2008 iTest Problems/Problem 4

Problem

The difference between two prime numbers is $11$ . Find their sum.

Solution

We know that any prime number, excluding $2$ , is congruent to $1 \pmod 2$ . Thus, if both of the primes are not $2$ , their difference would be congruent to $0 \pmod 2$ . Because $11 \equiv 1 \pmod 2$ , one of the primes must be $2$ . It follows that the other prime must then be $13$ . Therefore, the sum of the two is $13+2=\boxed{15}$ .

2008 iTest (Problems)
Preceded by: Problem 3	Followed by: Problem 5
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 • 41 • 42 • 43 • 44 • 45 • 46 • 47 • 48 • 49 • 50 • 51 • 52 • 53 • 54 • 55 • 56 • 57 • 58 • 59 • 60 • 61 • 62 • 63 • 64 • 65 • 66 • 67 • 68 • 69 • 70 • 71 • 72 • 73 • 74 • 75 • 76 • 77 • 78 • 79 • 80 • 81 • 82 • 83 • 84 • 85 • 86 • 87 • 88 • 89 • 90 • 91 • 92 • 93 • 94 • 95 • 96 • 97 • 98 • 99 • 100

Page

Toolbox

Search

2008 iTest Problems/Problem 4

Problem

Solution

See Also