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# Is p + pz = p? (1) p = 0 (2) z = 0

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Math Expert
Joined: 02 Sep 2009
Posts: 52294
Is p + pz = p? (1) p = 0 (2) z = 0  [#permalink]

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04 Jun 2017, 05:11
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Difficulty:

15% (low)

Question Stats:

73% (00:38) correct 27% (00:34) wrong based on 185 sessions

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Is p + pz = p?

(1) p = 0

(2) z = 0

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Senior Manager
Joined: 28 May 2017
Posts: 283
Concentration: Finance, General Management
Re: Is p + pz = p? (1) p = 0 (2) z = 0  [#permalink]

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04 Jun 2017, 05:33
Bunuel wrote:
Is p + pz = p?

(1) p = 0

(2) z = 0

We can rewrite the statement

P + pz =p

Is pz = 0?
Statement 1) If P = 0, pz = 0, SUFFICIENT
Statement 2) If z = 0, pz = 0, SUFFICIENT

Either Statement is Sufficient

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Re: Is p + pz = p? (1) p = 0 (2) z = 0  [#permalink]

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05 Jun 2017, 05:20
2
Top Contributor
1
Bunuel wrote:
Is p + pz = p?

(1) p = 0

(2) z = 0

Target question: Is p + pz = p?

This is a great candidate for rephrasing the target question.

Take Is p + pz = p? and subtract p from both sides to get: Is pz = 0?

In order for pz to equal 0, it must be the case that either p = 0 or z = 0 (or they both equal 0)

REPHRASED target question: Does either p or z equal 0?

Statement 1: p = 0
This answers our REPHRASED target question perfectly.
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: z = 0
This answers our REPHRASED target question perfectly.
Since we can answer the REPHRASED target question with certainty, statement 2 is SUFFICIENT

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Re: Is p + pz = p? (1) p = 0 (2) z = 0  [#permalink]

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06 Jun 2017, 15:49
Bunuel wrote:
Is p + pz = p?

(1) p = 0

(2) z = 0

Let’s simplify the question:

Is p + pz = p?

Is pz = 0?

Statement One Alone:

p = 0

Since p = 0, pz = 0. Statement one is sufficient to answer the question.

Statement Two Alone:

z = 0

Since z = 0, pz = 0. Statement two is sufficient to answer the question.

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Posts: 15
Re: Is p + pz = p? (1) p = 0 (2) z = 0  [#permalink]

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23 Oct 2017, 03:53
1
Bunuel wrote:
Is p + pz = p?

(1) p = 0

(2) z = 0

i took

First simplification as

p+pz = p
p(1+z)=p
1+z=p/p
1+z=1

then i got stuck with statement 1 ..

GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 619
Re: Is p + pz = p? (1) p = 0 (2) z = 0  [#permalink]

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12 Sep 2018, 14:01
Bunuel wrote:
Is p + pz = p?

(1) p = 0

(2) z = 0

$$?\,\,\,\,:\,\,\,\,\,p\left( {1 + z} \right)\,\,\mathop = \limits^? \,\,p$$

$$\left( 1 \right)\,\,\,p = 0\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\text{YES}}} \right\rangle$$

$$\left( 2 \right)\,\,\,z = 0\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\text{YES}}} \right\rangle$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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Posts: 619
Is p + pz = p? (1) p = 0 (2) z = 0  [#permalink]

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12 Sep 2018, 14:09
1
Bunuel wrote:
Is p + pz = p?

(1) p = 0

(2) z = 0

i took

First simplification as

p+pz = p
p(1+z)=p
1+z=p/p
1+z=1

then i got stuck with statement 1 ..

p+pz = p is true if, and only if, p(1+z)=p is true

This is perfect (and marvellous, see my post above)!

But the following stage: p(1+z) = p implies 1+z=p/p is wrong, because p IS zero, and you cannot divide both sides of the equation in bold by p because of that!

In fact, to divide an equation by ANY unknown value (a "letter", a "variable"), you must be sure it cannot assume the zero value... got it?

Example:

$$abc = {b^2} + \frac{{4bc}}{d}\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,ac = b + \frac{{4c}}{d}\,\,\,$$ only if b is different from zero!

(Important: we IMPLICITLY assume d is not zero, otherwise one of the parcels on the left equation - therefore the whole equation - would not have meaning...)

Regards,
Fabio.
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Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net

Is p + pz = p? (1) p = 0 (2) z = 0 &nbs [#permalink] 12 Sep 2018, 14:09
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# Is p + pz = p? (1) p = 0 (2) z = 0

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