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?

Answer: 71

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.

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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?
 
Answer: 4
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.
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SAT – remainders

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

Answer: Thursday

Explanation:  A week has 7 days.  Dividing 100 by 7, you get 14 remainder 2.  That’s 14 weeks and 2 days.  Beginning on a Tuesday, 14 weeks later would land on a Tuesday too.  Two more days brings you to Thursday.

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