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

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Bunuel
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If |x/4| > 1 which of the following must be true? [#permalink] New post   12 Mar 2019, 03:29
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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
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B
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KSBGC
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If |x/4| > 1 which of the following must be true? [#permalink] New post   Updated on: 12 Mar 2019, 06:35
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Bunuel wrote:
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. I and III only


|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.

Originally posted by KSBGC on 12 Mar 2019, 03:35.
Last edited by KSBGC on 12 Mar 2019, 06:35, edited 3 times in total.
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Re: If |x/4| > 1 which of the following must be true? [#permalink] New post   14 Mar 2019, 17:11
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Bunuel wrote:
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


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
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Re: If |x/4| > 1 which of the following must be true? [#permalink] New post   16 Jun 2019, 21:42
Bunuel wrote:
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


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?
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Re: If |x/4| > 1 which of the following must be true? [#permalink] New post   17 Jun 2019, 06:44
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NandishSS wrote:
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?


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.
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Subhrajyoti
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Re: If |x/4| > 1 which of the following must be true? [#permalink] New post   11 Jul 2020, 23:56
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
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If |x/4| > 1 which of the following must be true? [#permalink] New post   24 Dec 2021, 10:10
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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

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Re: If |x/4| > 1 which of the following must be true? [#permalink] New post   05 Jun 2022, 03:48
Subhrajyoti wrote:
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


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.
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Re: If |x/4| > 1 which of the following must be true? [#permalink] New post   14 Jun 2023, 05:40
Subhrajyoti wrote:
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


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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Re: If |x/4| > 1 which of the following must be true? [#permalink]
14 Jun 2023, 05:40
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