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# If a^6 + b^6 = 144 then the greatest possible value for b is between

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If a^6 + b^6 = 144 then the greatest possible value for b is between [#permalink]

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10 Sep 2017, 04:30
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If a^6 + b^6 = 144 then the greatest possible value for b is between

A. 8 and 10
B. 6 and 8
C. 4 and 6
D. 2 and 4
E. 2 and 0
[Reveal] Spoiler: OA

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Re: If a^6 + b^6 = 144 then the greatest possible value for b is between [#permalink]

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10 Sep 2017, 05:58
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greatest possible value of b is when a is zero.

so b^6 = 144
b^3 = 12 b = 2.xxx
b is between 3 and 4 so

Ans D

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Last edited by Ejiroghene on 10 Sep 2017, 07:20, edited 1 time in total.

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Re: If a^6 + b^6 = 144 then the greatest possible value for b is between [#permalink]

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10 Sep 2017, 06:14
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It's a D. Between 2 and 4.

B is maximum when value of A is zero.

And since no condition has been given for A and B to be integers, so B can take decimal values also.

Again b^6=144
b^3=12.
So B can also be 2.1 or 2.2.
But it cannot be 3 or greater than 3.
So it has to be somewhere between 2 and 3.
So option D holds good in this case.

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If a^6 + b^6 = 144 then the greatest possible value for b is between [#permalink]

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10 Sep 2017, 06:20
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Bunuel wrote:
If a^6 + b^6 = 144 then the greatest possible value for b is between

A. 8 and 10
B. 6 and 8
C. 4 and 6
D. 2 and 4
E. 2 and 0

The question states that $$b^6 = 144-a^6$$. Hence for $$b$$ to be maximum $$a=0$$
so $$b^6=144$$ taking square root of both the sides, we get
$$b^3 = 12$$. Now,
$$8<12<27$$ or $$8<b^3<27$$. Taking cube root of the inequality we get
$$2<b<3$$. Hence $$b$$ is definitely greater than $$2$$ but less than $$3$$ (to be precise; $$b^3 = 12$$, or $$b= 2.289428$$)

Ideally the greatest possible value of $$b$$ is between $$2$$ & $$3$$, but we don't have any option stating that.
Hi Bunuel can you confirm whether Option D is correct and there are no typo errors

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If a^6 + b^6 = 144 then the greatest possible value for b is between [#permalink]

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16 Oct 2017, 21:47
niks18 wrote:
Bunuel wrote:
If a^6 + b^6 = 144 then the greatest possible value for b is between

A. 8 and 10
B. 6 and 8
C. 4 and 6
D. 2 and 4
E. 2 and 0

The question states that $$b^6 = 144-a^6$$. Hence for $$b$$ to be maximum $$a=0$$
so $$b^6=144$$ taking square root of both the sides, we get
$$b^3 = 12$$. Now,
$$8<12<27$$ or $$8<b^3<27$$. Taking cube root of the inequality we get
$$2<b<3$$. Hence $$b$$ is definitely greater than $$2$$ but less than $$3$$ (to be precise; $$b^3 = 12$$, or $$b= 2.289428$$)

Ideally the greatest possible value of $$b$$ is between $$2$$ & $$3$$, but we don't have any option stating that.
Hi Bunuel can you confirm whether Option D is correct and there are no typo errors

niks18
hi

I agree with you completely
though I approached the problem similar way, I don't understand how everybody is claiming "b" to be between 2 and 4

certainly, we need some Bunuel here ..

Last edited by gmatcracker2017 on 16 Oct 2017, 23:56, edited 2 times in total.

Kudos [?]: 28 [0], given: 481

Math Expert
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Posts: 43323

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Re: If a^6 + b^6 = 144 then the greatest possible value for b is between [#permalink]

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16 Oct 2017, 22:22
gmatcracker2017 wrote:
niks18 wrote:
Bunuel wrote:
If a^6 + b^6 = 144 then the greatest possible value for b is between

A. 8 and 10
B. 6 and 8
C. 4 and 6
D. 2 and 4
E. 2 and 0

The question states that $$b^6 = 144-a^6$$. Hence for $$b$$ to be maximum $$a=0$$
so $$b^6=144$$ taking square root of both the sides, we get
$$b^3 = 12$$. Now,
$$8<12<27$$ or $$8<b^3<27$$. Taking cube root of the inequality we get
$$2<b<3$$. Hence $$b$$ is definitely greater than $$2$$ but less than $$3$$ (to be precise; $$b^3 = 12$$, or $$b= 2.289428$$)

Ideally the greatest possible value of $$b$$ is between $$2$$ & $$3$$, but we don't have any option stating that.
Hi Bunuel can you confirm whether Option D is correct and there are no typo errors

niks18
hi

I agree with you completely
though I approached the problem similar way, I don't understand how everybody is claiming "b" to be between 2 and 4

certainly, we need some Bunuel here ..

The greatest possible value of b turns out to be ~2.3, which is indeed between 2 and 3, but it will also be true to say that it's between -1,000 and 10,000 isn't it? Between x and y, here means in the range from x to y. So, we can say that 2.3 is between 2 and 4.
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Re: If a^6 + b^6 = 144 then the greatest possible value for b is between [#permalink]

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16 Oct 2017, 23:57
gmatcracker2017 wrote:
niks18 wrote:
Bunuel wrote:
If a^6 + b^6 = 144 then the greatest possible value for b is between

A. 8 and 10
B. 6 and 8
C. 4 and 6
D. 2 and 4
E. 2 and 0

The question states that $$b^6 = 144-a^6$$. Hence for $$b$$ to be maximum $$a=0$$
so $$b^6=144$$ taking square root of both the sides, we get
$$b^3 = 12$$. Now,
$$8<12<27$$ or $$8<b^3<27$$. Taking cube root of the inequality we get
$$2<b<3$$. Hence $$b$$ is definitely greater than $$2$$ but less than $$3$$ (to be precise; $$b^3 = 12$$, or $$b= 2.289428$$)

Ideally the greatest possible value of $$b$$ is between $$2$$ & $$3$$, but we don't have any option stating that.
Hi Bunuel can you confirm whether Option D is correct and there are no typo errors

niks18
hi

I agree with you completely
though I approached the problem similar way, I don't understand how everybody is claiming "b" to be between 2 and 4

certainly, we need some Bunuel here ..

thanks a lot to you Bunuel

thanks

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Re: If a^6 + b^6 = 144 then the greatest possible value for b is between [#permalink]

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19 Oct 2017, 09:21
Bunuel wrote:
If a^6 + b^6 = 144 then the greatest possible value for b is between

A. 8 and 10
B. 6 and 8
C. 4 and 6
D. 2 and 4
E. 2 and 0

Since we want to maximize the value of b, we want to minimize the value of a^6. Since a has an even power, the minimum value of a^6 is 0, which occurs when a = 0 (note: if a ≠ 0, then a^6 > 0). Thus, when a^6 = 0, we have:

b^6 = 144

Since 2^6 = 64 and 3^6 = 729, b is greater than 2 but less than 3.

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Re: If a^6 + b^6 = 144 then the greatest possible value for b is between   [#permalink] 19 Oct 2017, 09:21
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