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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.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS 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 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
Re: If x is to be chosen at random from the set {1, 2, 3, 4} and   [#permalink] 07 Apr 2014, 03:46
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