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

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Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 534
WE: Supply Chain Management (Energy and Utilities)
The number of integers values of 'x', for which (3-(10 -x^(1/2)  [#permalink]

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14 Jul 2018, 08:34
1
8
00:00

Difficulty:

85% (hard)

Question Stats:

48% (02:03) correct 52% (02:20) wrong based on 60 sessions

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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
Math Expert
Joined: 02 Aug 2009
Posts: 6556
Re: The number of integers values of 'x', for which (3-(10 -x^(1/2)  [#permalink]

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14 Jul 2018, 09:05
2
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
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Joined: 23 Nov 2017
Posts: 51
Location: Singapore
Concentration: Strategy, Other
GMAT 1: 640 Q42 V36
Re: The number of integers values of 'x', for which (3-(10 -x^(1/2)  [#permalink]

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19 Jul 2018, 01:17
Re: The number of integers values of 'x', for which (3-(10 -x^(1/2) &nbs [#permalink] 19 Jul 2018, 01:17
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