler:
\(xq = yp\)

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

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New post 13 Jan 2015, 13:56
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


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