CAT question and interesting solution
In a certain system product of 44 X 11 is represented as 2124 find how 1453 can be represented in decimal system ?
1)248 2) 346 3) 393 4) 410
Try to solve the above question.
A typical way people set out to try this one after giving it a thought is to come up with an equation as follows
2*(x^3) + 1*(x^1) + 2*(x^2) + 4*(x^0) = 44 * 11 = 484
But this being a quadratic there won't be easy methods of indentifying the roots and hence takes significant time to solve and get x=6 as the answer.
The intelligent way of tackling such a question would be, we are given that 484 of decimal system maps to 2124 of a system to the base x. Since in decimal system 2124 is more than 484, certainly base value should be less than 10 for the new system. So we have zero'd down the sample space to 9,8,...,3,2,1. We are asked to find what does 1453 of unknown base system correspond to in decimal system, as simple rule is that digits of a number in certain system with base=n will all be less than 'n'. So in our case the base value must be at least greater than 5. So the search space got reduced to 6,7,8 and 9. Now try substituting in the above equation x=6 and you see it satisfies, so you can quickly calculate the required answer i.e. 1*(6^3) + 4*(6^2) + 5*(6^1) + 3*(6^0) = 393.
This is the way to tackle a CAT question, there always will be a simpler way to unfold things than they appear infront of our eyes in the first glance, the one who identifies it wins the race.
Hope that helps at least some fellow aspirant out there.
cheers,
Jayachandra
1)248 2) 346 3) 393 4) 410
Try to solve the above question.
A typical way people set out to try this one after giving it a thought is to come up with an equation as follows
2*(x^3) + 1*(x^1) + 2*(x^2) + 4*(x^0) = 44 * 11 = 484
But this being a quadratic there won't be easy methods of indentifying the roots and hence takes significant time to solve and get x=6 as the answer.
The intelligent way of tackling such a question would be, we are given that 484 of decimal system maps to 2124 of a system to the base x. Since in decimal system 2124 is more than 484, certainly base value should be less than 10 for the new system. So we have zero'd down the sample space to 9,8,...,3,2,1. We are asked to find what does 1453 of unknown base system correspond to in decimal system, as simple rule is that digits of a number in certain system with base=n will all be less than 'n'. So in our case the base value must be at least greater than 5. So the search space got reduced to 6,7,8 and 9. Now try substituting in the above equation x=6 and you see it satisfies, so you can quickly calculate the required answer i.e. 1*(6^3) + 4*(6^2) + 5*(6^1) + 3*(6^0) = 393.
This is the way to tackle a CAT question, there always will be a simpler way to unfold things than they appear infront of our eyes in the first glance, the one who identifies it wins the race.
Hope that helps at least some fellow aspirant out there.
cheers,
Jayachandra
posted by Jayachandra at 5:08 AM
2 Comments:
sry I wrote that the equation is quadratic, what I actually meant was cubic. For quadratics we don't need to worry for roots. We have our beloved [-b +/- sqrt(b^2 - 4ac)]/2a . Its the complexity in solving the cubic equation that made me think of an alternate solution or rather search space limiting technique.
Jayachandra
i guess a betr way wud be :-
44 x 11=
44
440
-----
--24
nw this 2 can be arrived at only if the base is 6(as in 0,1,2,3,4,5,10,11,12)!!!
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