If -|x+1| = b, where b is a non-zero integer, which of the following s

Question

If -|x+1| = b, where b is a non-zero integer, which of the following statements must be true?

I. b < 0

II. x < -b

III. x > b

A. I only
B. II only
C. III only
D. I and II only
E. I and III only

Source: eGMAT

Bunuel · Accepted Answer

|x+1| = -b --> -b >=0 --> b <= 0. Since we are given that b is a non-zero integer, then b is a negative integer: -1, -2, -3, ... |x+1| = x+1, when x+1 > 0, so when x > -1. In this case x+1 = -b --> x = -b - 1. When -b = 1, x = 0; when -b = 2, then x = 1, ... --> x < -b . |x+1| = -(x+1), when x+1 <= 0, so when x <= 1. In this case -(x+1) = -b --> x = b - 1. When -b = 1, x = -2; when -b = 2, then x = -3, ... --> x < -b .

KarishmaB · Answer

-|x+1| = b
|x+1| = -b
Note that absolute value can never be negative and we know that b is not 0 so -b must be positive. This means b must be negative. I must be true.

For the others, use number line approach.

_______________(-1)_______0______________________________

-b is the distance of x from -1. If x is on the left of -1, it will be negative and since -b is positive, x < -b.
If x is to the right of 0, -b will still be 1 greater than x.
Say x = 5, then -b = 6 (distance of 5 from -1).
Hence x < -b. II will always hold.

III is not necessary. If x is say -2, -b = 1 so b = -1. Here x < b.

Answer (D)

Gau0809 · Answer

Hi

I am little confused.
I tried with the typical method.

Given that
 -|x+1| = b
|x+1| = -b....... hence b is a negative number, and -b is positive.. so I is true.

Next..
|x+1|...then x+1 = -b ...or..... -(x+1) = -b
When X+1 = -b
x = -b-1 
as -b is positive, x < -b

When -(X+1) = -b
x+1 = b
x = b-1
and then confusion..

can you please help..!!

KarishmaB · Answer

Bunuel has already solved your doubt so I will not provide the solution again but here is a link which tells you why it is very important to consider the range when you convert absolute value equation to a regular equation. i.e. when you substitute x+1 in place of |x+1|, it is very important to note that this is true only when x > -1. https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2014/06 ... -the-gmat/

Gau0809 · Answer

Thank you for sharing the link..
it is quite helpful
thanks Bunuel for the solution..!!

truongynhi · Answer

Hi,
I thought the second case should be  If x is to the right of -1 , since x can be zero and -b=1. What am I missing?

vshrivastava · Answer

If -|x+1| = b, where b is a non-zero integer, which of the following statements must be true?

I. b < 0

II. x < -b

III. x > b

Solution:

If -|x+1| = b then b is equal to a negative value of an absolute value. So, b < 0.

Secondly, If |x+1| = a negative value, then (x+1) < 0. So, x < -1.

So, both x and b are negative values. But magnitude of (x+1) equal to -b.

So x is one more negative than -b. Example: If x = -5, then b = -4.

Therefore, x < -b.

Lastly, x > b can't be true, because both the numbers have negative values. The negative value of x is more negative than that of b.

So, the answer is D.

Thanks in advance for the Kudos!!! :-D

Mo2men · Answer

ِAnother approach is plug in numbers but we need carefully to choose different numbers.

From the prompt  b  is non-zero integer so X does not equal to -1.

I will choose two values above and lower than -1.

x>-1.....choose x=1.......... b=-2

x,-1 .....choose x=-2.............b=-1

From above let's examine each statement

I. b < 0...... from above examples. it is evident that b<0 for all ranges. Eliminate B & C

II. x < -b .....from above examples 1< 2 & -2<1 .. it is always correct. Eliminate A & E

Answer :D

NoMatterWhat · Answer

equation -lx+1l = b

consider x = 3 and b = -4

-l3+1l = -4

the equation still holds true; then why option III is not correct.

Help me out HEROS!!!

bumpbot · Answer

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If -|x+1| = b, where b is a non-zero integer, which of the following s

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