inequalities

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maus: Senior | Next Rank: 100 Posts; Posts: 44; Joined: Thu Apr 07, 2011 6:29 pm; Thanked: 2 times; Followed by:1 members

inequalities

by maus » Wed May 11, 2011 9:12 pm

If 4<(7-x)/3, which of the following is true?

i) 5<x
ii) |x+3|>2
iii) -(x+5) is positive

A) 1 only
b) 3 only
c) 1 and 1 only
d) 2 and 3 only
e) 1 2 and 3

I chose b, but the ANSWER: D

I'm horrible with inequalities so I didn't really understand why 1 wasn't corrent and 2 was...i got why 3 wasn'.

Maus
<:3)))~~~

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Source: Beat The GMAT — Problem Solving | Wed May 11, 2011 9:12 pm

manpsingh87: Master | Next Rank: 500 Posts; Posts: 436; Joined: Tue Feb 08, 2011 3:07 am; Thanked: 72 times; Followed by:6 members

by manpsingh87 » Wed May 11, 2011 9:49 pm

maus wrote:If 4<(7-x)/3, which of the following is true?

i) 5<x
ii) |x+3|>2
iii) -(x+5) is positive

A) 1 only
b) 3 only
c) 1 and 1 only
d) 2 and 3 only
e) 1 2 and 3

I chose b, but the ANSWER: D

I'm horrible with inequalities so I didn't really understand why 1 wasn't corrent and 2 was...i got why 3 wasn'.

4<(7-x)/3;
12<(7-x);
x<-5; i.e. x lies to the left of -5 on the number line;

i) x>5; which is false;

ii)|x+3|>2;
if x>0; then we have; (x+3)>2;
x>-1;
if x<-3; we have;
|x+3|= -(x+3);
-x-3>2;
-x>5; or x<-5;

iii) -(x+5) is positive which is true as we have seen that x is negative;

hence answer should be D

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by Anurag@Gurome » Wed May 11, 2011 11:11 pm

maus wrote:If 4<(7-x)/3, which of the following is true?

i) 5<x
ii) |x+3|>2
iii) -(x+5) is positive

A) 1 only
b) 3 only
c) 1 and 1 only
d) 2 and 3 only

e) 1 2 and 3

I chose b, but the ANSWER: D

I'm horrible with inequalities so I didn't really understand why 1 wasn't corrent and 2 was...i got why 3 wasn'.

Solution:
4 < (7-x)/3 implies that x < -5.
Consider first 1.
x > 5. Obviously, it is not true.
Next, take 2.
lx + 3l > 2.
This means that either x+3 > 2 or x+3 < -2.
Or either x > -1 or x < -5.This means that either of two cases should occur.
Since the question says that x < -5, 2 is true.
Lastly, consider 3.
-(x+5) > 0.
Or -x-5 > 0.
Or x < -5.
So, 3 is also true.

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MAAJ: Master | Next Rank: 500 Posts; Posts: 243; Joined: Sun Jul 12, 2009 7:12 am; Location: Dominican Republic; Thanked: 31 times; Followed by:2 members; GMAT Score:480

by MAAJ » Thu May 12, 2011 3:56 pm

If 4<(7-x)/3, which of the following is true?
x < -5
x = LT(-5)

I) 5 < x False

II) |x + 3| > 2
|LT(-5)+3| > 2
|LT(-2)| > 2 True, because the absolute value will be greater than 2

iii) -(x+5) > 0
-(LT(-5)+5) > 0
-(LT(0)) > 0 True, because LT(0) means some number less than 0

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

by smackmartine » Thu May 12, 2011 5:03 pm

Hi Aunrag,

Statement 2 has two solutions. Why have you neglected the other value of x i.e x > -1 ? Just because the question is not a DATA SUFFICIENCY question or because of some other reason?

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by Anurag@Gurome » Thu May 12, 2011 8:00 pm

smackmartine wrote:Hi Aunrag,

Statement 2 has two solutions. Why have you neglected the other value of x i.e x > -1 ? Just because the question is not a DATA SUFFICIENCY question or because of some other reason?

Statement 2 means that either (1) x > -1 or (2) x < -5.
This means that either (1) or (2) is true.
Now the main question says that x < -5.
So, (2) is true.
This automatically means that statement 2 is true.