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# If b is selected at random from Set A, what is the probability that b

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Math Expert
Joined: 02 Sep 2009
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If b is selected at random from Set A, what is the probability that b  [#permalink]

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09 Feb 2015, 05:33
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55% (hard)

Question Stats:

53% (01:27) correct 47% (01:15) wrong based on 283 sessions

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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.

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Re: If b is selected at random from Set A, what is the probability that b  [#permalink]

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09 Feb 2015, 11:02
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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.

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Re: If b is selected at random from Set A, what is the probability that b  [#permalink]

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09 Feb 2015, 11:02
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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.
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Re: If b is selected at random from Set A, what is the probability that b  [#permalink]

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09 Feb 2015, 15:01
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Bunuel wrote:
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.

Statement 1:
the 10 integers could be anything. All 10 could be the number 15, which equates to 100% probability, or all 10 could be 17, which is 0% probability.
Insufficient.

Statement 2: All numbers in Set A are prime.
If 2, the smallest prime, is b, and is selected from the set, then 2-13=-11. primes cannot be negative. any other prime number selected (all odd primes) from there either results in a negative even number (not prime) or an even number (not prime again). So the probability is 0%.
Sufficient

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Posts: 50580
Re: If b is selected at random from Set A, what is the probability that b  [#permalink]

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16 Feb 2015, 04:20
Bunuel wrote:
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.

VERITAS PREP OFFICIAL SOLUTION

Statement (1) tells us nothing about the contents of Set A; not sufficient. Statement (2) seems like it shouldn't be sufficient, but there are no prime numbers that differ by 13: all prime numbers other than 2 are odd, so adding or subtracting 13 to them must yield an even integer. The only number from which one can subtract 13 and get 2 is 15 - which isn't prime. As a result, any prime number minus 13 must result in a non-prime number and the probability that b - 13 will be a prime number is zero, no matter how many numbers are in Set A; sufficient.
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If b is selected at random from Set A, what is the probability that b  [#permalink]

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03 Mar 2015, 04:42
Bunuel wrote:
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.

First thing to note here from question stem is that 'b' cannot be less than 13 as the smallest prime in history of number system is a positive number (i.e. 2 ) .

option A :
set of 10 integers
----->1,2,3,4,5,6,7,8,9,10
choose any number , b-13 will never be prime.
------>15,16,17,18,19,20,,21,22,21,22
we will get handful of primes if we choose 'b' from this set and do b-13 .
2 Answers , so A is NS.

option B :
A is a set of prime numbers, if prime numbers are less than 13 then the probability is 0 as we will get a -ive number (b-13) .
however, if prime numbers are greater than 13 then O-O will always be EVEN. so again the probability is 0.

Option B is sufficient .

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Re: If b is selected at random from Set A, what is the probability that b  [#permalink]

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03 Dec 2017, 08:41
Hi,
Is it understood that all the prime numbers in set A are greater than 13?
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Posts: 50580
Re: If b is selected at random from Set A, what is the probability that b  [#permalink]

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03 Dec 2017, 09:28
Spandan01 wrote:
Hi,
Is it understood that all the prime numbers in set A are greater than 13?

Not necessarily, there might be primes which are less than 13. What's your point?
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If b is selected at random from Set A, what is the probability that b  [#permalink]

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03 Dec 2017, 09:49
If Set A contains prime numbers less than 13, then the result "b-13" will be negative and hence not prime. Therefore the probability that b-13 is prime depends on the number of prime numbers less than 13 in set A.

I got it the probability will remain zero in any case. Thanks
If b is selected at random from Set A, what is the probability that b &nbs [#permalink] 03 Dec 2017, 09:49
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