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09 Feb 2015, 06:33
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
58% (01:35) correct
42%
(01:26)
wrong
based on 667
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If b is selected at random from Set A, what is the probability that b - 13 will be a prime number?
(1) A is a set of 10 integers
(2) A is a set of prime numbers
Kudos for a correct solution.
(1) A is a set of 10 integers
(2) A is a set of prime numbers
Kudos for a correct solution.
09 Feb 2015, 12:02
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(1) A is a set of 10 integers [Insufficient] There are infinite possibilities to what the ten integers could be.
(2) A is a set of prime numbers [Sufficient] The only even prime is 2. All the other primes are odd, meaning that n - 13 must result in an even number, because odd - odd = even. 15 is not a prime, so it cannot be included in Set A, and the difference between b and 13 cannot be 2. Therefore, the probability of b - 13 resulting in a prime number is zero.
The correct answer is B.
(2) A is a set of prime numbers [Sufficient] The only even prime is 2. All the other primes are odd, meaning that n - 13 must result in an even number, because odd - odd = even. 15 is not a prime, so it cannot be included in Set A, and the difference between b and 13 cannot be 2. Therefore, the probability of b - 13 resulting in a prime number is zero.
The correct answer is B.
09 Feb 2015, 12:02
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Hi Bunuel,
Is the answer (b) i.e. (2) can be used to answer the question.
If A is a set of prime nos, the probability will always be 0.
We know, all prime nos except 2 are odd. Also, (Odd no-Odd no) is an even no. So, for every no except 2 the difference b-13 will be even. Even if b is 2, then the difference will be -11 which is not a prime no as negative nos are not considered to be prime (in fact they are not even included in the definition of the prime nos).
So, whatever the no b is (if the set A is a set of prime nos), we will always get a non-prime difference. Hence the prob is 0.
If we consider (1), then we can have any set of 10 integers and we can take any value of b so that their difference can be a prime or cannot be a prime.
Is the answer (b) i.e. (2) can be used to answer the question.
If A is a set of prime nos, the probability will always be 0.
We know, all prime nos except 2 are odd. Also, (Odd no-Odd no) is an even no. So, for every no except 2 the difference b-13 will be even. Even if b is 2, then the difference will be -11 which is not a prime no as negative nos are not considered to be prime (in fact they are not even included in the definition of the prime nos).
So, whatever the no b is (if the set A is a set of prime nos), we will always get a non-prime difference. Hence the prob is 0.
If we consider (1), then we can have any set of 10 integers and we can take any value of b so that their difference can be a prime or cannot be a prime.
