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If any number from set A is multiplied by any number from set B, what

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If any number from set A is multiplied by any number from set B, what [#permalink]

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If any number from set A is multiplied by any number from set B, what is the probability that the product is a multiple of 4?
A = {21, 22, 23, 24, 25} B = {23, 24, 25, 26, 27}

Correct Answer:
[Reveal] Spoiler:
2/5

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Re: If any number from set A is multiplied by any number from set B, what [#permalink]

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New post 23 Apr 2010, 10:51
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gmatt14 wrote:
If any number from set A is multiplied by any number from set B, what is the probability that the product is a multiple of 4?
A = {21, 22, 23, 24, 25} B = {23, 24, 25, 26, 27}

Correct Answer: 2/5

How would you approach this? Please, explain in a simple way!

Thx.


Probability = required cases/total cases

total cases = 5*5 = 25
required cases:
if the number in A is 21...possibility in B = 24 only. -----1
if in A-> 22 ..in B -. 24 and 26---------2
if in A-< 23 in B 24 only -------------1
if in A ->25 in B -> 24 only -----------1
if in A 24 in B -> all the 5-------------5

add all the cases we get 10

probability = 10/25 =2/5
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Last edited by gurpreetsingh on 23 Apr 2010, 10:56, edited 1 time in total.

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Re: If any number from set A is multiplied by any number from set B, what [#permalink]

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New post 23 Apr 2010, 10:54
sorry, but the correct answer is 2/5.
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Re: If any number from set A is multiplied by any number from set B, what [#permalink]

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New post 23 Apr 2010, 10:57
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gmatt14 wrote:
sorry, but the correct answer is 2/5.


I have updated my post.
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Re: If any number from set A is multiplied by any number from set B, what [#permalink]

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New post 23 Apr 2010, 11:04
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gmatt14 wrote:
If any number from set A is multiplied by any number from set B, what is the probability that the product is a multiple of 4?
A = {21, 22, 23, 24, 25} B = {23, 24, 25, 26, 27}

Correct Answer: 2/5

How would you approach this? Please, explain in a simple way!

Thx.

first we need to count how many numbers are there when a number from set A is multiplied by a number from set B is divisible by 4.
let's start with 21 from set A, there is only one number we will get when 21 is multiplied by any number of set B which is divisible by 4. i.e. 21*24
when we take 22 from the set and multiply with numbers from set 2, there are 2 numbers namely 22*24 and 22*26 will be divisible 4.
similarly, from 23 there is only number i.e. 23*24
for 24 all the numbers are divisible by 4..
and for 25 again only one number will be divisible by 4.
so total number that can be divisible 4 = 1+2+1+5+1 = 10 ways

now we need to get all the possibilities = each number of set A can be multiplied with set B numbers in 5ways
so, total number of ways for multiplication of set A to set B = 5* = 25

therefore required probability = 10/25 = 2/5

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Re: If any number from set A is multiplied by any number from set B, what [#permalink]

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New post 23 Apr 2010, 11:07
Thx a lot.....;-)

But applying your procedure seems taking longer than 2 minutes............

Is there a short cut?
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Re: If any number from set A is multiplied by any number from set B, what [#permalink]

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New post 23 Apr 2010, 11:24
gmatt14 wrote:
Thx a lot.....;-)

But applying your procedure seems taking longer than 2 minutes............

Is there a short cut?


If you follow the steps above it will take 1 min or at most 1.5 minutes.
You dont have to write subjective ans, skip the steps and answer it quickly.
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Re: If any number from set A is multiplied by any number from set B, what [#permalink]

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Re: If any number from set A is multiplied by any number from set B, what [#permalink]

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New post 25 Sep 2017, 17:04
gmatt14 wrote:
If any number from set A is multiplied by any number from set B, what is the probability that the product is a multiple of 4?
A = {21, 22, 23, 24, 25} B = {23, 24, 25, 26, 27}

Correct Answer:
[Reveal] Spoiler:
2/5


We could have the following three cases:

Case 1:
If a number from set A is not a multiple of 2, then the number from set B must be a multiple of 4 in order for the product to be divisible by 4. The probability of this scenario is 3/5 x 1/5 = 3/25.

Case 2:
If a number from set A is a multiple of 2 but not a multiple of 4, then the number from set B must be a multiple of 2 or 4 for the product to be divisible by 4. The probability of this scenario is 1/5 x 2/5 = 2/25.

Case 3:
If a number from set A is a multiple of 4, then any number from set B will make the product divisible by 4. The probability of this scenario is 1/5 x 5/5 = 5/25.

Thus, the overall probability is 3/25 + 2/25 + 5/25 = 10/25 = 2/5.

Alternate Solution:

The total number of ways to pick one element from set A and one element from set B is 5C1 x 5C1 = 5 x 5 = 25.

The pairs of elements (where the first number comes from set A and the second number comes from set B) where the product is a multiple of 4 are (21, 24), (22, 24), (22, 26), (23, 24), (24, 23), (24, 24), (24, 25), (24, 26), (24, 27), and (25, 24).

Since there are 10 favorable outcomes from a total of 25 outcomes, the probability is 10/25 = 2/5.
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Re: If any number from set A is multiplied by any number from set B, what   [#permalink] 25 Sep 2017, 17:04
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