If |x| 5, is |x - 5| = 5 - x

Question

If  |x| > 5 , is  |x-5| = 5-x

(1)  -x(x^2) > 0 
(2)  x^5 < 0

I solved this problem and ended up with a different answer. I believe the correct answer should be E.

Any thoughts ???

mainhoon · Answer

I think it is D. The question is basically if x < 0 i.e x is negative. Either A or B tells us x is negative.

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nverma · Answer

For |x-5| = 5-x , it is required that x-5<0 >>> x < 5 From 1 : x^2 is always positive, so -x needs to be positive , so that -x(x^2) > 0 . Therefore x is a negative number, Also from the question |x| > 5 , So x < - 5. SUFFICIENT From 2 : x^5 is negative, so x needs to be negative, Also from the question |x| > 5 , So x < -5. SUFFICIENT it's D

ezhilkumarank · Answer

My bad. I misinterpreted the question.

From the question,  |x|>5 , I interpreted that x should be strictly less than -5 to satisfy the condition --  Is |x-5| = 5 - x .

But the two answer options note that x is negative but not strictly less than -5 hence I thought option E is the correct.

LogicGuru1 · Answer

This is a YES or NO question. Solving the original question stimulus will give us a value of x -5>x>5 (1) -x(x^2) > 0 Tells us that x is negative ; Meaning Positive values of x are not allowed -5>x >5 Therefore x<-5 Now, no need to solve, because the answer is will be either a definite Yes or a definite no SUFFICIENT (2) x^5 < 0 Only a negative number raised to an odd power is negative Again tells us that x is negative; Meaning Positive values of x are not allowed -5>x >5 Therefore x<-5 Now no need to solve, because the answer is will be either a definite Yes or a definite no SUFFICIENT ANSWER IS D

KanishkM · Answer

when the given if statement is solved

only one case will be applicable to both the conditions which is   x < -5  and not x > 5(when this is used both the statements wont be true)

Just use  this   to satisfy both the statements

D

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If |x| > 5, is |x - 5| = 5 - x

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