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# Out of all the points on line 3x + 2y = 6, where x & y are integers

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Manager
Joined: 08 Apr 2017
Posts: 83
Out of all the points on line 3x + 2y = 6, where x & y are integers  [#permalink]

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29 May 2018, 18:24
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00:00

Difficulty:

75% (hard)

Question Stats:

60% (02:23) correct 40% (02:30) wrong based on 52 sessions

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Out of all the points on line 3x + 2y = 6, where x & y are integers and |y|<12. What is the probability |x| = |y|?

A. $$\frac{1}{3}$$

B. $$\frac{1}{7}$$

C. $$\frac{2}{7}$$

D. $$\frac{1}{2}$$

E. $$\frac{2}{3}$$
Manager
Joined: 28 Nov 2017
Posts: 145
Location: Uzbekistan
Re: Out of all the points on line 3x + 2y = 6, where x & y are integers  [#permalink]

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29 May 2018, 21:43
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GMATSkilled wrote:
Out of all the points on line 3x + 2y = 6, where x & y are integers and |y|<12. What is the probability |x| = |y|?

A. $$\frac{1}{3}$$

B. $$\frac{1}{7}$$

C. $$\frac{2}{7}$$

D. $$\frac{1}{2}$$

E. $$\frac{2}{3}$$

$$3x=-2y+6$$,
$$x=-\frac{2}{3}y+2$$.
If $$x$$ and $$y$$ are integers, then $$y$$ must be divisible by $$3$$, and also $$-12<y<12$$. Thus $$y=-9,-6,-3,0,3,6,9$$.

Respective values of $$x$$ are: $$8,6,4,2,0,-2,-4$$.

So, only option out of $$7$$, where $$|x|=|y|$$ is $$(6,-6)$$.

Hence $$P=\frac{1}{7}$$

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Tulkin.

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Joined: 08 Sep 2016
Posts: 117
Re: Out of all the points on line 3x + 2y = 6, where x & y are integers  [#permalink]

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30 May 2018, 16:06
Why wouldn't 0 be conisdered for this question? Although |0| = 0, isn't it also equal to |0|?
Manager
Joined: 28 Nov 2017
Posts: 145
Location: Uzbekistan
Re: Out of all the points on line 3x + 2y = 6, where x & y are integers  [#permalink]

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30 May 2018, 21:13
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hdavies wrote:
Why wouldn't 0 be conisdered for this question? Although |0| = 0, isn't it also equal to |0|?

Point $$(0,0)$$ cannot meet the condition $$3x + 2y = 6$$.

Hope this helps!
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Tulkin.

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Joined: 17 Jan 2017
Posts: 137
Location: India
GPA: 4
WE: Information Technology (Computer Software)
Re: Out of all the points on line 3x + 2y = 6, where x & y are integers  [#permalink]

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03 Aug 2018, 12:13
I chose the least probability i.e., 1/7 without any calculation.

3x+2y=6 can't have many solutions when x=y. Hence the probability will be very very low.

A technique to guess when you don't have time

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Re: Out of all the points on line 3x + 2y = 6, where x & y are integers &nbs [#permalink] 03 Aug 2018, 12:13
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