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

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

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New post 21 Oct 2018, 22:04
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

58% (01:51) correct 42% (01:41) wrong based on 103 sessions

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VP
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Re: In which of the following choices must a be less than b?  [#permalink]

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New post 21 Oct 2018, 22:13
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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Re: In which of the following choices must a be less than b?  [#permalink]

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New post 22 Oct 2018, 11:33
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
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Re: In which of the following choices must a be less than b?  [#permalink]

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New post 22 Oct 2018, 11:41
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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Re: In which of the following choices must a be less than b?  [#permalink]

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New post 24 Oct 2018, 03:57
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.
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PKN

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Re: In which of the following choices must a be less than b?   [#permalink] 24 Oct 2018, 03:57
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