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Is x > y? (1) x^2 < y (2) x^(1/2) >y

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Is x > y? (1) x^2 < y (2) x^(1/2) >y  [#permalink]

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New post Updated on: 04 Nov 2018, 20:27
5
2
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

35% (01:33) correct 65% (00:43) wrong based on 20 sessions

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Is x > y?

(1) x^2 < y

(2) x^(1/2) >y

Originally posted by piyush26 on 04 Nov 2018, 12:00.
Last edited by Bunuel on 04 Nov 2018, 20:27, edited 2 times in total.
Renamed the topic and edited the question.
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Re: Is x > y? (1) x^2 < y (2) x^(1/2) >y  [#permalink]

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New post 04 Nov 2018, 12:15
2
piyush26 wrote:
Is x > y?

(1) x^2 < y

(2) x^1/2 >y

\(x\,\,\mathop > \limits^? \,\,y\)

We could go straight for the (1+2) BIFURCATION, to guarantee the correct answer is (E).

I will bifurcate each one separately first, for didactic reasons.

\(\left( 1 \right)\,\,{x^2} < y\,\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,\left( {x;y} \right) = \left( {0;1} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\, \hfill \cr
\,{\rm{Take}}\,\,\left( {x;y} \right) = \left( {{1 \over 2};{1 \over 3}} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\, \hfill \cr} \right.\)

\(\left( 2 \right)\,\,\sqrt x > y\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,\left( {x;y} \right) = \left( {1;0} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\, \hfill \cr
\,{\rm{Take}}\,\,\left( {x;y} \right) = \left( {{1 \over 4};{1 \over 3}} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\, \hfill \cr} \right.\)

\(\left( {1 + 2} \right)\,\,\,{x^2} < y < \sqrt x \,\,\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,\,\left( {x;y} \right) = \left( {{1 \over 4};{1 \over 4}} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\, \hfill \cr
\,{\rm{Take}}\,\,\left( {x;y} \right) = \left( {{1 \over 4};{1 \over 8}} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\, \hfill \cr} \right.\)


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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Fabio Skilnik :: https://www.GMATH.net (Math for the GMAT)
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Re: Is x > y? (1) x^2 < y (2) x^(1/2) >y &nbs [#permalink] 04 Nov 2018, 12:15
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