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If x is positive, is x > 4?

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If x is positive, is x > 4? [#permalink] New post 17 May 2014, 03:50
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If x is positive, is x > 4?

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

(2) (x-4)^2 < 1
[Reveal] Spoiler: OA

Last edited by Bunuel on 17 May 2014, 03:53, edited 1 time in total.
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Re: If x is positive, is x > 4? [#permalink] New post 17 May 2014, 04:00
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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.

Answer: E.
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Re: If x is positive, is x > 4? [#permalink] New post 17 May 2014, 04:01
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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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Re: If x is positive, is x > 4? [#permalink] New post 17 May 2014, 08:26
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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})
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Re: If x is positive, is x > 4? [#permalink] New post 18 Jun 2015, 03:56
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Re: If x is positive, is x > 4?   [#permalink] 18 Jun 2015, 03:56
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