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If x is to be chosen at random from the set {1, 2, 3, 4} and

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If x is to be chosen at random from the set {1, 2, 3, 4} and [#permalink] New post 05 Feb 2014, 01:29
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The Official Guide For GMAT® Quantitative Review, 2ND Edition

If x is to be chosen at random from the set {1, 2, 3, 4} and y is to be chosen at random from the set {5, 6, 7}, what is the probability that xy will be even?

(A) 1/6
(B) 1/3
(C) 1/2
(D) 2/3
(E) 5/6

Problem Solving
Question: 79
Category: Arithmetic; Algebra Probability; Concepts of sets
Page: 72
Difficulty: 600


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Re: If x is to be chosen at random from the set {1, 2, 3, 4} and [#permalink] New post 05 Feb 2014, 01:29
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SOLUTION

If x is to be chosen at random from the set {1, 2, 3, 4} and y is to be chosen at random from the set {5, 6, 7}, what is the probability that xy will be even?

(A) 1/6
(B) 1/3
(C) 1/2
(D) 2/3
(E) 5/6

Probably the best way to solve would be to use 1 - P(opposite event) = 1 - P(odd) = 1 - P(odd)*P(odd) = 1 - 2/4*2/3 = 8/12 = 2/3.

Answer: D.
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Re: If x is to be chosen at random from the set {1, 2, 3, 4} and [#permalink] New post 05 Feb 2014, 07:36
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Ans D

In order to make even nos. by multiplication,
we should have even * odd, odd * even or even * even

Total even nos. possible by multiplying nos. from the 2 sets:
(1*6);
2* any of the three from Set B;
3*6;&
4* any of the three from set B
1+3+1+3=8

Total possibilities=4 * 3=12

P(event)=8/12 or 2/3
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Re: If x is to be chosen at random from the set {1, 2, 3, 4} and [#permalink] New post 07 Feb 2014, 11:28
AKG1593 wrote:
Ans D

In order to make even nos. by multiplication,
we should have even * odd, odd * even or even * even

Total even nos. possible by multiplying nos. from the 2 sets:
(1*6);
2* any of the three from Set B;
3*6;&
4* any of the three from set B
1+3+1+3=8

Total possibilities=4 * 3=12

P(event)=8/12 or 2/3



I agree with you. But today, when I took the GMAT I encountered a similar question and my answer (according to that logic) wasn't there in the answer choices... So I assume it's not right..
I had x chosen at random from the numbers from 0 to 2 inclusive and y chosen at random from the numbers from 0 to 6 inclusive, what's the probability that x>y?
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Re: If x is to be chosen at random from the set {1, 2, 3, 4} and [#permalink] New post 07 Feb 2014, 11:42
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x*y is even only when they're both even or one of them is odd. The probability of any single outcome is given by 1/3*1/4 = 1/12.
Working through possible outcomes, we arrive at 8/12 -> 2/3, hence (D).

It took me around a minute and 40 seconds to solve this, I'm sure that a faster approach exists, waiting for others.
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Re: If x is to be chosen at random from the set {1, 2, 3, 4} and [#permalink] New post 07 Feb 2014, 11:56
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At least one of the numbers must be even.
Both even: 1/2 * 1/3 = 1/6.
At least one even: even from first set and odd from second set: 1/2 * 2/3 = 1/3
At least one even: odd from first set and even from second set: 1/2 * 1/3 = 1/6
Reqd prob = 1/6 + 1/3 + 1/6 = 2/3.
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Re: If x is to be chosen at random from the set {1, 2, 3, 4} and [#permalink] New post 07 Feb 2014, 20:58
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3 Scenario's

E * E = 2/4 * 1/3 = 1/6 ----- 1

E * O= 2/4 * 2/3 = 4/12-----2

O* E = 2/4 *1/3 = 2/12------3

Add 1+2+3 ==> 2/3 ----------D
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Re: If x is to be chosen at random from the set {1, 2, 3, 4} and [#permalink] New post 08 Feb 2014, 03:08
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SOLUTION

If x is to be chosen at random from the set {1, 2, 3, 4} and y is to be chosen at random from the set {5, 6, 7}, what is the probability that xy will be even?

(A) 1/6
(B) 1/3
(C) 1/2
(D) 2/3
(E) 5/6

Probably the best way to solve would be to use 1 - P(opposite event) = 1 - P(odd) = 1 - P(odd)*P(odd) = 1 - 2/4*2/3 = 8/12 = 2/3.

