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Permutations and Combinations
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Krisha Rao
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What is the integral number of solution for the equation x + 5y + 10z = 50?
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GMATGuruNY
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If x, y and z can be negative, then the number of solutions is infinite.
Perhaps the following reflects the intent of the problem above:
Since x must be positive, y can be any integer between 1 and 7, inclusive.
Total number of options = 7.
If z=2, then x+5y = 30, with the result that x=30-5y.
Since x must be positive, y can be any integer between 1 and 5, inclusive.
Total number of options = 5.
If z=3, then x+5y = 20, with the result that x=20-5y.
Since x must be positive, y can be any integer between 1 and 3, inclusive.
Total number of options = 3.
If z=4, then x+5y = 10, with the result that x=10-5y.
Since x must be positive, y = 1.
Total number of options = 1.
Total number of solutions = 7+5+3+1 = 16.
Perhaps the following reflects the intent of the problem above:
If z=1, then x+5y = 40, with the result that x=40-5y.What is the total number of solutions for the equation x + 5y + 10z = 50 such that x, y and z are positive integers?
Since x must be positive, y can be any integer between 1 and 7, inclusive.
Total number of options = 7.
If z=2, then x+5y = 30, with the result that x=30-5y.
Since x must be positive, y can be any integer between 1 and 5, inclusive.
Total number of options = 5.
If z=3, then x+5y = 20, with the result that x=20-5y.
Since x must be positive, y can be any integer between 1 and 3, inclusive.
Total number of options = 3.
If z=4, then x+5y = 10, with the result that x=10-5y.
Since x must be positive, y = 1.
Total number of options = 1.
Total number of solutions = 7+5+3+1 = 16.
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I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
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As a tutor, I don't simply teach you how I would approach problems.
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For more information, please email me (Mitch Hunt) at [email protected].
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Hi Krishna Rao,
When posting questions, you should make sure to post the ENTIRE question. If this is a Problem Solving question, then you should include the 5 answer choices (and post it in the PS forum). If it's a DS question, then you need to post the two Facts that appear as part of the prompt.
GMAT assassins aren't born, they're made,
Rich
When posting questions, you should make sure to post the ENTIRE question. If this is a Problem Solving question, then you should include the 5 answer choices (and post it in the PS forum). If it's a DS question, then you need to post the two Facts that appear as part of the prompt.
GMAT assassins aren't born, they're made,
Rich
