Problem: Let the product (12)(15)(16), each factor written in base b, equal 3146 in base b. Let s=12+15+16, each term expressed in base b. Then s, in base b, is:
Answer Choices:
A. 43
B. 44
C. 45
D. 46
E. 47
Solution:
Let P=(b+2)(b+5)(b+6)=3146 (base b) ∴b3+13b2+52b+60=3b3+b2+4b+6.
∴0=b3−6b2−24b−27 and b=9. But s=(b+2)+(b+5)+(b+6)=3b+9+4.
∴s=3⋅9+9+4=4⋅9+4=44 (base b).