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If the sum of three distinct positive integers is 25, what is the maxi

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Bunuel
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If the sum of three distinct positive integers is 25, what is the maxi [#permalink] If the sum of three distinct positive integers is 25, what is the maxi   20 May 2020, 03:21
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If the sum of three distinct positive integers is 25, what is the maximum value of their product?

A. 44
B. 120
C. 420
D. 560
E. 920


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D
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Re: If the sum of three distinct positive integers is 25, what is the maxi [#permalink] If the sum of three distinct positive integers is 25, what is the maxi   20 May 2020, 04:24
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Bunuel
If the sum of three distinct positive integers is 25, what is the maximum value of their product?

A. 44
B. 120
C. 420
D. 560
E. 920


Solution


    • We have a + b + c = 25
      o Where a, b, and c are distinct positive integers.
    • We need to find the maximum value of a*b*c
      o To maximize the value of a*b*c, integers a, b, and c should be as close as possible.
         Ideally, if \(a = b = c = \frac{25}{3}\) then product a*b*c will be maximum i.e. \((\frac{25}{3})^3 \)
         But here, a, b, and c are distinct integers, so let us consider \(a =\) integer nearest to \(\frac{25}{3 }= 8\)
          • So, \(b = 7 \)[ b cannot 9 since in that case a = c]
          • Thus, \(c = 10\)
         Therefore, maximum value of \(a*b*c = 8*7*10 = 560\)
          • a*b*c cannot be 920 as \(920 > (\frac{25}{3})^3\)
Thus, the correct answer is Option D.
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If the sum of three distinct positive integers is 25, what is the maxi [#permalink] If the sum of three distinct positive integers is 25, what is the maxi   20 May 2020, 06:19
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Bunuel
If the sum of three distinct positive integers is 25, what is the maximum value of their product?

A. 44
B. 120
C. 420
D. 560
E. 920


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Asked: If the sum of three distinct positive integers is 25, what is the maximum value of their product?

7+8+10 = 25
7*8*10 = 560

IMO D­
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Re: If the sum of three distinct positive integers is 25, what is the maxi [#permalink] If the sum of three distinct positive integers is 25, what is the maxi   20 May 2020, 06:27
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I solve these questions by having understanding of Minima and maxima, We get maximum value with minimum numbers addition. So we should try to take numbers close to each other possible and lower
e.g we can't take 22 +2+1 = 25 and 44 multiple., We should try to reduce 22 max possible.
So lets try 6+7+12 : 25 , multiplying we get :594, Not an option
7+8+10 : 25, multiplying we get :560

Here is our answer. IMO D
If you don't know any formula to extract exact values, Surely a understanding that trying with minimum no.s will help.
Cheers,
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Re: If the sum of three distinct positive integers is 25, what is the maxi [#permalink] If the sum of three distinct positive integers is 25, what is the maxi   20 May 2020, 06:32
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If the sum of three distinct positive integers is 25, what is the maximum value of their product?

A. 44
B. 120
C. 420
D. 560
E. 920

To maximize a product, the numbers should be as closely spaced as possible.

For three distinct positive numbers, a+b+c = 25, they can be 7, 8 and 10 (since they can't be equal)

So, 7x8x10 = 560. Answer is D
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Re: If the sum of three distinct positive integers is 25, what is the maxi [#permalink] If the sum of three distinct positive integers is 25, what is the maxi   28 Aug 2023, 10:44
8X8X9= 576
8+8+9=25
how to solve then?
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Re: If the sum of three distinct positive integers is 25, what is the maxi [#permalink] If the sum of three distinct positive integers is 25, what is the maxi   26 Sep 2024, 17:23
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