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If m and n are positive numbers, and m^5 = 200 - n^5, what is the
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12 Nov 2021, 06:47
12 Nov 2021, 06:47
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If m and n are positive numbers, and m5=200−n5, what is the greatest possible value of n ?
(A) Between 1 and 2
(B) Between 2 and 3
(C) Between 3 and 4
(D) Between 4 and 5
(E) Between 5 and 6
(A) Between 1 and 2
(B) Between 2 and 3
(C) Between 3 and 4
(D) Between 4 and 5
(E) Between 5 and 6
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Joined: 09 Nov 2021
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Re: If m and n are positive numbers, and m^5 = 200 - n^5, what is the
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12 Nov 2021, 07:49
12 Nov 2021, 07:49
1
Start here: we know that m^5 is a positive number.
Therefore, 200-n^5 must also be greater than zero. That implies that n^5 must be LESS THAN 200.
2^5 = 32 and 3^5 = 243. 200 is of course somewhere in this range.
This means that the maximum value for n would be somewhere between 2 and 3.
(Note that m and n can be any number, not just integers because the question says "positive numbers" rather than "positive integers." Pay attention to wording in cases such as this).
Therefore, 200-n^5 must also be greater than zero. That implies that n^5 must be LESS THAN 200.
2^5 = 32 and 3^5 = 243. 200 is of course somewhere in this range.
This means that the maximum value for n would be somewhere between 2 and 3.
(Note that m and n can be any number, not just integers because the question says "positive numbers" rather than "positive integers." Pay attention to wording in cases such as this).
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Joined: 10 Apr 2015
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Re: If m and n are positive numbers, and m^5 = 200 - n^5, what is the
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12 Nov 2021, 08:07
12 Nov 2021, 08:07
1
Carcass wrote:
If m and n are positive numbers, and m5=200−n5, what is the greatest possible value of n ?
(A) Between 1 and 2
(B) Between 2 and 3
(C) Between 3 and 4
(D) Between 4 and 5
(E) Between 5 and 6
(A) Between 1 and 2
(B) Between 2 and 3
(C) Between 3 and 4
(D) Between 4 and 5
(E) Between 5 and 6
Given: m5=200−n5
Add n5 to both sides of the equation to get: m5+n5=200
We can MAXIMIZE the value of n by MINIMIZING the value of m.
We're told that m is positive, so the smallest possible value of m will be just a tiny bit bigger than 0.
Since there is very little difference between a number like 0.00000000001 and 0, let's just make things easy on ourselves and let m=0
When we do this we get: 05+n5=200
Simplify: n5=200
We know that 25=32 and 35=243
Since 200 is between 32 and 243, we know that the value of n must be between 2 and 3
Answer: B
