Is x an integer? (1) x^3 = 8 (2) x = 4^(1/2)

1 stm: get rid of power, x=2. suff
2 stm: x=\(\sqrt{4}\)=2. suff

IMO
Ans: D

from 1 ; x= 2
and #2
x= +/-2
question has asked x is an integer answer yes
IMO D

Statement One Alone:

x^3 = 8

Since x^3 = 8, x = 2, then x is an integer.

Statement one alone is sufficient to answer the question.

Statement Two Alone:

x = √4

Since x = √4, x = 2, then x is an integer. (Recall that the square root symbol means to take the principal square root of a number, which is only the positive square root.)

Statement two alone is sufficient to answer the question.

Answer: D
_________________

Hi All,

We're asked if X is an INTEGER. This is a YES/NO question. This question is built around some standard math rules and Number Properties.

(1) X^3 = 8

With Fact 1, we're cubing the value of X and ending with a POSITIVE value - thus, X MUST be positive. Here, the value of X = +2 and the answer to the question is YES.
Fact 1 is SUFFICIENT

(2) X =√4

With Fact 1, we have a number that's square-rooted for the value of X. The square root of a number has just ONE solution: a POSITIVE one. Here, we're dealing with the positive square-root of 4, so the value of X = +2 and the answer to the question is YES.
Fact 2 is SUFFICIENT

Final Answer:

GMAT assassins aren't born, they're made,
Rich
_________________

X is an Integer?

Statement 1:\(X^3 = 8\)
This gives , X=2. Option A alone is sufficient

Statement 2: X = √4
This gives x=2 , Option B alone is sufficient

Ans: D
_________________

Bunuel. option B. according to Gmat, can we say that x!=2?

Not sure I understand what yo mean but \(x = \sqrt{4}\) means that x = 2 only, nothing else.
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Statement 1: x^3=8 > x has to be 2 which is an integer, note: x cannot be -2 as x^3 is equal to 8. SUFFICIENT
Statement 2: x=squareroot 4. Square root of 4 is (+)(-) 2, i.e it can be both positive and negative therefore integer. SUFFICIENT


Hope that helps!
_________________

Hi hemantbafna,

You selected the correct answer, but there's a subtle rule here that you appear to have missed. On the GMAT, the result of a square root of a positive number can ONLY be positive. For example....

√4 = +2

However, a squared-term that equals a positive number can lead to a positive or negative result. For example...

X^2 = 4..... X = +2 or -2.

GMAT assassins aren't born, they're made,
Rich
_________________

Answer: Option D

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x^3 = 8 actually has 3 solutions ;

\(x^3 - 8 =0\)
\((x-2)(x^2+2x+4)=0\)
1 for the above equation \(x=2\)
other 2 solutions are imaginary \( [-1+i\sqrt{3}], [-1-i\sqrt{3}]\)

so we cant say x is an interger or imaginary,
can someone please clarify.

Bunuel
EMPOWERgmatRichC

Hi Kanna444,

Imaginary numbers are NOT a subject that the GMAT 'tests' - and that ultimately means that you are NOT expected to think in those terms when answering GMAT questions.

GMAT assassins aren't born, they're made,
Rich
_________________

Is x an integer?

(1) x^3=8

Since 8 is a perfect cube, we can easily say x = 2 (INTEGER)

(2) x=√4

Since √4 = +2, we can say that X is an integer

OPTION D