Sam has forgotten his friend’s seven-digit telephone number. He remembers the following: the first three digits are either 635 or 674, the number is odd, and the number nine appears once. If Sam were to use a trial and error process to reach his friend, what is the minimum number of trials he has to make before he can be certain to succeed ?
Choose the correct choice from the following choices:
A) 1000
B) 2430
C) 3402
D) 3006
E) None of these
Explanation :   Let's check the number of ways for the first telephone number.   6 3 5 - - - -   a) 6 3 5 9 - - -   4 choices for last digit (1,3,5,7).   9 * 9 choices for 5th and 6th digits together.   So, 9 * 9 * 4 choices = 324 ways.   Similarly,   b.) 6 3 5 - 9 - - = 324 ways.   c.) 6 3 5 - - 9 - = 324 ways.   d.) 6 3 5 - - - 9 = 9 * 9 * 9= 
<gadget id="calculator">9 * 9 * 9</gadget>
<output>729</output>
729 ways.   Total= (324 + 324 + 324 + 729)= 
<gadget id="calculator">(324 + 324 + 324 + 729)</gadget>
<output>1_701</output>
1701.   It will be also the case with the phone number starting with 674.   Hence, the minimum number of trial required is 2 x 1701= 3402.   Answer : 3402
<result>C</result>
Sam has forgotten his friend’s seven-digit telephone number. He remembers the following: the first three digits are either 635 or 674, the number is odd, and the number nine appears once. If Sam were to use a trial and error process to reach his friend, what is the minimum number of trials he has to make before he can be certain to succeed ?