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Senior Manager  Joined: 21 Oct 2013
Posts: 411
If a is a number that is randomly selected from Set A, and b  [#permalink]

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7 00:00

Difficulty:   35% (medium)

Question Stats: 72% (01:41) correct 28% (01:37) wrong based on 195 sessions

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A = {0, 1, -3, 6, -8}
B = {-1, 2, -4, 7}

If a is a number that is randomly selected from Set A, and b is a number that is randomly selected from Set B, what is the probability that ab > 0?

A. 1/4
B. 1/3
C. 2/5
D. 4/9
E. 1/2

OE
Probability = (Desired outcomes / Possible outcomes)

Possible outcomes:
5 integers in Set A & 4 in Set B. An integer in Set A may be paired with each integer in Set B for total of 4 pairs. However, 5 integers in Set A → Overall 5 x 4 possible outcomes for ab.

Find how many positive & negative pairs are possible.
Set A contains 2 positive integers (1, 6), & Set B contains 2 positive integers (2, 7).
Together, they form 2 x 2 = 4 pairs.
Likewise, Set A contains 2 negative integers (-3, -8), & Set B contains 2 negative integers (-1, -4).
Together, they form 2 x 2 = 4 pairs.
0, member of Set A, is neither positive nor negative, and its product with any number will always result in 0.

Question stem specifies that ab must be positive and greater than 0, so do not need to consider pairs that contain 0 when finding desirable outcomes.

(Desired outcomes / Possible outcomes) = (4 + 4) / 20 = 8 / 20 = 2/5

Hi, I want to know whether OE is the fastest way to solve this question, please.

Originally posted by goodyear2013 on 06 Feb 2014, 05:57.
Last edited by Bunuel on 07 Feb 2014, 04:45, edited 1 time in total.
Edited the question.
Intern  Joined: 30 Nov 2013
Posts: 20
Re: If a is a number that is randomly selected from Set A, and b  [#permalink]

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1
goodyear2013 wrote:
A = {0, 1, -3, 6, -8}
B = {-1, 2, -4, 7}
If a is a number that is randomly selected from Set A, and b is a number that is randomly selected from Set B, what is the probability that ab > 0?
1/4
1/3
2/5
4/9
1/2

OE
Probability = (Desired outcomes / Possible outcomes)

Possible outcomes:
5 integers in Set A & 4 in Set B. An integer in Set A may be paired with each integer in Set B for total of 4 pairs. However, 5 integers in Set A → Overall 5 x 4 possible outcomes for ab.

Find how many positive & negative pairs are possible.
Set A contains 2 positive integers (1, 6), & Set B contains 2 positive integers (2, 7).
Together, they form 2 x 2 = 4 pairs.
Likewise, Set A contains 2 negative integers (-3, -8), & Set B contains 2 negative integers (-1, -4).
Together, they form 2 x 2 = 4 pairs.
0, member of Set A, is neither positive nor negative, and its product with any number will always result in 0.

Question stem specifies that ab must be positive and greater than 0, so do not need to consider pairs that contain 0 when finding desirable outcomes.

(Desired outcomes / Possible outcomes) = (4 + 4) / 20 = 8 / 20 = 2/5

Hi, I want to know whether OE is the fastest way to solve this question, please.

I am happy to help with that !! First you should pick one scenario in which you can get a positive number so let's say you pick "1" from Set A and "2" from Set B so probability of picking "1" is 1/5 and probability of picking "4" from Set B is 1/4 , count how many times this scenario can happen you will find that it is 8 times !! so 8*(1/5*1/4)= 8/20=2/5 !!! Hope it was clear Math Expert V
Joined: 02 Sep 2009
Posts: 58435
Re: If a is a number that is randomly selected from Set A, and b  [#permalink]

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2
goodyear2013 wrote:
A = {0, 1, -3, 6, -8}
B = {-1, 2, -4, 7}

If a is a number that is randomly selected from Set A, and b is a number that is randomly selected from Set B, what is the probability that ab > 0?

A. 1/4
B. 1/3
C. 2/5
D. 4/9
E. 1/2

OE
Probability = (Desired outcomes / Possible outcomes)

Possible outcomes:
5 integers in Set A & 4 in Set B. An integer in Set A may be paired with each integer in Set B for total of 4 pairs. However, 5 integers in Set A → Overall 5 x 4 possible outcomes for ab.

Find how many positive & negative pairs are possible.
Set A contains 2 positive integers (1, 6), & Set B contains 2 positive integers (2, 7).
Together, they form 2 x 2 = 4 pairs.
Likewise, Set A contains 2 negative integers (-3, -8), & Set B contains 2 negative integers (-1, -4).
Together, they form 2 x 2 = 4 pairs.
0, member of Set A, is neither positive nor negative, and its product with any number will always result in 0.

Question stem specifies that ab must be positive and greater than 0, so do not need to consider pairs that contain 0 when finding desirable outcomes.

(Desired outcomes / Possible outcomes) = (4 + 4) / 20 = 8 / 20 = 2/5

Hi, I want to know whether OE is the fastest way to solve this question, please.

