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# For how many real values of x is p √(120 − √x) an integer?

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Senior Manager
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Joined: 02 Nov 2018
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For how many real values of x is p √(120 − √x) an integer?  [#permalink]

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Updated on: 19 Mar 2019, 06:27
1
5
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Difficulty:

75% (hard)

Question Stats:

41% (01:48) correct 59% (02:16) wrong based on 69 sessions

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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, 06:09.
Last edited by Noshad on 19 Mar 2019, 06:27, edited 1 time in total.
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Re: For how many real values of x is p √(120 − √x) an integer?  [#permalink]

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19 Mar 2019, 04:49
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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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Re: For how many real values of x is p √(120 − √x) an integer?  [#permalink]

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19 Mar 2019, 04:34
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]

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19 Mar 2019, 11:38
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]

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08 Apr 2019, 08:44
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]

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08 Apr 2019, 09:50
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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Re: For how many real values of x is p √(120 − √x) an integer?   [#permalink] 08 Apr 2019, 09:50
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