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

Question

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

nalinnair · Accepted Answer

x = 2^b -   
 = 2^b -   
 =2^b -   
 = 2^b -   
 2^{70} + 1\approx2^{70} 
therefore,  x\approx2^b -   
 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^b -   
 = 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.

sashiim20 · Answer

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)...

viksingh15 · Answer

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

adyoy93 · Answer

Can the value of |y| < 0 because for b=90. 2^90 - 2^90 - 2^20 will be <0

saahulu · Answer

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?

ism1994 · Answer

More easily:

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

min(mod(x)) ≈ 0 if b = 90 ----> ans: B

MBAB123 · Answer

When dealing with such huge numbers +1 will hardly make a difference to the question and hence can be ignored.

Urvasi · Answer

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?

Urvasi · Answer

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?

ravi1522 · Answer

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

Bhavek · Answer

i am not able to understand where did +1 go 
cause it should also be multiplied by 2 raised 20

Bunuel · Answer

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

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

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