Anyone had a time to look at these two problems? I've tried and tried...but can't seem to get the "expected" answers.

Please help.

https://www.intmath.com/Inequalities/1_P ... lities.php

Both these questions are based on In-equalities.
Going through the info. provided in the above site will help in solving these problems.

Here is the solution of the first problem.

1. m>3z - Insuff
2. m<4z - Insuff

From 1 and 2 => 3z<m<4z => 3z < 4z => z>0

Since z >0 , Using 1 we can say that m>0

Since m,z>0 we can say that m+z>0.

You will be able to solve the second problem after going through the link provided in the previous post.

with statement 1 alone;
|x-3|>= y

we also know from the question that y>=0 so,

|x-3| >= y >= 0

because x-3 is in the absolute value notation x can be any number and the equation still works, so 1 is insufficient.

with statement 2 alone:

|x-3| <= -y

The only way that an absolute value can be less than or equal to a negative variable is if that variable is less than or equal to 0, so y<=0

but from the question y>=0.
The only way that this is true is if y=0 so, y=0

restating statement 2, |x-3| <= 0

The only way that an absolute value is less than or equal to zero is if that absolute value IS equal to zero...so x-3 = 0, thus x=3

B...Statement 2 alone is sufficient

jrbrown2 wrote:with statement 1 alone;
|x-3|>= y

we also know from the question that y>=0 so,

|x-3| >= y >= 0

because x-3 is in the absolute value notation x can be any number and the equation still works, so 1 is insufficient.

with statement 2 alone:

|x-3| <= -y

The only way that an absolute value can be less than or equal to a negative variable is if that variable is less than or equal to 0, so y<=0

but from the question y>=0.
The only way that this is true is if y=0 so, y=0

restating statement 2, |x-3| <= 0

The only way that an absolute value is less than or equal to zero is if that absolute value IS equal to zero...so x-3 = 0, thus x=3

B...Statement 2 alone is sufficient

Awesome... I was gunning for [C], but you are right, is correct...

jrbrown2,

When you say "he only way that an absolute value is less than or equal to zero is if that absolute value IS equal to zero.". Do you mean to say that as the absolute value is never less than 0, the only thing remains is the equal to zero?

Thanks

chatekar wrote:jrbrown2,

When you say "he only way that an absolute value is less than or equal to zero is if that absolute value IS equal to zero.". Do you mean to say that as the absolute value is never less than 0, the only thing remains is the equal to zero?

Thanks

I suppose that is correct. Mathematically,

|x| < 0 is never possible....

AND

|x| = 0, is only possible when x = 0

SO

|x| <= 0, must mean x = 0