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

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

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New post 29 May 2018, 18:24
5
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A
B
C
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Difficulty:

  75% (hard)

Question Stats:

61% (03:03) correct 39% (02:30) wrong based on 54 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. \(\frac{2}{3}\)
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Re: Out of all the points on line 3x + 2y = 6, where x & y are integers  [#permalink]

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New post 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 \(P=\frac{1}{7}\)

Answer: B
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Re: Out of all the points on line 3x + 2y = 6, where x & y are integers  [#permalink]

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

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New post 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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Re: Out of all the points on line 3x + 2y = 6, where x & y are integers  [#permalink]

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New post 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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