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Find an interval I on which

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Find an interval I on which  [#permalink]

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New post 15 Sep 2018, 16:55
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A
B
C
D
E

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Question Stats:

50% (01:54) correct 50% (01:44) wrong based on 2 sessions

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Find an interval I on which a < b implies a\(e^{−a}\) > b\(e^{−b}\), where \(e\) is mathematical constant approximately equal to 2.71

(A) (1, \(\infty\) )
(B) [1, \(\infty\) ]
(C) (- \(\infty\) ,0 ]
(D) (- \(\infty\) ,0 )
(E) (-\(\infty\), \(\infty\) )

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Re: Find an interval I on which  [#permalink]

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New post 15 Sep 2018, 19:19
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Probus wrote:
Find an interval I on which a < b implies a\(e^{−a}\) > b\(e^{−b}\), where \(e\) is mathematical constant approximately equal to 2.71

(A) (1, \(\infty\) )
(B) [1, \(\infty\) ]
(C) (- \(\infty\) ,0 ]
(D) (- \(\infty\) ,0 )
(E) (-\(\infty\), \(\infty\) )


I'm pretty sure the GMAT does not test the difference between ) and ]

I changed e to = 3 for the sake of easy numbers.

3a^(-a) > ab^-b and a < b


I first tested to see if a could be less than 1 and I used -3. Then made b = -2

\(-9^3\) > \(-6^2\)

This does not work.

Now try a >1 and b > a

Make a = 2 and b = 3

\(\frac{1}{6}\) > \(\frac{1}{9}\)

This works

Answer: A
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Re: Find an interval I on which   [#permalink] 15 Sep 2018, 19:19
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