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# If x is positive, is x > 4?

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Joined: 28 Jun 2011
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If x is positive, is x > 4?  [#permalink]

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Updated on: 17 May 2014, 04:53
1
1
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00:00

Difficulty:

45% (medium)

Question Stats:

67% (01:59) correct 33% (01:58) wrong based on 203 sessions

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If x is positive, is x > 4?

(1) (4-x)^2 < 1

(2) (x-4)^2 < 1

Originally posted by steilbergauf on 17 May 2014, 04:50.
Last edited by Bunuel on 17 May 2014, 04:53, edited 1 time in total.
Edited the question
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Joined: 02 Sep 2009
Posts: 58416
Re: If x is positive, is x > 4?  [#permalink]

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17 May 2014, 05:00
4
2
If x is positive, is x > 4?

First of all notice that $$(x-4)^2 =(4-x)^2$$. So, both options give the same exact information, which implies that the answer is either D or E.

(1) (4-x)^2 < 1 --> since both sides are non-negative, then we can take the square root from the inequality: $$|4-x|<1$$ --> $$-1<4-x<1$$ --> subtract 4 from all parts: $$-5<-x<-3$$ --> multiply by -1 and flip the sign: $$5>x>3$$. So, x may or may not be greater than 4. Not sufficient.

The answer cannot be D, thus it's E.

(2) (x-4)^2 < 1. Not sufficient.

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Re: If x is positive, is x > 4?  [#permalink]

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17 May 2014, 05:01
1
steilbergauf wrote:
If x is positive, is x > 4?

(1) (4-x)^2 < 1

(2) (x-4)^2 < 1

Hi there,

We know x is positive and we need to know if its greater than 4

St 1 says (4-x)^2 <1 ------> Since both LHS and RHS are positive (Non-Negative), we can take a sqaure root and see what we get

$$\sqrt{(4-x)^2}$$ < 1

or |4-x|<1 or -1<4-x<1 -------> Simplify and we get range for x as 3<x<5. So x may or may not be greater than 4

St 2 By same way can be reduced $$\sqrt{(x-4)^2}$$<1 or |x-4|<1 or -1<x-4<1 ---we get same range for x 3<x<5.

For such set of questions try and build your base in equalities and modulus properties. These topics will help you dissect the question stem.

_________________

“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”
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Joined: 17 May 2014
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Re: If x is positive, is x > 4?  [#permalink]

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17 May 2014, 09:26
1
steilbergauf wrote:
If x is positive, is x > 4?

(1) (4-x)^2 < 1

(2) (x-4)^2 < 1

As mentioned in posts above, first thing to notice is (4-x)^2 = (x-4)^2, making both the statements same.

Now lets take statement 1)

(x-4)^2 < 1
(x-4)^2 -1 < 0

using a^2-1 = (a-1)(a+1), we can write it as:

(x-4-1)(x-4+1) <0
(x-3)(x-5) <0
or 3<x<5

Hence x can be greater than 4 or less than 4. Thus, option (E) is valid.

If instead of 1 on RHS, we had any number b, we would have written a^2 - b = (a-\sqrt{b})(a+\sqrt{b})
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Joined: 26 Mar 2013
Posts: 2345
Re: If x is positive, is x > 4?  [#permalink]

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29 Sep 2017, 07:19
steilbergauf wrote:
If x is positive, is x > 4?

(1) (4-x)^2 < 1

(2) (x-4)^2 < 1

(1) (4-x)^2 < 1

Let x = 3.5.........(4-3.5)^2 < 1..........(1/2)^2 < 1.........Answer is No

Let x = 4.5.........(4-4.5)^2 < 1..........(-1/2)^2 < 1.........Answer is Yes

Insufficient

(2) (x-4)^2 < 1

Let x = 3.5.........(4-3.5)^2 < 1..........(1/2)^2 < 1.........Answer is No

Let x = 4.5.........(4-4.5)^2 < 1..........(-1/2)^2 < 1.........Answer is Yes

Combine 1 & 2

Use same examples above. Still Insufficient

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Posts: 13235
Re: If x is positive, is x > 4?  [#permalink]

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29 Mar 2019, 03:21
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Re: If x is positive, is x > 4?   [#permalink] 29 Mar 2019, 03:21
Display posts from previous: Sort by
The text passage provided is a GMAT question and solution. It contains a mathematical question and an answer to that question.

Content structure:
- The passage starts with a header indicating it is a GMAT question.
- It provides the question: "If x is positive, is x > 4?"
- It then lists two statements that provide information to solve the question.
- The passage ends with a note about the difficulty level and statistics on user performance.

Analysis:
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 17 Oct 2019, 05:53

### GMAT Club Daily Prep

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# If x is positive, is x > 4?

