Bunuel wrote:
mhill5446 wrote:
rpmodi wrote:
I think it should be E
you can represent 100X+10Y+Z as a three digit number XYZ
now from condition 1 and 2 , this three digit number is X63 , plug in different values for X : 163/7 --remainder is 2 , 263/7 ----remainder 4
One more comment on this solution : X , Y , Z can be > 10 ,so represtating 100X+10Y+Z as XYZ will not always be right , but by limiting the scope of X, Y, Z values we can simplyfy the solution
Hi - Why can we represent 100X+10Y+Z as a three digit number?
This is a way of writing an x-digit number.
For example, any two-digit integer can be represented as 10a+b (where a and b are single digit integers), for example 37=3*10+7, 88=8*10+8, etc.
Any three-digit integer can be represented as 100a+10b+c (where a, b and c are single digit integers), for example 371=3*100+7*10+1, ...
Hope it's clear.
Bunuel,
Hi i wanted to understand how did we come to know that its a three digit number ?
But we are told that that X,Y,Z are positive integers. Had we be given that they are digits we can express 100X+10Y+Z as three digit positive integer.
Here is what i mean if X= 2 Y=6 Z=3 then the number would be 263
But if X = 20 Y=6 and Z 3 then the number would be 2063.
So with certainty how can we say that its a three digit positive number, while we only know that X,Y,Z are positive integers.
But i had a different approach for this question
n= 100X+10Y+Z
n= 98X+2X+7Y+3Y+Z
\(\frac{n}{7}\)= \(\frac{98X+2X+7Y+3Y+Z}{7}\)
so remainder will be \(\frac{2X+3Y+Z}{7}\)
So to answer the question we need to know all the three variable X,Y,Z
_________________
Probus
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