Problem Solving

gauravgundal wrote:if 4< (7-x)/3, which of the following must be true?
1. 5 < x
2. |x+3|>2
3.-(x+5) is positive

A. 2 only
B. 3 only
C. 1 and 2 only
D. 3 and 2 only
E. 1 , 2 and 3 only

.

No.. from the original, we know that x > -5, so x could be -3 or -2. Since both -3 and -2 don't agree with (2), (2) isn't a MUST be true.

If x<-5, MUST |x+3|>2 ALWAYS yield an inequality that works? Yes it will, if FIRST off we know that x is already <-5. For any value where FIRST x<-5.... then |x+2| MUST ALWAYS be less than 2.

The reverse doesn't work though: for example, If |x+3|>2, MUST x<-5? No, because x can ALSO be >-1 which means that x MUST NOT ALWAYS be less than -5.

So how, then, could the absolute value inequality have been a COULD BE FALSE? Suppose roman numeral 2 actually read:

|x+3|>1

Then we would have:

case 1:
x+3>1
x>-2

case 2:
-(x+3)>1
x<-4

In this case, we would discard case 1, as it is known to contradict what is known of x (that x<-5). For case 2, if x<-4, then we can have x=-4.5, in which case x is not <-5 or x=-100, in which case x is <-5. Then, it would be a COULD BE FALSE, and we would eliminate it.

In order for an absolute value inequality to be proven as MUST BE TRUE here, one of the solutions had to perfectly match x<-5. That's what happened here. (And obviously, it is impossible that both of the inequality solutions will match because they are going to be different inequality solutions).

Well x<-4 must be true if we know that x<-5. Now if you had a absolute value inequality that yielded x<-6 then it doesn't have to be true is the question stem requires that x<-5

we can see that this means that x is either to the left of -5, or to the right of -1. So, since x might be to the right of -1, 2) does not need to be true.

If x<-5, MUST |x+3|>2 ALWAYS yield an inequality that works? Yes it will, if FIRST off we know that x is already <-5. For any value where FIRST x<-5.... then |x+2| MUST ALWAYS be less than 2.

The reverse doesn't work though: for example, If |x+3|>2, MUST x<-5? No, because x can ALSO be >-1 which means that x MUST NOT ALWAYS be less than -5.

I am little confused : The OG says that the answer is D .
if 2 . cannot be true then how the answer D is correct .Please explain me
GMAT Quantitative Review PS 156

If you plug any number that satisfies this inequality into |x+3|, you will see that the result must be >2. For example, let x=-6. Then, |-6+3| = 3. Is 3>2? Yes. Let x=-5.1. Then, |-5.1+3| = 2.1. Is 2.1>2? Yes. We've convinced ourselves that given x<-5, roman numeral 2 must be true.