The number A is a two-digit positive integer; the number B is the two-digit positive integer formed by reversing the digits of A.
If Q=10B-A, what is the value of Q?
(1) The tens digit of A is 7
(2) The tens digit of B is 6
[spoiler]OA=B[/spoiler]
Source: Manhattan Prep
Hi M7MBA.
Let's write \(A\) and \(B\) as follows:
\( A= xy=10x+y\)
and
\(B= yx=10y+x\),
where \(x,y\) are integer numbers from 0 to 9 with \(y\ne 0\).
Now, we just need to see if we can find the exact value of
\(Q= 10B-A \)
\(= 10(10y+x)-(10x+y) \)
\(= 100y+10x-10x-y\)
\(= 99y.\)
From the above, we can see that we just need to find the value of \(y\). In order to do that, let's check the given statements.
Statement 1:
(1) The tens digit of A is 7
This statement just tells us that \(x=7\) but it doesn't tell us anything about \(y\). So, this statement is
NOT SUFFICIENT.
Statement 1:
(2) The tens digit of B is 6
If the tens digit of B is 6 then we are told that \(y=6\). Therefore, \(Q=99y=604.\)
So, this statement is
SUFFICIENT.
Hence, the correct answer is the option
_B_.
I hope it helps you.
