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# In which of the following choices must a be less than b?

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Math Expert
Joined: 02 Sep 2009
Posts: 53069
In which of the following choices must a be less than b?  [#permalink]

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21 Oct 2018, 21:04
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Difficulty:

75% (hard)

Question Stats:

57% (01:53) correct 43% (01:43) wrong based on 92 sessions

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In which of the following choices must a be less than b?

(A) $$4^{(-2b)} = 4^{(-a)}$$

(B) $$-4^b < 4^a$$

(C) $$4^{(-b)} < 4^{(-a)}$$

(D) $$4^{(-b)} > 4^{(-a)}$$

(E) $$4^{(-b)} = 4^{(-2a)}$$

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WE: Supply Chain Management (Energy and Utilities)
Re: In which of the following choices must a be less than b?  [#permalink]

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21 Oct 2018, 21:13
1
1
Bunuel wrote:
In which of the following choices must a be less than b?

(A) $$4^{(-2b)} = 4^{(-a)}$$

(B) $$-4^b < 4^a$$

(C) $$4^{(-b)} < 4^{(-a)}$$

(D) $$4^{(-b)} > 4^{(-a)}$$

(E) $$4^{(-b)} = 4^{(-2a)}$$

Let's check each options:-

(A) $$4^{(-2b)} = 4^{(-a)}$$; a=2b, we can't conclude from here. DISCARD

(B) $$-4^b < 4^a$$ or,$$4^a+4^b>0$$;we can't conclude from here. DISCARD

(C) $$4^{(-b)} < 4^{(-a)}$$ Or, $$4^b>4^a$$ or, $$4^{b-a}>4^0$$ or, b-a>0 or, b>a . This is our ANSWER.

Ans. (C)
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PKN

Rise above the storm, you will find the sunshine

Intern
Joined: 15 Oct 2018
Posts: 14
Re: In which of the following choices must a be less than b?  [#permalink]

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22 Oct 2018, 10:33
Bunuel wrote:
In which of the following choices must a be less than b?

(A) $$4^{(-2b)} = 4^{(-a)}$$

(B) $$-4^b < 4^a$$

(C) $$4^{(-b)} < 4^{(-a)}$$

(D) $$4^{(-b)} > 4^{(-a)}$$

(E) $$4^{(-b)} = 4^{(-2a)}$$

Why E is wrong? From E : b = 2a; b always gonna be greater than a
GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 772
Re: In which of the following choices must a be less than b?  [#permalink]

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22 Oct 2018, 10:41
Bunuel wrote:
In which of the following choices must a be less than b?

(A) $$4^{(-2b)} = 4^{(-a)}$$

(B) $$-4^b < 4^a$$

(C) $$4^{(-b)} < 4^{(-a)}$$

(D) $$4^{(-b)} > 4^{(-a)}$$

(E) $$4^{(-b)} = 4^{(-2a)}$$

$$?\,\,\,\,:\,\,\,\,a\,\, < \,\,\,b$$

$$\left( {a,b} \right) = \left( {0,0} \right)\,\,{\text{satisfies}}\,\,\left( A \right),\left( B \right)\,\,{\text{and}}\,\,\left( E \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\text{they}}\,\,{\text{are}}\,\,{\text{out}}!$$

$$\left( {a,b} \right) = \left( {1,0} \right)\,\,{\text{satisfies}}\,\,\left( D \right)\,\,\,\,\, \Rightarrow \,\,\,{\text{out}}!$$

Alternative choice (C) is the only survivor, therefore it must be the right answer.

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

Regards,
Fabio.
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Joined: 01 Oct 2017
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WE: Supply Chain Management (Energy and Utilities)
Re: In which of the following choices must a be less than b?  [#permalink]

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24 Oct 2018, 02:57
VaCeFe wrote:
Bunuel wrote:
In which of the following choices must a be less than b?

(A) $$4^{(-2b)} = 4^{(-a)}$$

(B) $$-4^b < 4^a$$

(C) $$4^{(-b)} < 4^{(-a)}$$

(D) $$4^{(-b)} > 4^{(-a)}$$

(E) $$4^{(-b)} = 4^{(-2a)}$$

Why E is wrong? From E : b = 2a; b always gonna be greater than a

Hi VaCeFe,

1) Say a=1 then b=2a=2*1=2; b>a-------Your reasoning is CORRECT
2) Say a=-1 then b=2a=2*(-1)=-2; b<a-------Your reasoning is NOT CORRECT. (Since -2<-1)

This is the reason we have to DISCARD option(E).

Hope it helps.
_________________

Regards,

PKN

Rise above the storm, you will find the sunshine

Re: In which of the following choices must a be less than b?   [#permalink] 24 Oct 2018, 02:57
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