dhirajx wrote:
Bunuel wrote:
The answer is straight E. Notice that if q is some large enough number, say 100, then r could be more as well less than or equal to -12.
I solved this algebraically:
Question is asking if \(r > -12\)
1
\(q+r>-12\)
or \(r>-12-q\)
no info on q, so insufficient
2
\(q>-12\)
no info on r, so insufficient
1+2,
Since we can add or subtract inequalities with the same sign,
\(q+r>-12\) (from 1)
\(q>-12\) (from 2)
Subtract 2 from 1,
\(r+q (-) q >-12 (-) -12\)
Therefore,
\(r > 0\)
Hence, C.
Where am I going wrong?
Note from Bunuel:
ADDING/SUBTRACTING INEQUALITIES:
You can only add inequalities when their signs are in the same direction:If \(a>b\) and \(c>d\) (signs in same direction: \(>\) and \(>\)) --> \(a+c>b+d\).
Example: \(3<4\) and \(2<5\) --> \(3+2<4+5\).
You can only apply subtraction when their signs are in the opposite directions:If \(a>b\) and \(c<d\) (signs in opposite direction: \(>\) and \(<\)) --> \(a-c>b-d\) (take the sign of the inequality you subtract from).
Example: \(3<4\) and \(5>1\) --> \(3-5<4-1\).
RAISING INEQUALITIES TO EVEN/ODD POWER:
A. We can raise both parts of an inequality to an even power if we know that both parts of an inequality are non-negative (the same for taking an even root of both sides of an inequality).For example:
\(2<4\) --> we can square both sides and write: \(2^2<4^2\);
\(0\leq{x}<{y}\) --> we can square both sides and write: \(x^2<y^2\);
But if either of side is negative then raising to even power doesn't always work.
For example: \(1>-2\) if we square we'll get \(1>4\) which is not right. So if given that \(x>y\) then we can not square both sides and write \(x^2>y^2\) if we are not certain that both \(x\) and \(y\) are non-negative.
B. We can always raise both parts of an inequality to an odd power (the same for taking an odd root of both sides of an inequality).For example:
\(-2<-1\) --> we can raise both sides to third power and write: \(-2^3=-8<-1=-1^3\) or \(-5<1\) --> \(-5^2=-125<1=1^3\);
\(x<y\) --> we can raise both sides to third power and write: \(x^3<y^3\).
Coming back to the question
So, we have q+r >-12 and q > -12
Adding the 2 we get
\(q+r+q> 0\) or\(2q+r >0\)
So, we can have multiple option where r may be greater than or less than -12.
hope it helps.