# SAT – Remainders

Q: When the positive integer b is divided by 5, the remainder is 1. When b is divided by 7, the remainder is also 1. If b is less than 100, what is the largest possible value for b?

Explanation: b is an integer that is one more than a multiple of both 5 and 7.  The smallest such value is 35 +1 = 36.  But, we need the largest one less than 100.  The next common multiple of 5 and 7 is 70 (do 35 x 2), and the next one is 105 (35 x 3).  Use 70, and add 1.  71. Lorem ipsum dolor sit amet, consectetur adipisicing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat.

# SAT – Remainders

Q: When the positive integer k is divided by 6, the remainder is 2. What is the remainder when k+2 is divided by 6?

Explanation:  Choose a number for k that leaves a remainder of 2 when divided by 6.  For example, k = 8  (one group of 6, with 2 left, equals 8).  Now do k+2, or 10, divided by 6.  6 divides into 10 once, with 4 left.  The remainder is 4.  My TI-84 Plus program ‘REMAINDR’ will find this remainder for you. Lorem ipsum dolor sit amet, consectetur adipisicing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat.

# SAT – remainders

If summer begins on a Tuesday and ends 100 days later, on which day of the week does summer end? 