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Is root{x} a prime number?

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rohit8865
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Re: Is root{x} a prime number? [#permalink] New post   26 Jan 2016, 01:56
ArunpriyanJ wrote:
Bunuel, I have a question. Usually while solving modulus questions we take two cases 1) x>0 2) x<0. According to the first statement when x>0 we get x=9 which is valid, but when x<0 we get x=1 (which is not valid). Now, in some of the earlier questions when x<0 and if we got a positive value for it we neglected it and considered that x had only one valid value. In this question why hasn't something similar been done


Both x=1 and x=9 are valid for (1). Please elaborate what you mean?[/quote]

Bunel, I too have the same doubt in my mind. I will try to explain it.

By taking condition,
X>0, i got the value of X as 9

And by taking the condition X<0, I have got the solution as X=1, Which is not a valid solution with the given condition.

So i took X=9 only and got the answer as A.


Pls explain how X=1 with the condition X<0 is valid.

Thanks in advance[/quote]

we are taking condition x<=7/3 to be equation 3x-7 as <=0
So x=1 is acceptable
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Re: Is root{x} a prime number? [#permalink] New post   26 Jan 2016, 08:14
LM wrote:
Is \(\sqrt{x}\) a prime number?

(1) \(|3x-7|=2x+2\)

(2) \(x^2=9x\)


Fact (1) |3x-7|=2x+2
==> 3x-7=+(2x+2) or 3x-7=-(2x+2)
==> x=9 (\(\sqrt{9}=3\) YES) or x=1 (\(\sqrt{1}=1\) NO) Hence INSUFF.

Fact (2) x^2=9x
==> x^2-9x=0
==> x(x-9)=0
==> x=0 (\(\sqrt{0}=0\) NO) or x=9 (\(\sqrt{9}=3\) YES) Hence INSUFF.
(1)+(2) gives x=9 Hence SUFF
Ans: C
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Is root{x} a prime number? [#permalink] New post   05 Aug 2017, 02:39
From 1 x=1 or 9. Hence sqrt(x) has 2 values. Not sufficient.
From 2 x=0 or 9. Hence sqrt(x) has 2 values. Not sufficient.
Both: x=9. Hence sqrt(x) is 3 which is prime. Sufficient.
Hence C. :)

Press Kudos if this helped!! :-D
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Re: Is root{x} a prime number? [#permalink] New post   05 Aug 2017, 02:57
LM wrote:
Is \(\sqrt{x}\) a prime number?

(1) \(|3x-7|=2x+2\)

(2) \(x^2=9x\)


1) |3x - 7| = 2x + 2
=> x = 1, 9
Insufficient.

2) \(x^2\) = 9x
=> x = 0,9
Insufficient.

1+2)
x = 0,1,9
=> x = 0, 1 do not support both statements so we cannot use them.
Only value of x = 9 remains.
=> \(\sqrt{x}\) = 3
Sufficient.

C is the answer.
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Re: Is root{x} a prime number? [#permalink] New post   08 Aug 2017, 04:39
x=1 and x=9 both are valid

|3x-7|=|3*1-7|=|-4|=4(modulus of any value is +ve)

2x+2=2*1+2=4.

Hence valid



ArunpriyanJ wrote:
Bunuel, I have a question. Usually while solving modulus questions we take two cases 1) x>0 2) x<0. According to the first statement when x>0 we get x=9 which is valid, but when x<0 we get x=1 (which is not valid). Now, in some of the earlier questions when x<0 and if we got a positive value for it we neglected it and considered that x had only one valid value. In this question why hasn't something similar been done


Both x=1 and x=9 are valid for (1). Please elaborate what you mean?[/quote]

Bunel, I too have the same doubt in my mind. I will try to explain it.

By taking condition,
X>0, i got the value of X as 9

And by taking the condition X<0, I have got the solution as X=1, Which is not a valid solution with the given condition.

So i took X=9 only and got the answer as A.


Pls explain how X=1 with the condition X<0 is valid.

Thanks in advance[/quote]
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Re: Is root{x} a prime number? [#permalink] New post   08 Aug 2017, 06:10
gps5441 wrote:
x=1 and x=9 both are valid

|3x-7|=|3*1-7|=|-4|=4(modulus of any value is +ve)

2x+2=2*1+2=4.

Hence valid



ArunpriyanJ wrote:
Bunuel, I have a question. Usually while solving modulus questions we take two cases 1) x>0 2) x<0. According to the first statement when x>0 we get x=9 which is valid, but when x<0 we get x=1 (which is not valid). Now, in some of the earlier questions when x<0 and if we got a positive value for it we neglected it and considered that x had only one valid value. In this question why hasn't something similar been done

Both x=1 and x=9 are valid for (1). Please elaborate what you mean?

Bunel, I too have the same doubt in my mind. I will try to explain it.

By taking condition,
X>0, i got the value of X as 9

And by taking the condition X<0, I have got the solution as X=1, Which is not a valid solution with the given condition.

So i took X=9 only and got the answer as A.


Pls explain how X=1 with the condition X<0 is valid.

Thanks in advance


Statement 1
X = 1 or 9 (Both the values satisfy the equation)
If x = 1, then \(\sqrt{x}\) = 1 => Not a prime number.
If x = 9, then \(\sqrt{x}\) = 3 => Prime Number
2 different answers, so this is insufficient.

Statement 2
x = 0 or 9 (Both the values satisfy the equation)
If x = 0, then \(\sqrt{x}\) = 0 => Not a prime number.
If x = 9, then \(\sqrt{x}\) = 3 => Prime Number
2 different answers, so this is insufficient.

Statement 1 + Statement 2
x = 9 (The only common value)
=> \(\sqrt{x}\) = 3 => Prime Number
Unique Answer and hence, Sufficient.
C is the answer.

Hope this helps!
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Re: Is root{x} a prime number? [#permalink] New post   23 Mar 2024, 19:54
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Re: Is root{x} a prime number? [#permalink]
23 Mar 2024, 19:54
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