33 votes 33 votes Consider the equation $(123)_5=(x8)_y$ with $x$ and $y$ as unknown. The number of possible solutions is _____ . Digital Logic gatecse-2014-set2 digital-logic number-representation numerical-answers normal + – go_editor asked Sep 28, 2014 go_editor 9.4k views answer comment Share Follow See all 6 Comments See all 6 6 Comments reply priyanka gautam-piya commented Nov 29, 2016 reply Follow Share why (5,6) and (6,5) are not the possible pair n why ? the minimum base should be greater than 8 ? can someone expain ? 0 votes 0 votes priyanka gautam-piya commented Nov 29, 2016 reply Follow Share the minimum base should be greater than 8 ? can someone expain ? n why (5,6) (6,5) are not possible pairs 0 votes 0 votes sudsho commented Dec 11, 2016 reply Follow Share @priyanka gautam 1 here (x8)y means y>8 means from 9 onwards.. also x<y therefore,(5,6) is not possible because y is not >8 and (6,5) is not possible because x is not <y... 0 votes 0 votes priyanka gautam-piya commented Dec 11, 2016 reply Follow Share ok got it x<y but why y> 8 ? plz expalin ? 0 votes 0 votes sudsho commented Dec 11, 2016 reply Follow Share since (x8)..one number here is 8 so base has to be more than 8 for base 2 numbers are 0,1 base 3..0,1 2 and similarly if a number is 8...its base has to be more than 8.. 3 votes 3 votes priyanka gautam-piya commented Dec 11, 2016 reply Follow Share thnku 1 votes 1 votes Please log in or register to add a comment.
Best answer 51 votes 51 votes Converting both sides to decimal, $25+10+3=x$*$y+8$ So, $xy=30$ Possible pairs are $(1,30),(2,15),(3,10)$ as the minimum base should be greater than $8.$ tejas_manit answered Jan 3, 2015 edited Jun 26, 2018 by Milicevic3306 tejas_manit comment Share Follow See 1 comment See all 1 1 comment reply Ayush Upadhyaya commented Sep 5, 2017 reply Follow Share And also x<y (strictly). Otherwise pair (30,1), (15,2) can also be included. 26 votes 26 votes Please log in or register to add a comment.
8 votes 8 votes Changing (123) base 5 into base 10= 1*25+2*5+3*1=38 Changing x8 base y in decimal= x*y+8 Equating both we get xy+8=38 xy=30 possible combinations =(1,30),(2,15),(3,10) but we have ‘8’ present in x8 so base y>8 as all three are satisfying the conditions so total solutions =3 hence ans is ( C) part Regina Phalange answered Apr 3, 2017 Regina Phalange comment Share Follow See all 2 Comments See all 2 2 Comments reply sunita24 commented Dec 5, 2017 reply Follow Share why not 5,6 plz someone explain properly .. 0 votes 0 votes MIRIYALA JEEVAN KUMA commented Sep 24, 2018 reply Follow Share 8 can't be part of digits if we take 5,6 1 votes 1 votes Please log in or register to add a comment.
3 votes 3 votes here the equation is x*y=30 so the possible values for x and y is (5,6) other values like (6,5) (3,10)(10,3) etc are not valid. kireeti answered Dec 27, 2014 kireeti comment Share Follow See all 3 Comments See all 3 3 Comments reply sushant1221 commented Sep 25, 2016 reply Follow Share How can 5,6 be valid when the number with base x is 8? 2 votes 2 votes Brij Mohan Gupta commented Apr 9, 2017 reply Follow Share vlaue of y never less then 8 show (5,6) is also invalid 1 votes 1 votes Ridhi rajput commented Mar 15, 2021 reply Follow Share Can someone explain how we chhose the x and y pairs from xy= 30 0 votes 0 votes Please log in or register to add a comment.