Two distinct numbers a and b are chosen randomly from the set of first 20 positive integers. What is the probability that |a-b| would not be divisible by 3?
A. 49/380
B. 21/95
C. 49/190
D. 42/95
E. 133/190
OA is E.
I tried to do the list of possibilities but it is too large and I don't know how to use Probability here. Experts, can you show me how to solve this PS question?
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Two distinct numbers a and b are chosen
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Hi VJesus12,
There are a couple of different ways to approach this question, but you should pay attention to the answer choices - they provide a big potential 'shortcut' here (notice that 4 of the answers are LESS than 50%).
The question asks for the probability that (A-B) is NOT divisible by 3. To start, it's important to note that MOST integers are NOT divisible by 3, and since (A-B) will be an integer, it's likely that the correct answer is going to be greater than 50%. That having been said, here's how you can do a bit of work to prove it.
The real issue here is how A and B 'relate' to one another. We're dealing with distinct integers from 1-20, inclusive. As an example...
IF... A=20, then for (A-B) to be divisible by 3, B would have to be one of the following: 17, 14, 11, 8, 5 or 2. That's only 6 of the 19 possible options. 6/19 is about 1/3, so about 2/3 of the options would NOT lead to a result that was divisible by 3.
You can also take a look at a value of A that IS a multiple of 3....
IF... A=18, then for (A-B) to be divisible by 3, B would have to be one of the following: 15, 12, 9, 6 or 3. That's only 5 of the 19 possible options. 5/19 is less than 1/3, so over 2/3 of the options would NOT lead to a result that was divisible by 3.
Thus, regardless of the value that you pick for A, the limited number of options for B mean that MOST of the values for (A-B) will NOT be divisible by 3. The correct answer would have to be far greater than 50%, and there's only one answer that fits....
Final Answer: E
GMAT assassins aren't born, they're made,
Rich
There are a couple of different ways to approach this question, but you should pay attention to the answer choices - they provide a big potential 'shortcut' here (notice that 4 of the answers are LESS than 50%).
The question asks for the probability that (A-B) is NOT divisible by 3. To start, it's important to note that MOST integers are NOT divisible by 3, and since (A-B) will be an integer, it's likely that the correct answer is going to be greater than 50%. That having been said, here's how you can do a bit of work to prove it.
The real issue here is how A and B 'relate' to one another. We're dealing with distinct integers from 1-20, inclusive. As an example...
IF... A=20, then for (A-B) to be divisible by 3, B would have to be one of the following: 17, 14, 11, 8, 5 or 2. That's only 6 of the 19 possible options. 6/19 is about 1/3, so about 2/3 of the options would NOT lead to a result that was divisible by 3.
You can also take a look at a value of A that IS a multiple of 3....
IF... A=18, then for (A-B) to be divisible by 3, B would have to be one of the following: 15, 12, 9, 6 or 3. That's only 5 of the 19 possible options. 5/19 is less than 1/3, so over 2/3 of the options would NOT lead to a result that was divisible by 3.
Thus, regardless of the value that you pick for A, the limited number of options for B mean that MOST of the values for (A-B) will NOT be divisible by 3. The correct answer would have to be far greater than 50%, and there's only one answer that fits....
Final Answer: E
GMAT assassins aren't born, they're made,
Rich
