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# Is a < 2^(1/2)

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Intern
Joined: 25 Oct 2016
Posts: 5

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25 Oct 2016, 12:15
6
00:00

Difficulty:

65% (hard)

Question Stats:

51% (01:47) correct 49% (01:50) wrong based on 94 sessions

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Is $$a < \sqrt{2}$$?

(1) Point (a,0) is inside the circle $$x^2 + y^2 =3$$
(2) Point (a,1) is inside the circle $$x^2 + y^2 =3$$
Manager
Joined: 28 Jun 2016
Posts: 207
Concentration: Operations, Entrepreneurship
Re: Is a < 2^(1/2)  [#permalink]

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25 Oct 2016, 13:19
Statement 1:

a^2<3

a<sqrt(3)

Insufficient

Statement 2:

a^2 + 1 < 3

a^2<2

a<sqrt(2)

Sufficient

IMO B

Sent from my iPhone using GMAT Club Forum mobile app
VP
Joined: 05 Mar 2015
Posts: 1004
Re: Is a < 2^(1/2)  [#permalink]

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26 Oct 2016, 02:59
sitagupta385 wrote:
Is $$a < \sqrt{2}$$?

(1) Point (a,0) is inside the circle $$x^2 + y^2 =3$$
(2) Point (a,1) is inside the circle $$x^2 + y^2 =3$$

circle x^2 + y^2 =3 is centered at origin with radius sqrt.3

1)a can be anypoint inside circle such that
if 1.414<a<1.732 -----NO
if a<1.414-------YES---------->insuff

2) consider right triangle drawn
then a will always <1.414-------->suff

Ans B
Attachments

circle.png [ 7.94 KiB | Viewed 867 times ]

Manager
Joined: 06 Nov 2016
Posts: 62
Location: Viet Nam
GPA: 3.54
Re: Is a < 2^(1/2)  [#permalink]

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01 Aug 2018, 08:35
Is a<√2 ?

(1) Point (a,0) is inside the circle x^2+y^2=3
--> a^2 + 0^2 < 3 --> a^2 < 3 --> a<√3 --> If a = 1 then YES but If a = 1.5 then NO
---> Insufficient.

(2) Point (a,1) is inside the circle x^2+y^2=3
--> a^2 + 1^2 < 3 --> a^2 < 2 --> a<√2
---> Sufficient.

_________________
Re: Is a < 2^(1/2) &nbs [#permalink] 01 Aug 2018, 08:35
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