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.

Answer: D

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

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

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

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


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

Regards,
Fabio.

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.

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

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

Hence D