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anonymous

  • one year ago

Can you solve this? There are four girls and 2 boys in a study group on a test (with each problem worth the same value), each of the 6 students solved a different number of problems. The highest-scoring student solving 10 problems and the lowest-scoring student solving 4 problems. The highest scoring girl solved 4 more problems than the lowest-scoring boy The highest scoring boy solved 4 more problems than the lowest-scoring girl QUESTION: How many problems did the highest scoring boy solve?

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  1. mathstudent55
    • one year ago
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    |dw:1435632689410:dw|

  2. mathstudent55
    • one year ago
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    The girls are listed from G1 to G4 with G1 being the highest scoring girl to G4 being the lowest scoring girl. The same is done with the boys, B1 scored higher than B2

  3. mathstudent55
    • one year ago
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    |dw:1435632840162:dw|

  4. mathstudent55
    • one year ago
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    Now we know the highest scoring student scored 10. Let's first assume that the highest scoring student is the highest scoring girl.

  5. mathstudent55
    • one year ago
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    |dw:1435632978843:dw|

  6. mathstudent55
    • one year ago
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    Since the lowest scoring by has 6, and the lowest score of all is 4, that must be a girl.

  7. mathstudent55
    • one year ago
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    That makes the higher scoring boy score an 8. |dw:1435633064742:dw|

  8. mathstudent55
    • one year ago
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    Now we need to make the other assumption.

  9. mathstudent55
    • one year ago
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    Let's assume it's the higher scoring boy who got the 10.

  10. mathstudent55
    • one year ago
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    |dw:1435633167570:dw|

  11. mathstudent55
    • one year ago
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    With this assumption, we have the lowest girl score is 6 and the highest is 8. There are only 3 scores the girls could have had, 6, 7, and 8. There are 4 girls. That means two must have had the same score, but we were told each student had a different score, so this second assumption is incorrect. The first assumption is correct, and the higher boys' score is 8.

  12. anonymous
    • one year ago
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    Wow! I get it now. Thank you so much @mathstudent55 for answering my question.

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