If x is positive, is x 4?

Question

If x is positive, is x > 4?

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

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

Bunuel · Answer

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:

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.

WoundedTiger · Answer

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

mittalg · Answer

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})

Mo2men · Answer

(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

Answer: E

bumpbot · Answer

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If x is positive, is x > 4?

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