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# If x is positive, is x > 4?

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

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17 May 2014, 04:50
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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, 04:53, edited 1 time in total.
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Re: If x is positive, is x > 4? [#permalink]

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17 May 2014, 05:00
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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.

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

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17 May 2014, 05:01
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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.

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

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

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17 May 2014, 09:26
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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]

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18 Jun 2015, 04:56
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Re: If x is positive, is x > 4?   [#permalink] 18 Jun 2015, 04:56
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