Inequality values

Is it B ?

I substituted the lower limit -1 in all the inequalities and found only B to be satisfying the condition.

Value of x should be between -1 and 5 (0,1,2,3,4) -1 < x < 5 (not restricted to integers)


Since its a MUST be true question, we need to find at least one value outside this range so that the condition need not be true.

A. |3 - x| < -3 --- Value inside Mod is always +ve, LHS cannot be < -3 (This Options seems to be wrongly phrased)

B. -1< |x| < 5 - Sub x=-4 which satisfies this condition but is not in our set defined - Eliminate

C. |x| - 2 > 2 --- x can be 10 - Eliminate

D. |2 + x| > 3 ---- x can be 10 - Eliminate

E. |x - 2| < 3 - Since mod is always +ve or 0

x can only take 0,1,2,3,4 (-1<x<5) and all values are within our set defined. Hence this must be true. E IMO

Also helpful to know whenever there is a mod along with <,> signs, such as

|x| > 3(or) some number, we have no essential restrictions for values x can take

whereas, |x| < 3, limits the possibilities of values x can take.

In this problem, C and D can be checked last only when other options do not get you to the answer. Could save a few seconds/minutes in the exam.

This problem has to be solved by elimination method.
(A) is ruled out as |x| cannot be -ve
(B)0<|x|<5 = > -5<x<5, of which the set in the question is a subset if the set in the question is not inclusive set.
(C) |x| > 4 => x<-4 or x>4, eliminated
(D) |x+2| > 3 =>x>1 or x<-5, eliminated
(E) |x-2|<3 => x<5 or x>1 => 1<x<5, eliminated
Hence (B) is the correct answer, considering exclusive set.

karthikpandian19 wrote:Which of the following inequalities must be true for the value of x to be between -1 and 5?
A. |3 – x| < -3
B. -1< |x| < 5
C. |x| - 2 > 2
D. |2 + x| > 3
E. |x – 2| < 3

The correct answer must work for every value between -1 and 5.
Plug x=0 into each answer choice:

A. |3 – 0| < -3
3 < -3.
Doesn't work. Eliminate A.

B. -1< |0| < 5
-1 < 0 < 5
This works. Hold onto B.

C. |0| - 2 > 2
-2 > 2
Doesn't work. Eliminate C.

D. |2 + 0| > 3
2 > 3.
Doesn't work. Eliminate D.

E. |0 – 2| < 3
2 < 3.
This works. Hold onto E.

The correct answer should NOT work for any value NOT between -1 and 5.
Plug x = -2 into the remaining answer choices.

B: -1 < |-2| < 5
-1 < 2 < 5
Since x=-2 works in answer choice B, and x=-2 is NOT part of the given range, eliminate B.

The correct answer is E.