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form 213ab

by sanju09 » Fri Jun 18, 2010 4:03 am
A number of the form 213ab, where a and b are digits, has a remainder less than 10 when divided by 100. The sum of all the digits in the above number is equal to 13. What is the digit b?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9

edited just for the reminder of remainder
Last edited by sanju09 on Fri Jun 18, 2010 4:42 am, edited 1 time in total.
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by kvcpk » Fri Jun 18, 2010 4:06 am
213ab when divided by 100 will have reminder ab.
now ab is less than 10 means that a=0
so 2+1+3+0+b = 13
b= 7

Answer should be C
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by amising6 » Fri Jun 18, 2010 4:20 am
A number of the form 213ab, where a and b are digits, has a reminder less than 10 when divided by 100. The sum of all the digits in the above number is equal to 13. What is the digit b?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9

213ab when divide by 100 remainder will be ab. ab<10 (given , has a reminder less than 10 when divided by 100) so a will be 0.


sum of digit of 213ab=2+1+3+a+b=6+a+b
6+a+b=13 as given in prob
a+b=7 --- equation 1 subsituting a as 0

so we can conclude b will be 7
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by selango » Fri Jun 18, 2010 4:22 am
I got a doubt here.

ab<10 means a*b or ab just the digits.

If its a*b,since a+b=7,then a=1,b=6 or a=6,b=1 such that ab<10

b =6.
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by kvcpk » Fri Jun 18, 2010 4:26 am
selango wrote:I got a doubt here.

ab<10 means a*b or ab just the digits.

If its a*b,since a+b=7,then a=1,b=6 or a=6,b=1 such that ab<10

b =6.
Hi selango.. it cannot be a*b because the question says number of form 213ab
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by sanju09 » Fri Jun 18, 2010 4:31 am
selango wrote:I got a doubt here.

ab<10 means a*b or ab just the digits.

If its a*b,since a+b=7,then a=1,b=6 or a=6,b=1 such that ab<10

b =6.
When 100 divides its non-multiple, the remainder happens to be the number formed by the rightmost two digits. They said the remainder is less than 10, hence the rightmost two digits must look like 0b or something like that.

Take ab = 10 a + b in this case.
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by selango » Fri Jun 18, 2010 6:28 am
Got it..thanks
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