Positive integers are written on all the faces of a cube, one on each. At each corner (vertex) of the cube, the product of the numbers on the faces that meet at the corner is written. The sum of the numbers written at all the comer is 2004.

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Positive integers are written on all the faces of a cube, one on each. At each corner (vertex) of the cube, the product of the numbers on the faces that meet at the corner is written. The sum of the numbers written at all the comer is 2004. If T denotes the sum of the number on all the faces, the possible value of T are

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Correct answer: D. 505

Let A B C D P Q R S be a cube, the numbers a, b, c, d, e, f be written on the faces ade +a b e+a b f+a d f+c d e+b c e+b c f+c d f=2004 (e+f)(a+c)(b+d)=2^2 3 167 Possible combination are 4 3 167,2 6 167,2 3 334,2 2 501T=a+b+c+d+e+f=174,175,339 , or 505

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