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# Two sets are defined as follows (m25#17)

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CIO
Joined: 02 Oct 2007
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Two sets are defined as follows (m25#17) [#permalink]

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15 Feb 2012, 06:51
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Two sets are defined as follows:
$$\begin{eqnarray*} X &=& (4, 5, 8)\\ Y &=& (-1, 1, 2)\\ \end{eqnarray*}$$

If a number is taken from set $$X$$ at random and another number is taken from set $$Y$$ at random, what is the probability that the sum of these numbers will be an even integer?

(A) $$\frac{2}{9}$$
(B) $$\frac{1}{3}$$
(C) $$\frac{4}{9}$$
(D) $$\frac{5}{9}$$
(E) $$\frac{2}{3}$$
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Last edited by Bunuel on 15 Oct 2012, 10:28, edited 1 time in total.
OA edited.

Kudos [?]: 987 [0], given: 334

Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4501

Kudos [?]: 8780 [1], given: 106

Re: Two sets are defined as follows (m25#17) [#permalink]

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17 Feb 2012, 12:40
1
KUDOS
Expert's post
Hi, there. I'm happy to help with this.

Big idea #1:
(even) + (even) = even
(odd) + (odd) = even
but . . .
(odd) + (even) = odd

There are nine combinations here (any of the three of the first set with any of the three of the second set). The results are shown in the matrix attached (odds = green, evens = red).

Of the nine cases, five are odd.

[Reveal] Spoiler:

Does this make sense? Please let me know if anyone reading this has any questions on what I've said.

Mike
Attachments

matrix of odd & even sums.JPG [ 15.37 KiB | Viewed 2538 times ]

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Mike McGarry
Magoosh Test Prep

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Last edited by mikemcgarry on 15 Oct 2012, 13:07, edited 1 time in total.

Kudos [?]: 8780 [1], given: 106

Intern
Joined: 29 Dec 2011
Posts: 1

Kudos [?]: [0], given: 1

Re: Two sets are defined as follows (m25#17) [#permalink]

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07 Oct 2012, 04:07
As mentioned above for getting even we have 2 options e+e or o+o

set X SET Y

Considering E+E (selecting even from both the set )

2C1(4,8) * 1C1(2) =2

Considering O+O (selecting even from both the set )
1C1(5) * 2C1(-1,1)=2

As both the cases are independent of each other we will add the possibilities i.e 2+2=4

Total cases = 3C1*3C1 =9

required probability = desired outcome /total outcome =4/9 Ans

Hope it helps!

Sid

Kudos [?]: [0], given: 1

Senior Manager
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Re: Two sets are defined as follows (m25#17) [#permalink]

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15 Oct 2012, 10:23

i got 4/9...
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Kudos [?]: 238 [0], given: 82

Math Expert
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Kudos [?]: 133099 [0], given: 12408

Re: Two sets are defined as follows (m25#17) [#permalink]

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15 Oct 2012, 10:29
sanjoo wrote:

i got 4/9...

OA for this question is 4/9 not 5/9.
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Kudos [?]: 133099 [0], given: 12408

Manager
Joined: 24 Apr 2013
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Schools: Duke '16
If a numer is taken from set X [#permalink]

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20 May 2013, 15:21
If a number is taken from set X at random and another number is taken from set Y at random, what is the probability that the sum of these numbers will be an even integer?

29
13
49
59
23

Kudos [?]: 11 [0], given: 76

Math Expert
Joined: 02 Sep 2009
Posts: 42323

Kudos [?]: 133099 [0], given: 12408

Re: If a numer is taken from set X [#permalink]

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20 May 2013, 15:24
If a number is taken from set X at random and another number is taken from set Y at random, what is the probability that the sum of these numbers will be an even integer?

29
13
49
59
23

Merging similar topics.

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Kudos [?]: 133099 [0], given: 12408

Re: If a numer is taken from set X   [#permalink] 20 May 2013, 15:24
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# Two sets are defined as follows (m25#17)

Moderator: Bunuel

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