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# If 0.7^(2x2 - 3x + 4) < 0.343, then which of the following must be tru

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Re: If 0.7^(2x2 - 3x + 4) < 0.343, then which of the following must be tru [#permalink]
GMATinsight wrote:
Bunuel wrote:
If $$0.7^{(2x^2 - 3x + 4)} < 0.343$$, then which of the following must be true?

A. x < -1/2
B. -1/2 < x < 1/2
C. 1/2 < x < 1
D. x > 1
E. x < 1/2

RULE:
If $$0 < a < 1$$, then $$a^x < a^y$$ if $$y > x$$

i.e. $$0.7^{(2x^2 - 3x + 4)} < 0.343$$
i.e. $$0.7^{(2x^2 - 3x + 4)} < (0.7)^3$$

i.e. $$(2x^2 - 3x + 4) > 3$$
i.e. $$(2x^2 - 3x + 1) > 0$$

i.e. $$(2x^2 - 2x - x + 1) > 0$$

i.e. $$(2x - 1)*(x - 1) > 0$$

i.e. either both (2x - 1)*(x - 1) should be positive or both should be Negative

For both positive, x>1

For both negative, x<1/2

No match of answer... Let me check again

Bunuel I think the inequation sign should be reversed in this question. Please check.

____________________
Edited option E. Thank you.
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Re: If 0.7^(2x2 - 3x + 4) < 0.343, then which of the following must be tru [#permalink]
D and/or E

0.343 = 0.7^3

Also we know that :
If 0<a<1 , then for x>y a^x < a^y

==> 2x^2 -3x +4 >3
or 2x^2 - 3x +1 >0
or (2x-1)(x-1)> 0

==> X< 1/2 (Option E) or x>1 (Option D)

Am I wrong somewhere?
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Re: If 0.7^(2x2 - 3x + 4) < 0.343, then which of the following must be tru [#permalink]
GMATinsight wrote:
Bunuel wrote:
If $$0.7^{(2x^2 - 3x + 4)} < 0.343$$, then which of the following must be true?

A. x < -1/2
B. -1/2 < x < 1/2
C. 1/2 < x < 1
D. x > 1
E. x < 1/2

RULE:
If $$0 < a < 1$$, then $$a^x < a^y$$ if $$y > x$$

i.e. $$0.7^{(2x^2 - 3x + 4)} < 0.343$$
i.e. $$0.7^{(2x^2 - 3x + 4)} < (0.7)^3$$

i.e. $$(2x^2 - 3x + 4) > 3$$
i.e. $$(2x^2 - 3x + 1) > 0$$

i.e. $$(2x^2 - 2x - x + 1) > 0$$

i.e. $$(2x - 1)*(x - 1) > 0$$

i.e. either both (2x - 1)*(x - 1) should be positive or both should be Negative

For both positive, x>1

For both negative, x<1/2

GMATinsight Please correct my understanding --> If $$0 < a < 1$$, then $$a^x < a^y$$ if $$y > x$$

In the above rule, Shouldn't be y>x as x>y ???
Also guide me how did the sign (<) of the original equation $$0.7^{(2x^2 - 3x + 4)} < 0.343$$ changed to (>) in the new equation $$(2x^2 - 3x + 4) > 3$$.
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Re: If 0.7^(2x2 - 3x + 4) < 0.343, then which of the following must be tru [#permalink]
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Re: If 0.7^(2x2 - 3x + 4) < 0.343, then which of the following must be tru [#permalink]
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Re: If 0.7^(2x2 - 3x + 4) < 0.343, then which of the following must be tru [#permalink]
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