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12 Sep 2017, 05:27
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
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Question Stats:
65% (01:49) correct
35%
(01:48)
wrong
based on 417
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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
A. x^4 > 231
B. x^3 > 64
C. x^3 > 8
D. x^2 > 64
E. x^2 = 16
12 Sep 2017, 06:26
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Bunuel
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.
12 Sep 2017, 09:08
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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
Answer
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
Answer: A
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
Answer
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
Answer: A
