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# Given that x = 2^b – (8^30 + 16^5), which of the following values for

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Re: Given that x = 2^b – (8^30 + 16^5), which of the following values for [#permalink]
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Bunuel wrote:
Given that x = 2^b – (8^30 + 16^5), which of the following values for b yields the lowest value for |x|?

A) 35
B) 90
C) 91
D) 95
E) 105

$$x = 2^b – (8^{30} + 16^5)$$

$$x = 2^b – (2^{3(30)} + 2^{4(5)})$$

$$x = 2^b – (2^{90} + 2^{20})$$

$$x = 2^b – (2^{20}(2^{70} + 1))$$

$$2^{20}(2^{70} + 1)$$ can be written as approximately $$= 2^{20}(2^{70}) = 2^{90}$$

$$x = 2^b - 2^{90}$$

Lowest value of $$|x|$$ is $$0$$. Hence $$b$$ should be equal to $$90$$.

$$x = 2^{90} - 2^{90}$$

$$2^b = 2^{90} . b = 90$$. Answer (B)...
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Re: Given that x = 2^b – (8^30 + 16^5), which of the following values for [#permalink]
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Bunuel wrote:
Given that x = 2^b – (8^30 + 16^5), which of the following values for b yields the lowest value for |x|?

A) 35
B) 90
C) 91
D) 95
E) 105

Can the value of |y| < 0 because for b=90. 2^90 - 2^90 - 2^20 will be <0
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Re: Given that x = 2^b – (8^30 + 16^5), which of the following values for [#permalink]
sashiim20 wrote:
Bunuel wrote:
Given that x = 2^b – (8^30 + 16^5), which of the following values for b yields the lowest value for |x|?

A) 35
B) 90
C) 91
D) 95
E) 105

$$x = 2^b – (8^{30} + 16^5)$$

$$x = 2^b – (2^{3(30)} + 2^{4(5)})$$

$$x = 2^b – (2^{90} + 2^{20})$$

$$x = 2^b – (2^{20}(2^{70} + 1))$$

$$2^{20}(2^{70} + 1)$$ can be written as approximately $$= 2^{20}(2^{70}) = 2^{90}$$

$$x = 2^b - 2^{90}$$

Lowest value of $$|x|$$ is $$0$$. Hence $$b$$ should be equal to $$90$$.

$$x = 2^{90} - 2^{90}$$

$$2^b = 2^{90} . b = 90$$. Answer (B)...

Hi, I don't understand how from x=2^b–(2^20(2^70+1)) you get x=2^b−2^90... what happened to the +1?
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Re: Given that x = 2^b – (8^30 + 16^5), which of the following values for [#permalink]
More easily:

x = 2^b – (8^30 + 16^5) = 2^b - (2^90 + 2^20) = 2^b - 2^90*[1 + (2^-70)] ≈ 2^b - 2^90

min(mod(x)) ≈ 0 if b = 90 ----> ans: B
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Given that x = 2^b – (8^30 + 16^5), which of the following values for [#permalink]
saahulu wrote:
sashiim20 wrote:
Bunuel wrote:
Given that x = 2^b – (8^30 + 16^5), which of the following values for b yields the lowest value for |x|?

A) 35
B) 90
C) 91
D) 95
E) 105

$$x = 2^b – (8^{30} + 16^5)$$

$$x = 2^b – (2^{3(30)} + 2^{4(5)})$$

$$x = 2^b – (2^{90} + 2^{20})$$

$$x = 2^b – (2^{20}(2^{70} + 1))$$

$$2^{20}(2^{70} + 1)$$ can be written as approximately $$= 2^{20}(2^{70}) = 2^{90}$$

$$x = 2^b - 2^{90}$$

Lowest value of $$|x|$$ is $$0$$. Hence $$b$$ should be equal to $$90$$.

$$x = 2^{90} - 2^{90}$$

$$2^b = 2^{90} . b = 90$$. Answer (B)...

Hi, I don't understand how from x=2^b–(2^20(2^70+1)) you get x=2^b−2^90... what happened to the +1?

When dealing with such huge numbers +1 will hardly make a difference to the question and hence can be ignored.
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Re: Given that x = 2^b (8^30 + 16^5), which of the following values for [#permalink]
viksingh15 wrote:
Bunuel wrote:
Given that x = 2^b – (8^30 + 16^5), which of the following values for b yields the lowest value for |x|?

A) 35
B) 90
C) 91
D) 95
E) 105

is answer E, since we have 2^b - 2^90 - 2^20, only 105 is closest to 110(90+20).

Can anyone explain, why the answer is not E?
B) |x|= 2^90-2^90-2^-20= 2^20
D) |x|= 2^105-2^90-2^-20= 2^5

So my answer is E. Can you guide me?
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Re: Given that x = 2^b (8^30 + 16^5), which of the following values for [#permalink]
viksingh15 wrote:
Bunuel wrote:
Given that x = 2^b – (8^30 + 16^5), which of the following values for b yields the lowest value for |x|?

A) 35
B) 90
C) 91
D) 95
E) 105

is answer E, since we have 2^b - 2^90 - 2^20, only 105 is closest to 110(90+20).

Can anyone explain, why the answer is not E?
B) |x|= 2^90-2^90-2^-20= 2^20
D) |x|= 2^105-2^90-2^-20= 2^5

So my answer is E. Can you guide me?
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Re: Given that x = 2^b (8^30 + 16^5), which of the following values for [#permalink]
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Re: Given that x = 2^b (8^30 + 16^5), which of the following values for [#permalink]
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