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GRE Brain Twister – Prime Time (Answer)


We can’t just write down any prime number; we need to make sure that when you subtract one prime number from the others that you get a prime number. Since every prime number except for ‘2’ is odd, when you subtract a prime number by a prime number you will end up with an even number. Since ‘2’ is the only even number, which two primes, less than 20, result in two when you subtract one from the other?

19 and 17

13 and 11

7 and 5

5 and 3

The other prime numbers will result when we subtract 2 from a prime number. Note, how this will be the same as the greater of the prime numbers in each pair above:

19 and 2

13 and 2

7 and 2

5 and 2

That gives us a total of 8 cases. For each case, however, there are two cases, since the question is asking for absolute difference. In other words, 11 and 13 = -2, the absolute difference is 2. This gives us a total of 16 cases.

The new step is to find the total number of possible outcomes:

(21)(20) = 420.

Don’t forget to count ‘0’!

That gives us 16/420, which is 4/105, Answer (C).


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5 Responses to GRE Brain Twister – Prime Time (Answer)

  1. disha October 13, 2015 at 3:19 am #

    why are we counting the additional 8 cases?both cards are picked together right?13 11 or 11 13 how does it make a difference?

  2. Study Notes October 12, 2015 at 1:14 am #

    Well explained! thank you so much for these valuable explanation i i will keep them in my mind! Bookmarking now

  3. Pallavi Thakur October 8, 2015 at 1:23 am #

    Hi Chris,

    I have a question regarding MIS admission, did not get any blog for the same so I am posting it here.

    I have a score of 308(Q:155, V:153). Can you help me with the colleges where I can get with these scores?


  4. Utkarsh October 2, 2015 at 5:19 am #

    This is a conditional probability question.

    Event A – the two cards are prime
    Event B – difference between the two is prime


    Prime nos from 0-20 = 8 and total nos = 21
    P(A) = 8C2/21C2 = 2/15

    We have to calculate P(B and A)
    P(B and A) = P(A).P(BIA),

    where P(BIA) is conditional probability of occurrence of B given A has already taken place.

    There are 8 cases that satisfy B. Total no of cases are 28(Sum of total no of pairs of 8 prime nos), Thus
    P(BIA) = 8/28

    which gives P(BIA) = 2/15 * 8/28
    = 4/105

    • VerbalKamikazi October 5, 2015 at 12:51 am #


      Really helpful your explanation. And also MUCH faster than just counting the Integers..-.-

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