factor26 wrote:BEFORE POSTING THIS QUESTION ON THE SITE, I MADE SURE I REVIEWED PRIOR POSTIONS FOR THIS QUESTION. SEEMS LIKE EVEN SOME OF THE EXPERTS HAD SOME DIFFICULTY ANSWERING THIS QUESTION. I'M HOPING TO GET SOME EXPERT FEEDBACK AND SOME MEMBER CONTRIBUTION SO WE CAN ALL FINALLY BEAT THE GMAT!

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

OG ANSWER IS D BUT I CAN'T MAKE HEADS OR TAILS OF THIS QUESTION. IN PARTICULAR STATEMENT II

STATEMENT II: |X+3| > 2

SOLVING FOR X HERE;

X+3>2
X > -1

AND...

X+3 < -2
X < -5

PLUGGING IN VALUES FOR X IN THE ORIGINAL EQUATION SATISFYING STATEMENT 2'S CRITERIA WE GET:

X=0

SO ... 4 < 7-0 / 4 ... THIS ISNT TRUE

X= -6

4 < 7 - (-6) /3 ... THIS IS TRUE

CAN ANYONE EXPLAIN MY FLAW IN REASONING HERE ... HOW CAN THE ANSWER BE D WHEN ONE ANSWER YIELDS AND YES AND THE OTHER ANSWER YIELDS A NO!? HELPPPPPPPPP!!!

You reversed the process that you should be using.
Don't start with the statements, which might or might not be true.
Determine FIRST how x is restricted. THEN plug values into the statements to determine WHETHER the statements must be true.

The following information is given about x:
4< (7-x)/3
12 < 7-x
x < -5.

Thus, we can consider only values of x such that x < -5.

1: 5 < x.
Since x < -5, it is not possible that 5 < x.
Eliminate answers that include 1.
Eliminate C and E.

2. |x+3| > 2.
If x=-5 , then |x+3| = |-5+3| = 2.
Since x < -5, we know that |x+3| > 2.
To illustrate:
If x = -6, then |x+3| = |-6+3| = 3, which is greater than 2.
If x = -7, then |x+3| = |-7+3| = 4, which is greater than 2.
Since x<-5, as the value of x decreases, the value of |x+3| increases.
Thus, statement 2 must be true.
Eliminate answers that don't include 2.
Eliminate B.

3.-(x+5) is positive.
If x=-5, then -(x+5) = -(-5+5) = 0.
Since x < -5, we know that -(x+5) > 0.
To illustrate:
If x = -6, then -(x+5) = -(-6+5) = 1.
If x = -7, then -(x+5) = -(-7+5) = 2.
Since x<-5, as the value of x decreases, the value of -(x+5) increases.
Thus, statement 3 must be true.
Eliminate answers that don't include 3.
Eliminate A.

The correct answer is D.

As all the answer choises have the greater than sigh towards X its better that you get the sign towards X within the calculation of the given information.

4 < (7-x)/3
4*3 < 7-x
-x > 5

Moving to:
1.Opposite of what is available.
Incorrect.

2.-x > 5
-x > 2+3
-x-3>2
|x+3| > 2
Correct.

-x > 5
-x-5 > 0
-(x+5)> 0
So x+5 is positive.
Correct.

My two cents on statement II

Because the question is Problem solving type, you can always consider it "true" if one of the two solutions satisfies the question. In this case

x+3>2 => x>-1
or
x+3<-2 => x<-5 (inequality from the question)

Had this been a Data Sufficiency question, the statement would be clearly not sufficient.

Keep these differences in mind because there are several questions which test this concept.

smackmartine wrote:My two cents on statement II

Because the question is Problem solving type, you can always consider it "true" if one of the two solutions satisfies the question. In this case

x+3>2 => x>-1
or
x+3<-2 => x<-5 (inequality from the question)

Had this been a Data Sufficiency question, the statement would be clearly not sufficient.

Keep these differences in mind because there are several questions which test this concept.

thank you for valuable information. It is very important!

Ans is D.
First try to solve the given equation and bring the simplest form x< -5

factor26 wrote: STATEMENT II: |X+3| > 2

SOLVING FOR X HERE;

X+3>2
X > -1

AND...

X+3 < -2
X < -5

Put really, really simply, the flaw in your reasoning is the word "and." In fact, the appropriate word when there are two contradictory solutions (such as x > -1 and x < -5) is "or." X must be > -1 or < -5. This is always true logically. For instance, if I say "My name is either Adam or Sally," this is also a true statement (even though my name is never Sally, although it is a pretty name).