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playthegame
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­If a + b = 10, what is the maximum value of a^3*b^2? 22 Feb 2024, 22:23
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

95% (hard)

Question Stats:

43% (02:38) correct 57% (01:50) wrong based on 72 sessions

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Date
Time
Result
Not Attempted Yet
­If a + b = 10, what is the maximum value of a^3*b^2?

A. 2125
B. 3125
C. 3456
D. 4125
E. 4456
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C
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Oppenheimer1945
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­If a + b = 10, what is the maximum value of a^3*b^2? 24 Feb 2024, 10:11
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(a/3+a/3+a/3+b/2+b/2)/5>=((a/3)^3(b/2)^2)^1/5
AM>=GM

=> 2^5 * 3^3 2^2 >=a^3b^2
3456

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­If a + b = 10, what is the maximum value of a^3*b^2? 24 Feb 2024, 11:38
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5^3 + 5^2 gives option B.

Share the OA please.
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­If a + b = 10, what is the maximum value of a^3*b^2? 24 Feb 2024, 19:11
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samagra__
(a/3+a/3+a/3+b/2+b/2)/5>=((a/3)^3(b/2)^2)^1/5
AM>=GM

=> 2^5 * 3^3 2^2 >=a^3b^2
3456

Posted from my mobile device
­Thank you very much, I was looking for the AM and GM solution but I was not able to form the pieces like you did with a/3 and b/2 thank you very much for sharing.

Do you have any notes on what to look for on problems like these where you have to make the different terms to get to the answer?
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­If a + b = 10, what is the maximum value of a^3*b^2? 24 Feb 2024, 19:11
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LamboWalker
5^3 + 5^2 gives option B.

Share the OA please.
­Thanks I landed at option B as well and it is not correct. The correct answer is C. 3456

We can solve it pretty quickly with the AM GM inequality
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­If a + b = 10, what is the maximum value of a^3*b^2? 24 Feb 2024, 22:55
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playthegame
samagra__
(a/3+a/3+a/3+b/2+b/2)/5>=((a/3)^3(b/2)^2)^1/5
AM>=GM

=> 2^5 * 3^3 2^2 >=a^3b^2
3456

Posted from my mobile device
­Thank you very much, I was looking for the AM and GM solution but I was not able to form the pieces like you did with a/3 and b/2 thank you very much for sharing.

Do you have any notes on what to look for on problems like these where you have to make the different terms to get to the answer?
­if question asks for max value of a^n b^m, you distribute a/n (n times) and b/m (m times) and apply AM>=GM
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