Is a negative?

Is A negative?

(1) (1 + a)^3 is negative.
(2) 1 – a is positive.

A is not shown to be an integer.
Statement 1:
if a = -0.1, (1 + a)^3 will not be negative
if a = -1.1, (1 + a)^3 will be negative
so, isn't statement 1 insufficient?

Statement 2:
if a = -0.1, (1 - a) will be positive
if a = 0.9, (1 - a) will be positive
so, isn't statement 2 insufficient?

Combining both of them,
(1 + a)^3 will be negative and (1-a) to be positive

if a = -0.1, (1 + a)^3 will not be negative and (1-a) will be a positive.... This also doesn't satisfy the condition
Hence, shouldn't the answer be E?

IMO A

statment 1

(1+a)^3 is negative is only possible when a is negative

becase (x)^odd number is negative only when x is negative

here 1+a can be negative only when a is negative

sufficient


statement 2
for 0<a<1

and it is valid for a<0, and for 0<a<1 also

so a can be positive and negative both

insufficient


IMOA

award kudos if helpful

Posted from my mobile device

Statement 1:
here 1+a can be negative only when a is negative: this need not be necessarily true. if -1<a<0, then inspite of a being engative, (1+a)^3 is positive

Target question: Is a < 0?

Statement 1: (1 + a)³ is negative
KEY CONCEPT: Odd powers preserve the sign of the base
So, POSITIVE^(odd number) = some POSITIVE number
and NEGATIVE^(odd number) = some NEGATIVE number

So, if (1 + a)³ is NEGATIVE , then we can be certain that (1 + a) is NEGATIVE (since 3 is an odd power)
That is, 1+a < 0
Since it is also true that a < a + 1 (for all values of a), we can COMBINE the inequalities to get: a < 1+a < 0
So, as we can see, it is definitely the case that a < 0
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: 1 - a is positive.
There are several values of a that satisfy statement 2. Here are two:
Case a: a = 0.3. Notice that 1 - 0.3 = 0.7, which is positive. In this case, a > 0
Case b: a = -2 Notice that 1 - (-2) = 3, which is positive. In this case, a < 0
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

RELATED VIDEO