2007 iTest Problems

Problem 1

A twin prime pair is a set of two primes $(p, q)$ such that $q$ is $2$ greater than $p$ . What is the arithmetic mean of the two primes in the smallest twin prime pair?

$\mathrm{(A)}\, 4$

Solution

Problem 2

Find $a + b$ if $a$ and $b$ satisfy $3a + 7b = 1977$ and $5a + b = 2007$ .

$\mathrm{(A)}\, 488\quad\mathrm{(B)}\, 498$

Solution

Problem 3

An abundant number is a natural number that's proper divisors sum is greater than the number. Which one of the following natural numbers is an abundant number?

$\mathrm{(A)}\, 14\quad\mathrm{(B)}\, 28\quad\mathrm{(C)}\, 56$

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2007 iTest Problems

Problem 1

Problem 2

Problem 3