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If m and n are positive integers, what is the greatest possible value

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New post 13 Apr 2018, 01:49
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If m and n are positive integers, what is the greatest possible value  [#permalink]

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New post 13 Apr 2018, 09:06
Bunuel wrote:
If m and n are positive integers, what is the greatest possible value of n?

(1) m^5 + n^5 < 1,200
(2) m^5 = 0



I) m^5 + n^5 < 1,200 ==> gives you nothing for n ==> not sufficient

II) m^5 = 0 ==> this can be true when m=0 but still not sufficient as it gives nothing for n

But using I and II together, we have

n^5 < 1200 ==> n is positive interger, so there will multiple values of n and there will be one greatest value which when raised to power 5 will be less than 1200
or we know 2^10 = 1024 = 4^5, anything above 4^5 will be greater than 1200 so greatest possible value for n=4 ==>sufficient

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Re: If m and n are positive integers, what is the greatest possible value  [#permalink]

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New post 14 Apr 2018, 09:29
AV24 wrote:
Bunuel wrote:
If m and n are positive integers, what is the greatest possible value of n?

(1) m^5 + n^5 < 1,200
(2) m^5 = 0



I) m^5 + n^5 < 1,200 ==> gives you nothing for n ==> not sufficient

II) m^5 = 0 ==> this can be true when m=0 but still not sufficient as it gives nothing for n

But using I and II together, we have

n^5 < 1200 ==> n is positive interger, so there will multiple values of n and there will be one greatest value which when raised to power 5 will be less than 1200
or we know 2^10 = 1024 = 4^5, anything above 4^5 will be greater than 1200 so greatest possible value for n=4 ==>sufficient

Ans C


My understanding is different. Tell me, please, if it is wrong.

1) m and n are positiv integers.
m could be 1, hence greatest possible value of n is 4 —> sufficient

2) m^5=0 -> greatest possible value of n is 4 —> sufficient
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If m and n are positive integers, what is the greatest possible value  [#permalink]

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New post 14 Apr 2018, 12:04
I don't get this question.

If the stem says m and n are positive integers, how can we have statement 2) m^5=0? If m is a positive integer, how can it be 0?

In any case, the answer IMO remains A. The greatest value of n is possible when m has the smallest possible value which can be 1 given it is a positive integer.

Please correct me if I am wrong.
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New post Updated on: 14 Apr 2018, 12:56
AV24 wrote:
Bunuel wrote:
If m and n are positive integers, what is the greatest possible value of n?

(1) m^5 + n^5 < 1,200
(2) m^5 = 0



I) m^5 + n^5 < 1,200 ==> gives you nothing for n ==> not sufficient

II) m^5 = 0 ==> this can be true when m=0 but still not sufficient as it gives nothing for n

But using I and II together, we have

n^5 < 1200 ==> n is positive interger, so there will multiple values of n and there will be one greatest value which when raised to power 5 will be less than 1200
or we know 2^10 = 1024 = 4^5, anything above 4^5 will be greater than 1200 so greatest possible value for n=4 ==>sufficient

Ans C


1)Since m>0 then max n(max) can be when m=1, hence n^5<1199 n(max) = 4 - closest integer. Sufficient
2) Not sufficient

Answer is (A)

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Originally posted by Iamnowjust on 14 Apr 2018, 12:46.
Last edited by Iamnowjust on 14 Apr 2018, 12:56, edited 1 time in total.
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Re: If m and n are positive integers, what is the greatest possible value  [#permalink]

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New post 14 Apr 2018, 12:55
Bunuel wrote:
If m and n are positive integers, what is the greatest possible value of n?

(1) m^5 + n^5 < 1,200
(2) m^5 = 0



Dear Bunuel

In statement 2, How come is m = 0 and in same time m is positive value? 0 is not positive integer.

I think there is mistake in question stem.
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Re: If m and n are positive integers, what is the greatest possible value  [#permalink]

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New post 15 Apr 2018, 09:08
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Re: If m and n are positive integers, what is the greatest possible value   [#permalink] 15 Apr 2018, 09:08
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