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Four positive integers A, B, C and D have a sum of 36. If A+2 = B-2 = C+2 = D-2, what is the value of the product ABCD?

 Jun 15, 2022
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A + 2  = B -2   →  B = A + 4

A + 2 = C + 2 →  A = C

A + 2 = D - 2 →   D = A + 4

 

So

 

A + B + C + D = 36

 

A + (A + 4)  + A  + (A + 4) =  36

 

4A  + 8 =  36

 

4A = 28

 

A = 7   C  = 7    B =  11     D =   11

 

ABCD =  7^2 * 11^2  =    5929

 

 

cool cool cool

 Jun 15, 2022

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