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3y + 2|x| = 33. How many positive integral values of (x, y) are

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Director
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Joined: 20 Jul 2017
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Concentration: Entrepreneurship, Marketing
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3y + 2|x| = 33. How many positive integral values of (x, y) are  [#permalink]

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New post 03 Aug 2019, 22:40
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3y + 2|x| = 33. How many positive integral values of (x, y) are possible?

A. 5
B. 6
C. 10
D. 11
E. 12
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3y + 2|x| = 33. How many positive integral values of (x, y) are  [#permalink]

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New post 04 Aug 2019, 11:09
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1
How many positive integral values of (x, y) are possible?

Solution:
x,y must be positive and has to be an integer
\(3y + 2|x| = 33\)

\(2|x| = 33-3y\)
in the equation Right hand side must be an even number to balance LHS, for which y must be an odd number
=>since, odd-odd=even => 33 is odd... 3y must be odd

y cannot be >10 because |x| has to be >0 ( positive and integer)

y can be [1,3,5,7,9]

Answer A


To explain further \(2|x| = 33-3y\) => \(|x| = \frac{{33-3y}}{{2}}\) (To make |x| an even integer, \(\frac{{33-3y}}{{2}}\) should be equal to an even integer

\(2|x| = 33-3y\)
2|x| = 33-3=30=2*15
2|x| = 33-9=24=2*12
2|x| = 33-15=18=2*9
2|x| = 33-21=12=2*6
2|x| = 33-27=6=2*3
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3y + 2|x| = 33. How many positive integral values of (x, y) are   [#permalink] 04 Aug 2019, 11:09
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3y + 2|x| = 33. How many positive integral values of (x, y) are

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