When positive integer N is divided by positive integer P, the quotient is 18, with a remainder of 7. When N is divided by (P + 2), the quotient is 15 and the remainder is 1. What is the value of N? Select the correct option:  A) 151  B) 331  C) 511  D) 691  E) 871
Use the rule dividend = (integer quotient)*(divisor) + remainder to translate each sentence.   The first sentence becomes N = 18P + 7. The second equation becomes N = (P + 2)*15 + 1, which simplifies to N = 15P + 31. These are ordinary simultaneous equations Since they both equal N already, let’s set them equal and solve for P.   18P + 7 = 15P + 31   3P + 7 = 31   3P = 24   P = 8   Now that we know P = 8, we can just plug in. The product 15*8 is particularly easy to do, without a calculator, by using the “doubling and halving” trick. Double 15 to get 30, and take half of 8 to get 4 —- 15*8 = 30*4= 
<gadget id="calculator">30*4</gadget>
<output>120</output>
120. So   N= 15(8) + 31 = 120 + 31= 
<gadget id="calculator">120 + 31</gadget>
<output>151</output>
151   N= 151, answer = 151.
<result>A</result>
When positive integer N is divided by positive integer P, the quotient is 18, with a remainder of 7. When N is divided by (P + 2), the quotient is 15 and the remainder is 1. What is the value of N?