Answer: D.
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Re: If x is to be chosen at random from the set {1, 2, 3, 4} and [#permalink] New post 18 Feb 2014, 20:19
If x is to be chosen at random from the set {1, 2, 3, 4} and y is to be chosen at random from the set {5, 6, 7}, what is the probability that xy will be even?

(A) 1/6
(B) 1/3
(C) 1/2
(D) 2/3
(E) 5/6


The set {1, 2, 3, 4} contains 2 odd and 2 even numbers
The set {5, 6, 7} contains 2 odd and 1 even numbers

Possible even xy = 2*2 + 2*2 = 8 and possible odd xy = 2*2 = 4

So, probability that xy is even = 8/(8 + 4) = 2/3

Answer: (D)
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Re: If x is to be chosen at random from the set {1, 2, 3, 4} and [#permalink] New post 12 Mar 2014, 04:37
arunspanda wrote:
[color=#0000ff]

Possible even xy = 2*2 + 2*2 = 8 and possible odd xy = 2*2 = 4




how did you come up with this?
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Re: If x is to be chosen at random from the set {1, 2, 3, 4} and [#permalink] New post 12 Mar 2014, 06:05
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i just saw there were only 12 possibilities so counted all.
Time taken 1:10
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Re: If x is to be chosen at random from the set {1, 2, 3, 4} and [#permalink] New post 07 Apr 2014, 03:46
arunspanda wrote:
If x is to be chosen at random from the set {1, 2, 3, 4} and y is to be chosen at random from the set {5, 6, 7}, what is the probability that xy will be even?

(A) 1/6
(B) 1/3
(C) 1/2
(D) 2/3
(E) 5/6




I got it wrong the firs time, but 2nd time I used following method.

# of ways to select x = 4
# of ways to select y = 3
Total # of ways of getting xy = 4 * 3 = 12

If value of x is 1 then # of ways to get even value for xy = 1 (only 6 is possible value from set y)
If value of x is 2 then # of ways to get even value for xy = 3
If value of x is 3 then # of ways to get even value for xy = 1
If value of x is 4 then # of ways to get even value for xy = 3

Total # of ways to get desired outcome = 1+3+1+3 = 8

Probability = desired outcome/ all possible outcomes = 8/12 = 2/3

Choice D
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Probability- May i request you to help me in this one ? [#permalink] New post 27 Sep 2014, 06:34
If x is to be chosen at random from the set {1,2,3,4) and y is to be chosen at random from the set {5,6,7},what is the probability that xy will be even?
A) 1/6
B) 1/3
C) 1/2
D) 2/3
E) 5/6
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Re: Probability- May i request you to help me in this one ? [#permalink] New post 27 Sep 2014, 06:46
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xy will be even when either x or y or both are even.
Let's consider both x and y are old, so the product will be odd, not even. How many values can x take? There are only two odd values in the given set. Likewise, there are only two odd values possible for y. Since we want x and y to be odd, the total possible odd values for xy is 2*2=4.
Total number of possible xy values is 4*3=12 (x can take any 4 values from the set and y can take any 3 values from the set). So probability of xy to be odd is 4/12=1/3. So probability of xy to be even is 1-(probability of being odd) = 1-1/3 = 2/3.
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Probability- May i request you to help me in this one ? [#permalink] New post 27 Sep 2014, 06:50
Also, please read the rules of forum. The title should be the first part of the question. Requests need to be made in the body of the question. Also, before posting please use the search box. This question and explanation already exist.
search-results.xhtml?cx=009332468639467955845%3Ah-z9cduzcoi&cof=FORID%3A10&ie=UTF-8&q=If+x+is+to+be+chosen+at+random+from+the+set+

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Re: If x is to be chosen at random from the set {1, 2, 3, 4} and [#permalink] New post 27 Sep 2014, 11:42
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enggag wrote:
If x is to be chosen at random from the set {1,2,3,4) and y is to be chosen at random from the set {5,6,7},what is the probability that xy will be even?
A) 1/6
B) 1/3
C) 1/2
D) 2/3
E) 5/6


Merging similar topics. Please refer to the discussion above.

P.S. Please search before posting and name topics properly (rules 1 and 3: rules-for-posting-please-read-this-before-posting-133935.html).
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Re: If x is to be chosen at random from the set {1, 2, 3, 4} and   [#permalink] 27 Sep 2014, 11:42
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