If a and b are integers, is ab 0? (1) b = a (2) a 2

Question

If a and b are integers, is ab > 0?

(1) b =  a^3 - a
 (2) a > 2

chetan2u · Answer

If a and b are integers, is ab > 0?

Do a and b have same sign??

(1) b =  a^3 - a=a( a^2-1 )=a(a-1)(a+1)...
a=0, b=0 and ab=0, so NO..
a=2, b= 2^3-2=6 , then ab=12..YES
Insufficient

(2) a > 2
Nothing about b..
Insufficient

Combined..
Least value of ab..
ab>2*6=12...YES
Sufficient

C

firas92 · Answer

(1)  b  =  a^3 -  a

=>  b  =  a ( a^2 -1)
=>  b = a(a+1)(a-1)

This tells us that  b  is the product of 3 consecutive integers but we don't know anything about the value of  a

Insufficient

(2)  a > 2

This tells us nothing about  b

Insufficient

(1)+(2)

b  is the product of three consecutive integers and  a  is at least 3

So minimum value of  b  is going to 2*3*4 = positive

Therefore  ab>0

Sufficient

(C)

usmangshams · Answer

Hi,

from the first conditon, we can establish that 
if a-> +ve then b-> +ve and vice versa, implying ab>0. 
Then why isn't the answer A?

chetan2u · Answer

It does not convey that. 
If a=1, b=1^3-1=0.. ab=0....so ab>0 is not true. 
If a=2, b=2^3-2=6 and ab=12>0..true
Different answers. So not sufficient

If a and b are integers, is ab > 0? (1) b = a (2) a > 2