Is zp negative?

jjjinapinch wrote:Is zp negative?
(1) p(z^4) < 0
(2) p + (z^4) = 14

Official Guide question
Answer: E

Target question: Is zp negative?

Statement 1: p(z^4) < 0
This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several values of p and z that satisfy statement 1. Here are two:
Case a: p = -1 and z = 1. In this case, pz = (-1)(1) = -1. So, pz IS negative.
Case b: p = -1 and z = -1. In this case, pz = (-1)(-1) = 1. So, pz is NOT negative.
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: p + (z^4) = 14
There are several values of p and z that satisfy statement 1. Here are two:
Case a: p = -2 and z = 2. In this case, pz = (-2)(2) = -4. So, pz IS negative.
Case b: p = -2 and z = -2. In this case, pz = (-2)(-2) = 4. So, pz is NOT negative.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
There are still several values of p and z that satisfy BOTH statements. Here are two:
Case a: p = -2 and z = 2. In this case, pz = (-2)(2) = -4. So, pz IS negative.
Case b: p = -2 and z = -2. In this case, pz = (-2)(-2) = 4. So, pz is NOT negative.
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent

jjjinapinch wrote: ↑

Thu Aug 03, 2017 12:12 pm

Is zp negative?
(1) p(z^4) < 0
(2) p + (z^4) = 14

Official Guide question
Answer: E

Solution:

Question Stem Analysis:

We need to determine whether zp < 0. Recall that in order for zp to be negative, one of the values z or p must be positive and the other negative.

Statement One Only:

Since pz^4 < 0, neither p nor z is 0. Since z^4 > 0 regardless whether z is positive or negative, we see that p must be negative in order for pz^4 < 0. However, since z could be either positive or negative, we can’t determine whether zp < 0. Statement one alone is not sufficient.

Statement Two Only:

If z = 1, then p = 13, and zp = 13 is not negative. However, if z = 2, then p = -2, and zp = -4 is negative. Statement two alone is not sufficient.

Statements One and Two Together:

From statement one, we see that p is negative. Now, using statement two and letting p = -2, we’ll have z equal to 2 or -2. If z = 2, then zp = -4 is negative. However, if z = -2, then zp = 4 is not negative. Both statements are not sufficient.

Answer: E