TOUGH PROBLEM SOLVING QUESTION

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factor26: Senior | Next Rank: 100 Posts; Posts: 99; Joined: Sun Mar 13, 2011 12:42 pm

by factor26 » Sun Jul 24, 2011 9:55 am

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!!!

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Source: Beat The GMAT — Problem Solving | Sun Jul 24, 2011 9:55 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sun Jul 24, 2011 10:20 am

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.

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winniethepooh: Master | Next Rank: 500 Posts; Posts: 370; Joined: Sat Jun 11, 2011 8:50 pmFollowed by: 2 members; Location: Arlington, MA.; Thanked: 27 times

by winniethepooh » Sun Jul 24, 2011 5:05 pm

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.

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smackmartine: Legendary Member; Posts: 516; Joined: Fri Jul 31, 2009 3:22 pmFollowed by: 13 members; Thanked: 112 times

by smackmartine » Sun Jul 24, 2011 10:11 pm

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.

Smack is Back ...
It takes time and effort to explain, so if my comment helped you please press Thanks button

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Ozlemg: Master | Next Rank: 500 Posts; Posts: 407; Joined: Tue Jan 25, 2011 9:19 amFollowed by: 7 members; Thanked: 25 times

by Ozlemg » Mon Jul 25, 2011 3:21 am

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!

The more you suffer before the test, the less you will do so in the test!

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navami: Legendary Member; Posts: 540; Joined: Sat Dec 20, 2008 7:24 pmFollowed by: 6 members; Thanked: 37 times

by navami » Mon Jul 25, 2011 7:00 am

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

This time no looking back!!!
Navami

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SticklorForDetails: GMAT Instructor; Posts: 66; Joined: Wed Jul 20, 2011 3:39 pmFollowed by: 22 members; Location: New York, NY; Thanked: 39 times; GMAT Score:780

by SticklorForDetails » Tue Jul 26, 2011 8:03 am

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).

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