For the product of 2 numbers to be positive either both of them must be positive or both of them must be negative:

P(positive, positive) = 2/5*2/4 = 4/20;
P(negative, negative) = 2/5*2/4 = 4/20.

P = 4/20 + 4/20 = 8/20 = 2/5.

Hope it's clear.
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Intern  Joined: 01 Aug 2006
Posts: 31
Re: If a is a number that is randomly selected from Set A, and b  [#permalink]

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Pick both +ve: 2/5 * 2/4 =1/5.
Pick both -ve: 2/5 * 2/4 = 1/5.
Required prob = 1/5 + 1/5 = 2/5.

Remember: "0" is neither +ve nor -ve.
EMPOWERgmat Instructor V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15271
Location: United States (CA)
GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: If a is a number that is randomly selected from Set A, and b  [#permalink]

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1
HI All,

As far as probability questions are concerned, this one is fairly straight-forward. Even if you're not perfectly knowledgeable about all of the variations that probability questions can take and/or you might not be comfortable with all of the math 'steps' involved, you can still answer this question with a bit of 'brute force'...

A = {0, 1, -3, 6, -8}
B = {-1, 2, -4, 7}

Since Set A has 5 terms and Set B has 4 terms, there are (5)(4) different 'pairs' of numbers that can be selected. We're asked for the probability that the product of that pair is POSITIVE. We can simply list out the possible pairs that fit this restriction:

1 and 2
1 and 7
-3 and -1
-3 and -4
6 and 2
6 and 7
-8 and -1
-8 and -4

There are 8 pairs (out of 20 possible) that fit what we're looking for. 8/20 = 2/5

GMAT assassins aren't born, they're made,
Rich
_________________
Senior Manager  S
Joined: 12 Sep 2017
Posts: 302
Re: If a is a number that is randomly selected from Set A, and b  [#permalink]

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Hello everyone!

I understood the problem but, does anyone know why at the end we need to sum instead of multiply the possibilities of +ve and -ve?

P = 4/20 + 4/20 = 8/20 = 2/5

Kind regards!
EMPOWERgmat Instructor V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15271
Location: United States (CA)
GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: If a is a number that is randomly selected from Set A, and b  [#permalink]

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1
jfranciscocuencag wrote:
Hello everyone!

I understood the problem but, does anyone know why at the end we need to sum instead of multiply the possibilities of +ve and -ve?

P = 4/20 + 4/20 = 8/20 = 2/5

Kind regards!

Hi jfranciscocuencag,

When a question asks for a TOTAL, then addition is always a possible 'approach.' Multiplication is SOMETIMES a possible approach (depending on what you're asked for and how the various pieces of information relate to one another).

A = {0, 1, -3, 6, -8}
B = {-1, 2, -4, 7}

Here, Set A has 5 elements and Set B has 4 elements. The TOTAL number of pairs (meaning 1 element from Set A and one element from Set B) can be determined either by listing out every possible pair (re: addition) or by multiplying 5 and 4 (since the nature of the question requires all possible pairs, multiplication is an option since it leads to that total result).

The total probability that we're asked to solve for here requires that we define 2 DIFFERENT groups (every pair of 2 POSITIVE terms and every pair of 2 NEGATIVE terms). Obviously, addition is an option - since we can total up those DIFFERENT options and get a grand TOTAL. Those two groups have NOTHING to do with one another though, so there's no logical reason to multiply those results (and doing so would NOT lead to the correct answer.

GMAT assassins aren't born, they're made,
Rich
_________________
Senior Manager  S
Joined: 12 Sep 2017
Posts: 302
Re: If a is a number that is randomly selected from Set A, and b  [#permalink]

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EMPOWERgmatRichC wrote:
jfranciscocuencag wrote:
Hello everyone!

I understood the problem but, does anyone know why at the end we need to sum instead of multiply the possibilities of +ve and -ve?

P = 4/20 + 4/20 = 8/20 = 2/5

Kind regards!

Hi jfranciscocuencag,

When a question asks for a TOTAL, then addition is always a possible 'approach.' Multiplication is SOMETIMES a possible approach (depending on what you're asked for and how the various pieces of information relate to one another).

A = {0, 1, -3, 6, -8}
B = {-1, 2, -4, 7}

Here, Set A has 5 elements and Set B has 4 elements. The TOTAL number of pairs (meaning 1 element from Set A and one element from Set B) can be determined either by listing out every possible pair (re: addition) or by multiplying 5 and 4 (since the nature of the question requires all possible pairs, multiplication is an option since it leads to that total result).

The total probability that we're asked to solve for here requires that we define 2 DIFFERENT groups (every pair of 2 POSITIVE terms and every pair of 2 NEGATIVE terms). Obviously, addition is an option - since we can total up those DIFFERENT options and get a grand TOTAL. Those two groups have NOTHING to do with one another though, so there's no logical reason to multiply those results (and doing so would NOT lead to the correct answer.

GMAT assassins aren't born, they're made,
Rich

Thank you EMPOWERgmatRichC !

Now is clear for me. Re: If a is a number that is randomly selected from Set A, and b   [#permalink] 19 Jan 2019, 17:50
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