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scale of five

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scale of five

by rupsk » Thu Jul 28, 2011 8:18 am
The result of addition of 23241, 4032, 300421 in the scale of five is


A. 243024

B. 333244

C. 312404

D. 322444

e. 333144

what it mean by scale of five?
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by ECMoyano » Thu Jul 28, 2011 8:36 am
No idea what scale of 5 is. I don't even know how to approach this problem

:(
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by rupsk » Thu Jul 28, 2011 8:40 am
by basic way of guessing i nailed it down to B and E but then do not know how to go down further. One way though of summing digits in the number but that is also not multiple of 5. so got confused
Last edited by rupsk on Thu Jul 28, 2011 9:13 am, edited 1 time in total.
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by Frankenstein » Thu Jul 28, 2011 9:10 am
Hi,
In base 10: 23241 = 2(10^4)+3(10^3)+2(10^2)+4(10)+1
In base 5 : 23241 = 2(5^4)+3(5^3)+2(5^2)+4(5)+1
scale of 5 means base 5. The number system we follow is base 10. Binary system is base 2. Similarly this is base 5. So, the maximum a digit can be is 4(5-1) just as it is 9 for base 10 and 1 for base 2. Consider sum of units digit ->1+2+1 = 4
consider sum of 5s(similar to 10s digit) digit -> 4+3+2 = 9 in base 10 = 14 in base 5 because (14)base 5 = 1(5) + 4 = 9. So, carry will be 1
consider sum of 5^2s(similar to 100s digit) -> 2+0+4+1(carry from 14) = 7(base 10) = 12(base 5)
You can stop here because only B has 244 at the end
023241
004032
300421
------
333244

Hence, B

P.S.: I doubt GMAT has such questions.
Cheers!

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