BTGmoderatorLU wrote:Source: Official Guide
If \(x\) and \(y\) are integers between 10 and 99, inclusive, is \((x - y)/9\) an integer?
1) x and y have the same two digits but in reverse order.
2) The tens' digit of \(x\) is 2 more than the units digit, and the tens' digit of \(y\) is 2 less than the units digit.
The OA is A
Let's take each statement one by one.
1) x and y have the same two digits but in reverse order.
Say x = [mn]; thus, y =[nm]
=> x = 10m + n and y = 10n + m
Thus, x - y = (10m + n) - (10n + m) = 9(m - n)
Thus, 9(m - n)/9 = (m - n), an integer. Sufficient
2) The tens' digit of \(x\) is 2 more than the units digit, and the tens' digit of \(y\) is 2 less than the units digit.
Say x = [(n + 2)n] = 10(n + 2) + n = 11n + 20; similarly,
Say y = [(m - 2)m] = 10(m - 2) + m = 11m - 20;
Thus, (x - y) = (11n + 20) - (11m - 20) = 11(n - m) + 40
Let's see whether 11(m - n) + 40 is completely divisible by 9.
[11(m - n) + 40] / 9 = 4 + [11(m - n) + 4] /9.
At m = n, we see that 11(m - n) + 40 is not divisible by 9. The answer is no.
Note that this is a DS question; the question narration with two statements, together make a holistic scenario. Since Statement 1 is sufficient on the basis of YES, if Statement 2 itself is also sufficient, it must also render a unique answer YES. In this question, it cannot render a unique answer NO.
Since we above saw that at m = n, we got the answer NO, there must be at least one value of (m - n) that will render the answer in YES, making Statement 2 insufficient.
So, by logical deduction, we can conclude that Statement 2 is insufficient.
For the sake of completeness, we see that at m - n = 7, we have [11(m - n) + 4] /9 = 81/9 = 9, an integer. The answer is yes.
No unique answer. Insufficient.
The correct answer:
A
Hope this helps!
-Jay
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