Author Message
TAGS:

### Hide Tags

Intern
Joined: 28 Jun 2011
Posts: 11
If x is positive, is x > 4?  [#permalink]

### Show Tags

Updated on: 17 May 2014, 04:53
1
1
10
00:00

Difficulty:

45% (medium)

Question Stats:

67% (01:59) correct 33% (01:58) wrong based on 203 sessions

### HideShow timer Statistics

If x is positive, is x > 4?

(1) (4-x)^2 < 1

(2) (x-4)^2 < 1

Originally posted by steilbergauf on 17 May 2014, 04:50.
Last edited by Bunuel on 17 May 2014, 04:53, edited 1 time in total.
Edited the question
Math Expert
Joined: 02 Sep 2009
Posts: 58416
Re: If x is positive, is x > 4?  [#permalink]

### Show Tags

17 May 2014, 05:00
4
2
If x is positive, is x > 4?

First of all notice that $$(x-4)^2 =(4-x)^2$$. So, both options give the same exact information, which implies that the answer is either D or E.

(1) (4-x)^2 < 1 --> since both sides are non-negative, then we can take the square root from the inequality: $$|4-x|<1$$ --> $$-1<4-x<1$$ --> subtract 4 from all parts: $$-5<-x<-3$$ --> multiply by -1 and flip the sign: $$5>x>3$$. So, x may or may not be greater than 4. Not sufficient.

The answer cannot be D, thus it's E.

(2) (x-4)^2 < 1. Not sufficient.

_________________
##### General Discussion
Director
Joined: 25 Apr 2012
Posts: 660
Location: India
GPA: 3.21
Re: If x is positive, is x > 4?  [#permalink]

### Show Tags

17 May 2014, 05:01
1
steilbergauf wrote:
If x is positive, is x > 4?

(1) (4-x)^2 < 1

(2) (x-4)^2 < 1

Hi there,

We know x is positive and we need to know if its greater than 4

St 1 says (4-x)^2 <1 ------> Since both LHS and RHS are positive (Non-Negative), we can take a sqaure root and see what we get

$$\sqrt{(4-x)^2}$$ < 1

or |4-x|<1 or -1<4-x<1 -------> Simplify and we get range for x as 3<x<5. So x may or may not be greater than 4

St 2 By same way can be reduced $$\sqrt{(x-4)^2}$$<1 or |x-4|<1 or -1<x-4<1 ---we get same range for x 3<x<5.

For such set of questions try and build your base in equalities and modulus properties. These topics will help you dissect the question stem.

_________________

“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”
Intern
Joined: 17 May 2014
Posts: 37
Re: If x is positive, is x > 4?  [#permalink]

### Show Tags

17 May 2014, 09:26
1
steilbergauf wrote:
If x is positive, is x > 4?

(1) (4-x)^2 < 1

(2) (x-4)^2 < 1

As mentioned in posts above, first thing to notice is (4-x)^2 = (x-4)^2, making both the statements same.

Now lets take statement 1)

(x-4)^2 < 1
(x-4)^2 -1 < 0

using a^2-1 = (a-1)(a+1), we can write it as:

(x-4-1)(x-4+1) <0
(x-3)(x-5) <0
or 3<x<5

Hence x can be greater than 4 or less than 4. Thus, option (E) is valid.

If instead of 1 on RHS, we had any number b, we would have written a^2 - b = (a-\sqrt{b})(a+\sqrt{b})
SVP
Joined: 26 Mar 2013
Posts: 2345
Re: If x is positive, is x > 4?  [#permalink]

### Show Tags

29 Sep 2017, 07:19
steilbergauf wrote:
If x is positive, is x > 4?

(1) (4-x)^2 < 1

(2) (x-4)^2 < 1

(1) (4-x)^2 < 1

Let x = 3.5.........(4-3.5)^2 < 1..........(1/2)^2 < 1.........Answer is No

Let x = 4.5.........(4-4.5)^2 < 1..........(-1/2)^2 < 1.........Answer is Yes

Insufficient

(2) (x-4)^2 < 1

Let x = 3.5.........(4-3.5)^2 < 1..........(1/2)^2 < 1.........Answer is No

Let x = 4.5.........(4-4.5)^2 < 1..........(-1/2)^2 < 1.........Answer is Yes

Combine 1 & 2

Use same examples above. Still Insufficient

Non-Human User
Joined: 09 Sep 2013
Posts: 13235
Re: If x is positive, is x > 4?  [#permalink]

### Show Tags

29 Mar 2019, 03:21
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: If x is positive, is x > 4?   [#permalink] 29 Mar 2019, 03:21
Display posts from previous: Sort by
user
The text passage provided is a GMAT question and solution. It contains a mathematical question and an answer to that question.

Content structure:
- The passage starts with a header indicating it is a GMAT question.
- It provides the question: "If x is positive, is x > 4?"
- It then lists two statements that provide information to solve the question.
- The passage ends with a note about the difficulty level and statistics on user performance.

Analysis:
TYPE: SINGLE_QUESTION_WITH_ANSWER