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# If x is an even integer and x^2 + 6 > 22, which of the following inequ

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Joined: 02 Sep 2009
Posts: 43359
If x is an even integer and x^2 + 6 > 22, which of the following inequ [#permalink]

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12 Sep 2017, 04:27
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If x is an even integer and x^2 + 6 > 22, which of the following inequalities must be true?

A. x^4 > 231
B. x^3 > 64
C. x^3 > 8
D. x^2 > 64
E. x^2 = 16
[Reveal] Spoiler: OA

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If x is an even integer and x^2 + 6 > 22, which of the following inequ [#permalink]

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12 Sep 2017, 05:26
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Bunuel wrote:
If x is an even integer and x^2 + 6 > 22, which of the following inequalities must be true?

A. x^4 > 231
B. x^3 > 64
C. x^3 > 8
D. x^2 > 64
E. x^2 = 16

Since x is an even integer and we have the inequality $$x^2 + 6 > 22$$

This can also be written as $$x^2 > 22 - 6(16)$$
The inequality which satisfies this equation are $$x > 4$$ and $$x < -4$$

Only $$x^4 > 231$$ will be true for both $$x = -6$$(which is an negative even integer)
as $$x^3$$ will yield a negative number which is not greater than 8 or 64.
Similarly x = -6 or 6(both even numbers) does not satisfy the inequality $$x^2 > 64$$
x^2 = 16 is also not possible because the lower/upper bound is 4,-4 which cannot be considered!

Hence, Option A is the correct answer.
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Re: If x is an even integer and x^2 + 6 > 22, which of the following inequ [#permalink]

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12 Sep 2017, 08:08
x : even integer
x^2 + 6 > 22
Find: must be true condition

Here we know x is even but we don't know if x is -ve or +ve
x^2 + 6 > 22 => x^2>16 so implies x<-4 or x>4

Now going through options

A. x^4 > 231
x^2 > 16
=> x^4 > 16^2 => x^4>256 => x^4>256 > 231
Always true condition: for both x -ve or x +ve

B. x^3 > 64
we know x^2 >16 => x =+ve or x=-ve
what if x =-ve so x^3 will be -ve so x^3 > 64 will not be true if x =-ve

C. x^3 > 8
we know x^2 >16 => x =+ve or x=-ve
what if x =-ve so x^3 will be -ve so x^3 > 8 will not be true if x =-ve

D. x^2 > 64
we know x^2 >16 => x <-4 or x>4
if x=5 , x^2 =25 >64 False

E. x^2 = 16
we know x^2 >16
so x^2 can never be equal to 16. False

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Re: If x is an even integer and x^2 + 6 > 22, which of the following inequ [#permalink]

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15 Sep 2017, 08:40
Bunuel wrote:
If x is an even integer and x^2 + 6 > 22, which of the following inequalities must be true?

A. x^4 > 231
B. x^3 > 64
C. x^3 > 8
D. x^2 > 64
E. x^2 = 16

We can simplify the given inequality:

x^2 + 6 > 22

x^2 > 16

Squaring both sides, we have:

x^4 > 256

We see that x must be greater than 4 or less than -4. However, we are given that x is an even integer, and so we know that x is greater than or equal to 6, or x is less than or equal to -6.

Since x^4 > 256, and since we know that x is greater than or equal to 6 or is less than or equal to -6, we know that x^4 > 231.

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Re: If x is an even integer and x^2 + 6 > 22, which of the following inequ   [#permalink] 15 Sep 2017, 08:40
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