Can x equal 0 ? (1) x^2 + 1 2x + 4 (2) (x + 1)^2 – 2x 2(x + 1) +

Question

Can x equal 0 ?

(1)  x^2 + 1 > 2x + 4

(2)  (x + 1)^2 – 2x > 2(x + 1) + 2

Archit3110 · Answer

target is x=0 #1 x^2 + 1 > 2x + 4 x^2-2x-3>0 x^2-3x+x-3>0 x*(x-3)+1(x-3)>0 (x-3)(x+1)>0 x>3 and x<-1 sufficient that x cannot be 0 #2 (x + 1)^2 – 2x > 2(x + 1) + 2 x^2+2x+1-2x>2x+4 x^2-2x-3>0 same as #1 x>3 and x<-1 sufficient that x cannot be 0 option D

sanjitscorps18 · Answer

Is x = 0 ?

A. x^2 + 1 > 2x + 4
=> x^2 - 2x - 3 > 0
=> (x - 3)(x + 1) > 0
=> x > 3 or x < -1
Hence x not equal to 0 - Sufficient

(2) (x+1)^2 – 2x > 2(x+1) + 2
=> x^2 + 1 > 2x + 4
=> x^2 - 2x - 3 > 0
=> x > 3 or x < -1
Same as statement 1 hence sufficient

Option D

IanStewart · Answer

What is the source? It doesn't make sense to ask a DS question in this way. In a DS question, except in certain specific situations (e.g. involving functions f(x)) a letter 'x' stands for a single unknown value. We may not have enough information to pin down that value exactly, but x still stands for one number in a DS question. So either x is zero or it isn't; x is not a variable that 'can equal zero'. The question should instead asking something like "Is |x| > 0?" or "Is x ≠ 0?"

You'd often want to analyze Statements like 1 and 2 here using quadratic inequality techniques (there are a few ways to go about that, but you can get 0 on one side, factor the quadratic on the other, then work out when the resulting product will be positive or negative). But that's overkill here; if we only care whether x can be zero, we can just plug x = 0 into each Statement to see if the inequality is true or false. If the inequality is false, x cannot be zero, and unless I made an arithmetic error, both inequalities are false when x = 0, so x cannot be zero and D is the answer.

errorlogger · Answer

A quicker approach to this problem would be to directly put x = 0 and verify:

1)Is  0^2 + 1 > 0 + 4 
Is 1 > 4? No - Sufficient!

2)Is  (0 + 1)^2 - 0 > 2(1) + 2 ?
Is 1 > 4? No - Sufficient!

IMO D!

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Can x equal 0 ? (1) x^2 + 1 > 2x + 4 (2) (x + 1)^2 – 2x > 2(x + 1) +

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