If |x/4| 1 which of the following must be true?

Question

If  |\frac{x}{4}| > 1  which of the following must be true?

I.  x > 4

II.  x ≠ 4

III.  x < -4

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

KSBGC · Answer

|x/4| >1

Since x/4 is inside a absolute value notation , x can be positive or negative both but x mustn't be 4. If x were 4 the ultimate result couldn't be greater than 1.

|x/4|>1 is true for all values of x>4 or x<-4. but x mustn't be 4. In that case result will be equal.

B is the correct answer.

ScottTargetTestPrep · Answer

Looking at the given inequality, we see it’s true when either x > 4 or x < -4; thus, of the choices, only II, x does not equal 4, MUST be true.
 
Answer: B

NandishSS · Answer

HI Bunuel , IanStewart , generis One small doubt |\frac{x}{4}| > 1 is true only for all values of x>4 or x<-4. But not for x>4 & x<-4 when we consider x<-4 alone?

IanStewart · Answer

I'm afraid I don't understand the question. But here we know that x is either greater than 4, or less than -4. It can't be true that x > 4  and  x < -4, because there is no number x that satisfies both of those inequalities.

Subhrajyoti · Answer

if X= -3, then mod of -3/4 or 3/4 --- how is this >1 in both the cases. I am not sure i understand why b is the correct answer

BrushMyQuant · Answer

Given that \mid \frac{x}{4} \mid > 1 and we need to find the range of values of x \mid \frac{x}{4} \mid > 1 can be written as \frac{\mid x \mid }{\mid 4 \mid } > 1 And we know that | 4 | = 4 as 4 is a positive number => \frac{\mid x \mid }{ 4} > 1 => | x | > 4 Now, this is of the form | x | > a and we know that we can open it as Either x > a or x < -a => x > 4 or x < -4 Now, lets look at the answer choices I. x > 4 -> this is partially true it covers only a part of the answer which is x > 4 and does not cover x < -4. So this cannot be "Must be true" II. x ≠ 4 -> this is true as x cannot be equal to 4 III. x < -4 -> Same as option I. This is partially true it covers only a part of the answer which is x < -4 and does not cover x > 4. So this cannot be "Must be true" So, Answer will be B Hope it helps! Watch the following video to learn the Basics of Absolute Values https://www.youtube.com/watch?v=huFiBk8PaGY

WilliamKane · Answer

All the three options are partial,
option 1 and 2 dismiss each other, but option 2 just says that X is not supposed to be 4.

mysterymanrog · Answer

By looking at the fraction given in the problem, x must either be less than -4, or greater than 4. X=-3 is not admitted - since it would break the inequality as you pointed out. 
If we consider each statement individually:

I) This is not a must be true. Consider the case x=-5. The inequality holds, but x is not greater than 4. Out.

II) This must be true. If x is equal to 4, then the inequality does not hold - therefore X cannot ever be equal to 4.

III) This is like I, but in the opposite direction. Consider the case of x=5. The equation does hold, but x is not less than -4. Out.

Only II is a must be true, therefore the correct answer is B.

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If |x/4| > 1 which of the following must be true?

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