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

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Director
Joined: 20 Jul 2017
Posts: 636
Location: India
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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03 Aug 2019, 22:40
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65% (hard)

Question Stats:

58% (02:19) correct 42% (02:04) wrong based on 31 sessions

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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
Manager
Joined: 19 Apr 2017
Posts: 172
Concentration: General Management, Sustainability
Schools: ESSEC '22
GPA: 3.9
WE: Operations (Hospitality and Tourism)
3y + 2|x| = 33. How many positive integral values of (x, y) are  [#permalink]

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04 Aug 2019, 11:09
2
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]

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
3y + 2|x| = 33. How many positive integral values of (x, y) are   [#permalink] 04 Aug 2019, 11:09
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