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How to use algebra to solve?

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by MakeUrTimeCount » Tue Jan 31, 2012 1:19 pm
Hi,
I don't know how you really want to solve the problem by algebra. Hope following helps:

1) x divided by 100 has a remainder of 30
x = 100K + 30 where 1 <= K <= 9
where K is a positive integer and less than equal to 9 (because x is 3 digit number)

Put different values for k and check if ten's digit changes:
K = 1 => x = 130
K = 2 => x = 230
.....
.....
K = 9 => x = 930

So x =K30


2) x divided by 110 has a remainder of 30
x = 110M + 30
where M is a positive integer and less than equal to 9 (because x is 3 digit number)

Here you will not a fixed form as we were able to acheive in previous case.

Here again you may put different values for M and check if ten's digit changes.
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by pemdas » Tue Jan 31, 2012 3:50 pm
use algebra in combination with plug-in/analyze strategy here

st(1) implies x/100=integer+30/100. Hence, integer=(x-30)/100. Analyze x, it can be >=30 and should return integer for (x-30)/100. All possible values should contain digit 3 in tens'

st(2) implies x/110=integer+30/110. Hence, integer=(x-30)/110. Analyze x, it can be >=30 and should return integer for (x-30)/110. Possible x=140 and x=250 with digits 4 and 5 in tens'

Answer A
fangtray wrote:What is the tens digit of a positive integer x?

1) x divided by 100 has a remainder of 30
2) x divided by 110 has a remainder of 30
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