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gmatt14
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If any number from set A is multiplied by any number from set B, what 23 Apr 2010, 11:43
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75% (hard)

Question Stats:

50% (02:07) correct 50% (02:08) wrong based on 113 sessions

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A = {21, 22, 23, 24, 25}
B = {23, 24, 25, 26, 27}

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. 8/25
B. 9/25
C. 2/5
D. 3/5
E. 4/5
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C
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If any number from set A is multiplied by any number from set B, what Updated on: 23 Apr 2010, 11:56
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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gmatt14
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.
Show more

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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If any number from set A is multiplied by any number from set B, what 23 Apr 2010, 12:04
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gmatt14
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.
Show more
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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If any number from set A is multiplied by any number from set B, what 23 Apr 2010, 12:07
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Thx a lot.....;-)

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

Is there a short cut?
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If any number from set A is multiplied by any number from set B, what 23 Apr 2010, 12:24
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gmatt14
Thx a lot.....;-)

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

Is there a short cut?
Show more

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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If any number from set A is multiplied by any number from set B, what 25 Sep 2017, 18:04
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gmatt14
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:
Show Spoiler
2/5
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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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If any number from set A is multiplied by any number from set B, what 02 Feb 2024, 07:49
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The following is the logic I applied. Please let me know why the answer is correct even though I did not consider the case of 22 times 26.

From both the sets (A and B), we can clearly see that only 24 is the number that can break down to give a factor of 4.
Thus, if you pick any number from set A, the number from set B MUST be 24 OR if you pick any number from set B, the number from set A MUST be 24.
Both the sets have 5 numbers each. And Total possibilities of picking the numbers will be 5*5 as no restriction on repetition of the numbers has been given. So, the calculation will be as follows:
[(Any # from A * Only 24 from B)+ (Any # from B * Only 24 from A)] / Total possibilities of picking the numbers

[(5*1) + (5*1)] / 5*5
= [5+5]/25
=10/25
=2/5
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