MathDB

15

Part of 2002 AMC 10

Problems(3)

Making Primes from Digits

Source:

2/11/2008
The digits 1 1, 2 2, 3 3, 4 4, 5 5, 6 6, 7 7, and 9 9 are used to form four two-digit prime numbers, with each digit used exactly once. What is the sum of these four primes? (A) 150(B) 160(C) 170(D) 180(E) 190 \text{(A)}\ 150 \qquad \text{(B)}\ 160 \qquad \text{(C)}\ 170 \qquad \text{(D)}\ 180 \qquad \text{(E)}\ 190
number theoryprime numbers
Sum of Four Primes

Source:

2/27/2008
The positive integers A A, B B, A \minus{} B, and A \plus{} B are all prime numbers. The sum of these four primes is <spanclass=′latex−bold′>(A)</span> even<spanclass=′latex−bold′>(B)</span> divisible by 3<spanclass=′latex−bold′>(C)</span> divisible by 5<spanclass=′latex−bold′>(D)</span> divisible by 7<spanclass=′latex−bold′>(E)</span> prime <span class='latex-bold'>(A)</span>\ \text{even} \qquad <span class='latex-bold'>(B)</span>\ \text{divisible by }3 \qquad <span class='latex-bold'>(C)</span>\ \text{divisible by }5 \qquad <span class='latex-bold'>(D)</span>\ \text{divisible by }7 \\ <span class='latex-bold'>(E)</span>\ \text{prime}
Two Numbers which Differ by 8

Source:

4/2/2013
What is the smallest integer nn for which any subset of {1,2,3,…,20}\{1,2,3,\ldots,20\} of size nn must contain two numbers that differ by 88?
<spanclass=′latex−bold′>(A)</span>2<spanclass=′latex−bold′>(B)</span>8<spanclass=′latex−bold′>(C)</span>12<spanclass=′latex−bold′>(D)</span>13<spanclass=′latex−bold′>(E)</span>15<span class='latex-bold'>(A) </span>2\qquad<span class='latex-bold'>(B) </span>8\qquad<span class='latex-bold'>(C) </span>12\qquad<span class='latex-bold'>(D) </span>13\qquad<span class='latex-bold'>(E) </span>15