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

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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
Math Expert V
Joined: 02 Sep 2009
Posts: 58416
Re: If x is positive, is x > 4?  [#permalink]

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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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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.

Hence answer is E....

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

Check out Gmatclub Mathbook to find more information on these topics.
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Intern  Joined: 17 May 2014
Posts: 37
Re: If x is positive, is x > 4?  [#permalink]

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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  V
Joined: 26 Mar 2013
Posts: 2345
Re: If x is positive, is x > 4?  [#permalink]

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

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_________________ Re: If x is positive, is x > 4?   [#permalink] 29 Mar 2019, 03:21
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