Is x an even number? (1) x^3 + x^2 = 0 (2) x^2 + |x| = 0

Question

Is x an even number?

(1) x^3 + x^2 = 0

(2) x^2 + |x| = 0

M36-28

Bunuel · Accepted Answer

Official Solution:

Is  x  an even number? 
 
(1)  x^3 + x^2 = 0 
 
Factor out  x^2  to get  x^2(x + 1) = 0 .
 
From  x^2(x + 1) = 0  it follows that  x=0=even  or  x=-1=odd . Not sufficient.
 
(2)  x^2 + |x| = 0 
 
 x^2 + |x|  is the sum of two non-negative values (the square of an integer and the absolute value of a number). The sum of two non-negative values to be 0, each of them must be 0. Thus,  x=0=even . Sufficient.

Answer: B

Archit3110 · Answer

from stmt 1:
x^3 + x^2 = 0 
this would be true for x=-1 and 0
not sufficient

from 2:
x^2 + |x| = 0[

when x=0 only possible hence sufficient IMO B

jashandeep2332 · Answer

It's a Yes/No Data Sufficiency i.e the options must suggest a bold Yes or a bold No.

1. x^3+x^2=0
 => (x^2)(x+1)=0 
 We state that either x=0 or x=-1. Not sufficient.

2. x^2+|x|=0 
 Positive+Positive=0 only when the value is 0. 
Hence x is even.

Hence correct answer is B.

Posted from my mobile device

EncounterGMAT · Answer

(1) x^3 + x^2 = 0 
 x^2 (x+1)=0 =>  x^2 =0 or x+1=0 => x=0 or x=-1 
We have 2 values of x. NOT SUFFICIENT

(2) x^2  + |x| = 0 
Squaring both sides.  x^4 + x^2 =0 =>  x^2 ( x^2 +1)=0 => x^2 =0 or  x^2 =-1(not possible as square root of negative number is an imaginary number) Thus x=0 SUFFICIENT.

IMO answer is option B

gota900 · Answer

you made a mistake here mate: factoring out the x^2, leaves us with x^2(x^2+1)

best gota900

EncounterGMAT · Answer

Thanks friend. Done.

Posted from my mobile device

Bunuel · Answer

Par of  GMAT CLUB'S New Year's Quantitative Challenge Set

kashishaggarwal · Answer

But o is neither positive nor negative. So how can we say x is positive ?

philu · Answer

Why is statement 1 not sufficient? The question asks whether x is an even number. I thought neither -1 nor 0 are an even number, so it is sufficient. Could someone please explain why the answer is B and not D?

Archit3110 · Answer

philu Refer below link this may help answer your question related to 0... https://gmatclub.com/forum/is-zero-even ... 2#p1512948 Posted from my mobile device

AnirudhaS · Answer

(1)
 x^3 + x^2 = 0 
or,  x^2(x+1)=0 
so, x= 0 or -1
Not Sufficient

(2)
 x^2 + |x| = 0 
or, x=0
Sufficient

Answer:  B

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Is x an even number? (1) x^3 + x^2 = 0 (2) x^2 + |x| = 0

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GMAT Data Sufficiency (DS) Questions

Is x an even number? (1) x^3 + x^2 = 0 (2) x^2 + |x| = 0

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