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For how many real values of x is p √(120 − √x) an integer?
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Noshad
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For how many real values of x is p √(120 − √x) an integer? [#permalink] New post  Updated on: 19 Mar 2019, 05:27
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For how many real values of x is \(\sqrt{120 − √ x}\) an integer?

(A) 3

(B) 6

(C) 9

(D) 10

(E) 11
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Originally posted by Noshad on 14 Mar 2019, 05:09.
Last edited by Noshad on 19 Mar 2019, 05:27, edited 1 time in total.
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razaaquib18
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Re: For how many real values of x is p √(120 − √x) an integer? [#permalink] New post  19 Mar 2019, 03:34
How to solve this? Me really confused about P.
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Re: For how many real values of x is p √(120 − √x) an integer? [#permalink] New post  19 Mar 2019, 03:49
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Noshad wrote:
For how many real values of x is p \(\sqrt{120 − √ x}\) an integer?

(A) 3

(B) 6

(C) 9

(D) 10

(E) 11


Bunuel

is the question p=\(\sqrt{120 − √ x}\). Or it is correct as it is.I feel there is missing "=" sign.

My approach

For \(\sqrt{120 − √ x}\) to be an integer. The 120-√x must be a perfect square. Less than 120

So the value of the expression can be 100,81,64,49,36,25,16,9,4,1,0 total 11 values. For each of which there will be a corresponding value of x

x will have values √400,\(√39^2\),\(√56^2\) ..... \(√120^2\) . 11 values .Hence ans (E)
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Archit3110
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Re: For how many real values of x is p √(120 − √x) an integer? [#permalink] New post  19 Mar 2019, 10:38
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Noshad wrote:
For how many real values of x is \(\sqrt{120 − √ x}\) an integer?

(A) 3

(B) 6

(C) 9

(D) 10

(E) 11



total square values upto 120 ; 11 viz. 0,1,4,9,16,25,36,49,64,81,100
IMO E ; 11
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Re: For how many real values of x is p √(120 − √x) an integer? [#permalink] New post  08 Apr 2019, 07:44
but at x = 0 , this is not an integer


Am I missing something here ?

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Re: For how many real values of x is p √(120 − √x) an integer? [#permalink] New post  08 Apr 2019, 08:50
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IMO D
At x=0, sqrt(120) is not an integer, so we have only 10 real values of X for P to be an integer

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Dvaishnav
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Re: For how many real values of x is p √(120 − √x) an integer? [#permalink] New post  05 Dec 2020, 08:37
shuvodip04 wrote:
Noshad wrote:
For how many real values of x is p \(\sqrt{120 − √ x}\) an integer?

(A) 3

(B) 6

(C) 9

(D) 10

(E) 11


Bunuel

is the question p=\(\sqrt{120 − √ x}\). Or it is correct as it is.I feel there is missing "=" sign.

My approach

For \(\sqrt{120 − √ x}\) to be an integer. The 120-√x must be a perfect square. Less than 120

So the value of the expression can be 100,81,64,49,36,25,16,9,4,1,0 total 11 values. For each of which there will be a corresponding value of x

x will have values √400,\(√39^2\),\(√56^2\) ..... \(√120^2\) . 11 values .Hence ans (E)


I also selected E. However, the question only says that x has to be real, not positive. Hence, x can also be (-39)^2, (-56)^2 ... Hence, we will have 22 possible values. Isn't it?
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Re: For how many real values of x is p √(120 − √x) an integer? [#permalink]
05 Dec 2020, 08:37
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