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The number of integers values of 'x', for which (3-(10 -x^(1/2)

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The number of integers values of 'x', for which (3-(10 -x^(1/2) [#permalink] New post   14 Jul 2018, 08:34
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The number of integer values of 'x', for which \((3-(10 -x^{\frac{1}{2}})^{\frac{1}{2}})^{\frac{1}{2}}\) is a real number, lies between :

(A) 89 and 95
(B) 94 and 100
(C) 99 and 105
(D) 104 and 110
(E) 109 and 115
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C
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Re: The number of integers values of 'x', for which (3-(10 -x^(1/2) [#permalink] New post   14 Jul 2018, 09:05
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Lupine wrote:
Can anyone please tell, how to attempt this question.


Hi..
attempt this by ensuring the part under square root is NOT <0

so the solution would be

\((3-(10 -x^{\frac{1}{2}})^{\frac{1}{2}})^{\frac{1}{2}}\)

so \(\sqrt{10-x^{1/2}}\geq{0}.................\sqrt{x}\leq{10}...............x\leq{100}\)

Also \(\sqrt{10-x^{1/2}}\leq{3}....................10-\sqrt{x}\leq{9}.............\sqrt{x}\geq{1}..........x\geq{1}\)

so values are from 1 to 100, so 100 values

since we are looking for a choice which includes 100 in the range
C. between 99 to 104 is the answer
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Re: The number of integers values of 'x', for which (3-(10 -x^(1/2) [#permalink] New post   19 Jul 2018, 01:17
the question is testing real numbers.. should I be worried about this one?
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The number of integers values of 'x', for which (3-(10 -x^(1/2) [#permalink] New post   25 Mar 2020, 01:11
chetan2u wrote:
Lupine wrote:
Can anyone please tell, how to attempt this question.


Hi..
attempt this by ensuring the part under square root is NOT <0

so the solution would be

\((3-(10 -x^{\frac{1}{2}})^{\frac{1}{2}})^{\frac{1}{2}}\)

so \(\sqrt{10-x^{1/2}}\geq{0}.................\sqrt{x}\leq{10}...............x\leq{100}\)

Also \(\sqrt{10-x^{1/2}}\leq{3}....................10-\sqrt{x}\leq{9}.............\sqrt{x}\geq{1}..........x\geq{1}\)

so values are from 1 to 100, so 100 values

since we are looking for a choice which includes 100 in the range
C. between 99 to 104 is the answer



[m]\sqrt{3-[square_root]10[square_root]x}[/square_root][/square_root][m]

which means [m]\sqrt{x} <= 10[m] , i.e. x<= 100

also [m]\sqrt{10-[square_root]x}[/square_root]<=3[m], i.e. x>= 1

THIS 1<=X<=100 , X can take 100 value

Hence C
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Re: The number of integers values of 'x', for which (3-(10 -x^(1/2) [#permalink] New post   22 Sep 2021, 16:45
Just using > instead of ≥ cost me this question.
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Re: The number of integers values of 'x', for which (3-(10 -x^(1/2) [#permalink]
22 Sep 2021, 16:45
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