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# Find an interval I on which

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Joined: 10 Apr 2018
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Find an interval I on which  [#permalink]

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15 Sep 2018, 16:55
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Difficulty:

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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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Probus

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

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15 Sep 2018, 19:19
1
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

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