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

Question

If -|x| = b, where b is a non-zero integer, which of the following statements can 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, II, and III

philipssonicare · Answer

Substitute in numbers
-|2|=-2 or -|-2|=-2. We can't use 0 as x or b due to the original condition.

I) The negative sign is outside of the absolute value sign. Thus, the negative is applied to a positive number. B is negative. b<0.
II) 2<--2(x) as they are equal; -2<--2 (o)
III) 2>-2(o); -2>-2(x) as they are equal

pandeyashwin · Answer

b can be any integer other than 0.
Case 1 : If x > 0 , b is < 0
Case 2 : If x < 0 , b is < 0

Statement I is always true.
Statement II can be true in case 2 but not in case 1
Statement III can be true in case 1 but not in case 2

Answer E

rnn · Answer

3 conditions

1. b obviously can take any value
2. b=-1, x=-1 results in -|x|=b, -1=-1 and satisfies x<-b
3. b=-1, x=1 results in -|x|=b, -1=-1 and satisfies x>b

nick1816 · Answer

I) -|x| = b Since b or x are non-zero integer, |x|>0. hence, -|x| <0 b<0 (always true) Must be true II) If x is negative, x< -b . (-b is always positive) Can be true III) If x is positive, x>b (b is always negative) Can be true

Fdambro294 · Answer

Q comes down to Analyzing the Modulus and the Output/Outcome

(1st) we are told that B = a NON-Zero Integer

Given:

(-)[X] = B

X must also be = a NON-Zero Integer

(2nd)

(-)[X] = B

The OUTPUT of the Modulus [X] must be (+)Pos. since X can NOT be 0

(-)[X] = (-) * (+Pos. Integer Output) = (-)Negative Integer = B

thus, we know for Sure that B must be a (-)Negative Integer

I not only can be true: I must be True

II. X < (-)B

Since we know that B must = (-)Negative Integer:

The Expression (-)B ------> (-) * (-Neg. Integer) = (+)Positive Integer

If the INPUT X into the Modulus is (-)Negative, then we can have a case where ----> X < (-)B

Case: X = (-)5

(-) * [-5] = B
(-) * +5 = B

B = (-)5

and therefore ------> (-)B = (-) * (-5) = +5

X = (-)5 -------- and ------- (-)B = +5

it can be true that: X < (-)B

II can be True

III. X > B

Again, since we know that B must be = (-)Neg. Integer

If the Input X = (+)Pos. Integer, then we can easily Find a Case where X > B

Case:
Given ----> (-) * [X] = B

If X = +2

(-) * [+2] = B

(-) * +2 = B

B = (-)2

X (+2) > B (-2)

III. Can be True

-E-

I, II, and III all can be True

chetan2u · Answer

a) |x|=-b, so b is surely negative, as b is non-zero. However x can be both positive and negative. Clearly I is MUST be true. b) If x is negative, then x=b, and x=b<-b II can be true, when x<0 c)If x is positive, then x=-b, and x=-b>b III can be true, when x>0 All three CAN be true. E

LeenaSai · Answer

Hi chetan2u , Could you please take any example , such as any internet value for x and b and explain the same .. I don’t know why I am getting confused everytime while seeing this question At times , I am thinking that -|x| = b means b is negative so -|x| = -b which Means |x| = b is what we have in the given part . Now , option is alwys correct b < 0 => b is negative integer. Coming to Option which states x< - b is not true ( as per my understanding) Option x>b is alwys true as we know that b Will alwys be negative Plz guide Posted from my mobile device

chetan2u · Answer

Hi

When we say b is negative, remember that the NEGATIVE sign is already included in b. The moment you add another negative, say -b, the - sign will get multiplied by the negative sign in b and make it positive. 
Example. 
Say b=-2, then -b=-(-2)=2=|2|
b=-2=-|2|

Kinshook · Answer

@rencseeIf -|x| = b, where b is a non-zero integer, which of the following statements can be true?
|x| = -b > 0; b<0

I. b < 0: TRUE
II. x < -b; |x| = - b>0: If x<0; x<|x|=-b; CAN BE TRUE
III. x > b; If x>0; b<0<x; x>b: CAN BE TRUE
IMO E

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

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