Is r more than -12?

Question

Is r more than -12?

(1) q + r > -12
(2) q > -12

Bunuel · Answer

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.

Griffins · Answer

Both, statement 1 and statement 2 are insufficient. So the correct option is E

dxx · Answer

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?

WoundedTiger · Answer

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 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^2-2 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 we can raise both sides to third power and write: x^3-12 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.

bumpbot · Answer

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Is r more than -12?

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Is r more than -12?

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