If p, q, R & S are positive integers and pq, what is the units digit

Question

If p, q, R & S are positive integers and p>q, what is the units digit of the integer R?

1)  10^p S -  10^q R =  10^q 
2  p - q = 3

globaldesi · Answer

r has to be one since the right hand side of the expression is of order of power of 10
Thus A is sufficient

NHiromoto · Answer

I suppose the below reasoning works although this contradicts to that of  globaldesi .
Any corrections are welcome.

Statement1
Let's say p = 3 and q =2,  10^pS  = XYZ000 and  10^qR  = ABC00.
Since the right side of the expression is 100, in XYZ000 - ABC00 C has to be 9.
If C is 0, the subtraction can be 10^n, but in this case n will never be equal to q.
Hence, the units digit of R has to be 9.
SUFFICIENT

Statement2
Assuming the statement 2 is p-q = 3, no information related to R and S is given.
INSUFFICIENT.

Isa1989 · Answer

Let's first look at statement 2 which is p-q=3.
This tell us nothing about R or S and so would be insufficient.

Now let's consider statement 1:-
(10^p)*S-(10^q)*R=(10^q)
Rearranging this would give us (10^p)*S=(10^q)*(1+R)
or, *S=(1+R)
or, *S=(1+R)

Now since p>q, we know that 10^(p-q)*S would result in some number with a 0 in the units digit.For the left hand side to have a 0 in the units digit, R must have a 9 in the units digit, hence sufficient.

We can take simple examples.Let p=3 and q=2 and let S=6
then, 10^(p-q)=10 and so 10*S=60
Therefore R must be 5 9 .

Hope this helps.

Harshani · Answer

Here is my explanation in the attachment. hope it helps

bumpbot · Answer

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If p, q, R & S are positive integers and p>q, what is the units digit

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