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GRE Brain Twister – Prime Time

Terrence writes down one of the numbers from 0-20 on one index card each until he has written each number exactly once and then faces all the cards down. Next, he randomly chooses two cards without turning them over. What is the probability that a prime number will be written on each card and that the absolute difference between the two prime numbers will itself be a prime number?

(A) 1/35

(B) 4/95

(C) 4/105

(D) 8/95

(E) 8/105

Answer is here!


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7 Responses to GRE Brain Twister – Prime Time

  1. Arjun October 12, 2015 at 6:39 am #

    Total possible as per requirement = 21 * 20
    with difference of 2 = 16 pairs

    probability = 16 / (21 * 20)

  2. majed September 30, 2015 at 7:52 am #

    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

  3. Srinivas September 30, 2015 at 3:05 am #

    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 🙁

  4. HASAN September 30, 2015 at 12:08 am #

    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

  5. Asha September 29, 2015 at 7:26 am #

    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?

  6. Ashok Tak September 29, 2015 at 5:22 am #

    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 )

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