53 x 22 = 1276 then (4221)n=()10? Pick
A) 3896
B) 3897
C) 3898
D) 3899
E) None
Sol:   As we don't know the base system here we take the base as n. So 53 in base n can be written as 5n+3, and 22 as 2n+2 and 1276 as n3+2n2+7n+6   ⇒⇒ (5n + 3)(2n + 2) = n3+2n2+7n+6   ⇒⇒ 10n2+16n+6=n3+2n2+7n+6   ⇒⇒ n3−8n2−9n=0   ⇒⇒ n(n2−8n−9)=0   ⇒⇒ (n + 1)(n - 9) = 0   So n = 9   (4221)9=4×93+2×92+2×9+1   = 3716 + 162 + 18 + 1= 
<gadget id="calculator">3716 + 162 + 18 + 1</gadget>
<output>3_897</output>
3897   Answer 3897
<result>B</result>
53 x 22 = 1276 then (4221)n=()10?