Data Sufficiency

Gmat_mission wrote: ↑

Wed Feb 23, 2022 8:32 am

Is \(zp\) negative?

(1) \(pz^4 < 0\)
(2) \(p + z^4 = 14\)

Answer: E

Source: Official Guide

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