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If any number from set A is multiplied by any number from set B, what
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23 Apr 2010, 11:43
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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:
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Re: If any number from set A is multiplied by any number from set B, what
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Updated on: 23 Apr 2010, 11:56
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 262 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 55 add all the cases we get 10 probability = 10/25 =2/5
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Originally posted by gurpreetsingh on 23 Apr 2010, 11:51.
Last edited by gurpreetsingh on 23 Apr 2010, 11:56, 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
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23 Apr 2010, 11:54
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
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23 Apr 2010, 11:57
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
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23 Apr 2010, 12:04
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: 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
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23 Apr 2010, 12:07
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
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23 Apr 2010, 12:24
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
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25 Sep 2017, 18:04
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: 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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