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Total possible as per requirement = 21 * 20

with difference of 2 = 16 pairs

probability = 16 / (21 * 20)

hi

I think the answer should be ” C ”

my description is :

we have to choose 2 cards out of 21 card which will be 21 C 2 = 210

then we have the prime numbers which their absolute difference is a prime number as well and following combination of prime numbers would meet the criteria :

2,5 2,7 2,13 2,19 3,5 5,7 11,13 17,19

as you can see we have 8 possible ways of choosing prime numbers with prime absolute difference

the final answer is : 8/210 = 4/105 ——> C

All,

The answer has been posted!

GRE Brain Twister – Prime Time (Answer)

The answer is E) 8/105

The probability of selecting two prime number and probability of the absolute difference between two numbers being another prime = p(selecting two prime numbers)* p(absolute difference is another prime).

P(selecting two prime numbers)= (8/21)*(7/20)=2/15

P(absolute difference is another prime)= 16/8C2 = 4/7

Probability of selecting two prime AND absolute difference is another prime= (2/15)*(4/7)=8/105

Anybody else has an efficient way to find out the probability of the second part? I can only solve it through counting 🙁

It is C. No. of total ways to choose two card 20C2=210

No. of ways the absolute difference between the two prime numbers will itself be a prime number= 8 [(2,19),(2,13),(2,7),(2,5),(3,5),(5,7),(11,13),(17,19)]

So the probability is 8/210= 4/105

Hi Chris,

Is it E , 8/105 ?

Selecting 2 cards out of 21 is 21C2 =210 and the given condition gives total of 16 outcomes

ie, (2,5) (2,7) (2,13) ………..(19,17)

So the probability is 16/210 or 8/105

Is it correct?

Answer : B 4/95 = 8/190

Solution :

No. of total ways to choose prime numbers = 20 C 8 = 190

No. of cases when prime numbers with difference 2 occurs = 8

(I’m sorry if it is not true )