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Bunuel
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Bunuel
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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Bunuel
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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sashiim20
Bunuel
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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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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saahulu
sashiim20
Bunuel
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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viksingh15
Bunuel
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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Bunuel
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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Hello ,
Given that x = 2^b – (8^30 + 16^5), which of the following values for b yields the lowest value for |x|?

X=2^b – (2^90 + 2^20)
=2^b-2^90(1+(1/2^70)
so (1/2^70) will almost equal to zero

so x=2^b-2^90 ,Hence value of b for lowest value of |x| will be 90

Hence option B is correct
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