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Given that x = 2^b – (8^30 + 16^5), which of the following values for
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Bunuel
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Given that x = 2^b – (8^30 + 16^5), which of the following values for [#permalink] New post  29 Feb 2016, 11:55
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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
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nalinnair
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Re: Given that x = 2^b – (8^30 + 16^5), which of the following values for [#permalink] New post  29 Feb 2016, 21:09
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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


\(x = 2^b - [8^{30} + 16^5]\)
\(= 2^b - [(2^3)^{30} + (2^4)^5]\)
\(=2^b - [(2^{90}) +(2^{20})]\)
\(= 2^b - [(2^{20})(2^{70} + 1)]\)
\(2^{70} + 1\approx2^{70}\)
therefore, \(x\approx2^b - [(2^{20})(2^{70})]\)
\(x\approx2^b - 2^{90}\)
for lowest value of \(|x|\), \(b = 90\)
hence, B is the correct answer.

Alternatively,
\(x = 2^b - (8^{30} + 16^5)\)
\(= 2^b - [(2^3)^{30} + (2^4)^5]\)
\(= 2^b - [(2^{90}) +(2^{20})]\)
\(= 2^b - 2^{90} - 2^{20}\)
to find the lowest value of \(|x|\), ignore the smaller exponent.
therefore, \(b = 90\)
hence, B is the correct answer.
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viksingh15
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Re: Given that x = 2^b – (8^30 + 16^5), which of the following values for [#permalink] New post  29 Feb 2016, 12:30
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).
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sashiim20
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Re: Given that x = 2^b – (8^30 + 16^5), which of the following values for [#permalink] New post  26 Jun 2017, 13:36
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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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adyoy93
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Re: Given that x = 2^b – (8^30 + 16^5), which of the following values for [#permalink] New post  11 Jun 2019, 09:53
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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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saahulu
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Re: Given that x = 2^b – (8^30 + 16^5), which of the following values for [#permalink] New post  17 Nov 2020, 02:40
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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ism1994
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Joined: 08 Nov 2020
Posts: 6
Re: Given that x = 2^b – (8^30 + 16^5), which of the following values for [#permalink] New post  22 Nov 2020, 23:19
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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Brian123
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GMAT 1: 720 Q49 V38
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Given that x = 2^b – (8^30 + 16^5), which of the following values for [#permalink] New post  23 Nov 2020, 21:10
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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