Name: Kevin

Who is asking: Student
Level: Middle

I cannot figure this one out:

A company manufactures golf balls. Golf balls are each numbered consecutively 0 to 4, and then the numbering starts over with zero again. Every 12th golf ball is yellow. Every 8th golf ball is tested for defects. The company produces 120,000 golf balls in an eight-hour shift.

A. How many yellow golf balls are tested for defects during the day? Explain your reasoning.

B. How many of these yellow balls that are tested are imprinted with the numeral 2? Explain your reasoning.


Hi Kevin,

Imagine also that the balls are numbered 1; 2; 3; 4;...;120,000. With this numbering the yellow balls are numbered

12; 24; 36; 48; 60;... and the balls that are tested for defects are numbered

8; 16; 24; 32; 40; 48;...

These two lists meet for the first time at 24 and then at 48, 72,... That is they meet at multiples of 24 since 24 is the smallest number that is a multiple of 8 and 12. Thus one ball in twenty-four is yellow and is tested for defects. Since  120,000/24 = 5,000, the number of balls that are yellow and are tested for defects is 5,000.

In the original numbering 0,1,2,3,4,0,1,2,3,4,... the balls with the numeral 2 are the balls which, in the new numbering, are numbered 3,8,13,... Can you now complete the problem?

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