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17 Jan 2020, 02:44
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C
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Difficulty:
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64% (02:10) correct
36%
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Is \(x\) a prime number, given that \(x\) is a positive integer?
(1) \(x^4 > 3000\)
(2) \(x^4 < 10000\)
Are You Up For the Challenge: 700 Level Questions
(1) \(x^4 > 3000\)
(2) \(x^4 < 10000\)
Are You Up For the Challenge: 700 Level Questions
17 Jan 2020, 04:28
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x is a positive integer,
—> is x a prime number???
(Statement1): \(x^{4} > 3000\)
\(55^{2}= 3025\)
Approximately,
—>\(( x^{2}—54)(x^{2}+ 54) >0\)
\(( x—7.3)(x+ 7.3)( x^{2} +54) > 0\)
—> x > 7.3
x could be 8,9,10,11...
Insufficient
(Statement2): \(x^{4} < 10000\)
\((x^{2} —100)(x^{2} +100) < 0\)
\((x—10)(x+10)(x^{2} +100) < 0\)
—> 0 <x <10
x could be 1,2,3,4,5,6,7,8 or 9
Insufficient
Taken together 1&2,
—> 7.3 < x < 10
x could be 8,9
x is not a prime number (always)
Sufficient
The answer is C
Posted from my mobile device
—> is x a prime number???
(Statement1): \(x^{4} > 3000\)
\(55^{2}= 3025\)
Approximately,
—>\(( x^{2}—54)(x^{2}+ 54) >0\)
\(( x—7.3)(x+ 7.3)( x^{2} +54) > 0\)
—> x > 7.3
x could be 8,9,10,11...
Insufficient
(Statement2): \(x^{4} < 10000\)
\((x^{2} —100)(x^{2} +100) < 0\)
\((x—10)(x+10)(x^{2} +100) < 0\)
—> 0 <x <10
x could be 1,2,3,4,5,6,7,8 or 9
Insufficient
Taken together 1&2,
—> 7.3 < x < 10
x could be 8,9
x is not a prime number (always)
Sufficient
The answer is C
Posted from my mobile device
17 Jan 2020, 06:17
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Each statement is clearly insufficient alone. Since 10^4 = 10,000, we know from Statement 2 that x < 10. Since 7^4 = 49^2 < 50^2 = 2500, we know from Statement 1 that x > 7. So x can only be 8 or 9 using both Statements, and in either case is not prime, and the answer is C.
