Is a negative?

Question

Is a negative?

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

yezz · Answer

from 1 1+a < 0 i.e. 1<-a thus a<-1 , a is negative ... suff from 2 1-a >0 1>a ( a could be +ve fraction 0 or negative ... insuff A

msk0657 · Answer

Given

Stat 1: (1 + a)^3 is negative

We can take it as (1 + a)^3 = -ve and when we are getting -ve result with cube power then 1+a = - ve => a = -ve - 1 .... a = - ve ... Sufficient.

Stat 2: 1-a = +ve => 1 - ve = a...now we can plug values...when -ve is 1 then we get a as 0....when a as 2,3... we get a as some -ve result...There are two sufficient cases possible to eliminate this option.

Option A is correct.

rajeshmoh · Answer

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?

m1033512 · Answer

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

rajeshmoh · Answer

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

BrentGMATPrepNow · Answer

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 
 https://www.youtube.com/watch?v=S_fjYmCtvy0

Is a negative?

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