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If 3x+2y = 22 and |2x| < 10, how many pair of values {x,y} exist where

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If 3x+2y = 22 and |2x| < 10, how many pair of values {x,y} exist where  [#permalink]

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New post 16 Feb 2019, 22:31
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If 3x+2y = 22 and |2x| < 10, how many pair of values {x,y} exist where x and y are both integers?

A. 5
B. 6
C. 7
D. 10
E. 14

Source: Experts Global

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If 3x+2y = 22 and |2x| < 10, how many pair of values {x,y} exist where  [#permalink]

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New post Updated on: 17 Feb 2019, 01:59
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pushpitkc wrote:
If 3x+2y = 22 and |2x| < 10, how many pair of values {x,y} exist where x and y are both integers?

A. 5
B. 6
C. 7
D. 10
E. 14

Source: Experts Global


|2x|<10

-10<2x<10

-5<x<5

we are looking for integer pair of both x and y.

x = -4, -3, -2, -1, 0, 1, 2, 3, 4.

3x + 2y = 22

2y = 22 - 3x

y =\(\frac{22 - 3x}{2}\)

Thus , 22 - 3x has to be even. It means x has to be even.

For each even integer of x , we will get an even value of y.

There are 5 even values of x. Thus, we will have 5 even values of y.

A is the correct answer.

Originally posted by KSBGC on 17 Feb 2019, 01:40.
Last edited by KSBGC on 17 Feb 2019, 01:59, edited 1 time in total.
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Re: If 3x+2y = 22 and |2x| < 10, how many pair of values {x,y} exist where  [#permalink]

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New post 17 Feb 2019, 01:50
Isn't the answer 9 since -5<x<5 and x is an integer?
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Re: If 3x+2y = 22 and |2x| < 10, how many pair of values {x,y} exist where  [#permalink]

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New post 17 Feb 2019, 02:12
Hello ,
-5<x< 5 , so 9 is not the value x can take .

Also , 22x- 3y should be an even number .

So only 5 integer values of x will make it even number ,

-4, -2,0,2,4

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Re: If 3x+2y = 22 and |2x| < 10, how many pair of values {x,y} exist where   [#permalink] 17 Feb 2019, 02:12
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