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# If x is an integer and x not = 0, is x^4 < 90? 1) x^{ 4

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Intern
Joined: 28 May 2010
Posts: 4
If x is an integer and x not = 0, is x^4 < 90? 1) x^{ 4  [#permalink]

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11 Jun 2010, 21:14
3
6
00:00

Difficulty:

75% (hard)

Question Stats:

54% (02:04) correct 46% (02:05) wrong based on 267 sessions

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If x is an integer and x not = 0, is x^4 < 90?

1) $$x^{\sqrt{4}}<10$$
2) $$\frac{2}{x^4} >0.2$$

My answer was but the original answer is .

Here is the explaination given for the correct answer -

This is a yes/no problem, so you should plug in. Since , you can rewrite the inequality given in statement 1 as . If x = 3, then , so the answer to the question is "yes." If x = 1, then , so the answer is "yes" again. If x = – 3 then , so the answer to the question is "yes" again, and you should write down AD. For statement 2, if x = 3 then the answer to the question is "yes." If x = 1, then the answer is "yes." If x = – 3, then the answer is "yes" again, so the answer is D.

However, I feel that statement 1 is not sufficient given that \sqrt{4} should result in +/-2 and just not +2. If -2 is considered, then x can take any value to be less than 10.

What do you think? Thanks.
Math Expert
Joined: 02 Sep 2009
Posts: 52938
Re: Doubtful answer for DS question  [#permalink]

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12 Jun 2010, 05:47
3
narisipalli wrote:
If x is an integer and x not = 0, is x^4 < 90?

1) $$x^{\sqrt{4}}<10$$
2) $$\frac{2}{x^4} >0.2$$

My answer was but the original answer is .

Here is the explaination given for the correct answer -

This is a yes/no problem, so you should plug in. Since , you can rewrite the inequality given in statement 1 as . If x = 3, then , so the answer to the question is "yes." If x = 1, then , so the answer is "yes" again. If x = – 3 then , so the answer to the question is "yes" again, and you should write down AD. For statement 2, if x = 3 then the answer to the question is "yes." If x = 1, then the answer is "yes." If x = – 3, then the answer is "yes" again, so the answer is D.

However, I feel that statement 1 is not sufficient given that \sqrt{4} should result in +/-2 and just not +2. If -2 is considered, then x can take any value to be less than 10.

What do you think? Thanks.

If x is an integer and x not = 0, is x^4 < 90?

Given: $$x=integer\neq{0}$$. Question: is $$x^4<90$$?

(1) $$x^{\sqrt{4}}<10$$ --> $$x^2<10$$. Now, since $$x$$ is an integer, then max value of $$x$$ is 3 --> $$3^4=81<90$$. Sufficient. (Side note: possible values of $$x$$ from this statement are: -3, -2, -1, 1, 2, and 3).

(2) $$\frac{2}{x^4} >0.2$$ --> $$\frac{1}{x^4} >\frac{1}{10}$$ --> $$x^4<10$$. Sufficient. (Side note: the possible values of $$x$$ from this statement are: -1 and 1).

As for your doubt (red part):

Square root function cannot give negative result.

Any nonnegative real number has a unique non-negative square root called the principal square root and unless otherwise specified, the square root is generally taken to mean the principal square root.

When the GMAT provides the square root sign for an even root, such as $$\sqrt{x}$$ or $$\sqrt[4]{x}$$, then the only accepted answer is the positive root.

That is, $$\sqrt{25}=5$$, NOT +5 or -5. In contrast, the equation $$x^2=25$$ has TWO solutions, +5 and -5. Even roots have only non-negative value on the GMAT.

Odd roots will have the same sign as the base of the root. For example, $$\sqrt[3]{125} =5$$ and $$\sqrt[3]{-64} =-4$$.

Hope it helps.
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Re: If x is an integer and x not = 0, is x^4 < 90? 1) x^{ 4  [#permalink]

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13 Oct 2018, 10:38
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Re: If x is an integer and x not = 0, is x^4 < 90? 1) x^{ 4   [#permalink] 13 Oct 2018, 10:38
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# If x is an integer and x not = 0, is x^4 < 90? 1) x^{ 4

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