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# ds: Is X > Y?

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Director
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ds: Is X > Y? [#permalink]

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10 Dec 2007, 15:28
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Is X > Y?

(1) sqrt(X) > Y
(2) X^3 > Y

Do we consider sqrt(X) to be +ve?
Intern
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Re: ds: Is X > Y? [#permalink]

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10 Dec 2007, 15:46
eyunni wrote:
Is X > Y?

(1) sqrt(X) > Y
(2) X^3 > Y

Do we consider sqrt(X) to be +ve?

C

1) NS because x>y is true if x is 4 but not true if x is 1/4

2) NS because x>y is true if x is 2 but not true if x is -1/2

1&2 Sufficient - after plugging in 2 and 1/4.

1) says that x is postive so no need to test negative numbers.
Director
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10 Dec 2007, 19:28
Manager
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10 Dec 2007, 20:48
Yes - 1 makes X positive

solutions for sqrt a^2 can be +/- a but a^2 (in this case X) is always a positive number

Someone correct me if I'm wrong
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Re: ds: Is X > Y? [#permalink]

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11 Dec 2007, 03:15
eyunni wrote:
Is X > Y?

(1) sqrt(X) > Y
(2) X^3 > Y

Do we consider sqrt(X) to be +ve?

Rule that comes out of this: If sqrt(x) > y and x^3 >y then x > y.
Director
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11 Dec 2007, 07:20

(1) sqrt(X) > Y

Is sqrt(X) +ve in this question?
CEO
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11 Dec 2007, 08:05
√X > Y is true only when √X is defined. Therefore x e (0,+∞]
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11 Dec 2007, 08:06
eyunni wrote:

(1) sqrt(X) > Y

Is sqrt(X) +ve in this question?

sqrt(X) +ve if x is positive and -ve if x is negative..

C is the answer. Whats the OA??
Director
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11 Dec 2007, 08:38
walker wrote:
shubhampandey wrote:
sqrt(X) +ve if x is positive and -ve if x is negative..

√X is always positive.

Very basic question: If √2 = +/- 1.414, why is √X always +ve?
CEO
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11 Dec 2007, 12:03
eyunni wrote:
Very basic question: If √2 = +/- 1.414, why is √X always +ve?

√2 always equal +1.414 not -1.414.
maybe you think about questions like: x²=2, what is x?
in this case we have two solutions: x1=+√2 and x2=-√2, so x=+/-√2
but √2 itself is always positive.
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11 Dec 2007, 12:25
walker wrote:
eyunni wrote:
Very basic question: If √2 = +/- 1.414, why is √X always +ve?

√2 always equal +1.414 not -1.414.
maybe you think about questions like: x²=2, what is x?
in this case we have two solutions: x1=+√2 and x2=-√2, so x=+/-√2
but √2 itself is always positive.

I agree with Walker...

Also, there is the confusing definition of roots (that is related to x^2 = something).... Any number has 2 roots : sqrt(this number) and -sqrt(this number).
Director
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11 Dec 2007, 12:57
Thanks Fig. OA is C. Also, drawing the graphs for (1) and (2) proves that x > y.
11 Dec 2007, 12:57
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