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

Question

Is p + pz = p?

(1) p = 0

(2) z = 0

BrentGMATPrepNow · Accepted Answer

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

Answer:  D

RELATED VIDEO
 https://www.youtube.com/watch?v=MyG1K3ee69w

elegantm · Answer

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

Answer D

JeffTargetTestPrep · Answer

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.
 
Answer: D

hkotadiya · Answer

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 ..

please help

fskilnik · Answer

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

\left( 1 ight)\,\,\,p = 0\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{	ext{YES}}} ightangle

\left( 2 ight)\,\,\,z = 0\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{	ext{YES}}} ightangle

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

Regards,
Fabio.

fskilnik · Answer

Hi Harikrushna Kotadiya!

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.

nivivacious · Answer

Question asks whether p+pz=0
rather pz=0

1. Sufficient if p=0
2. Sufficient if z=0

Hence D

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards