Problem Solving

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.

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.