Data Sufficiency

Sorry typo error...i have corrected the question.

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.

OA is A
I checked the beat the gmat forums for the answer explanation and found them correct. But my problem lies in here.What if both x and y are the same ?...will not the first option be ruled out in that case ?

please check the question again... the question is not complete...

I dont think it should be A, or the ques...is left out with some more words....

Ans should be a.

If we consider option 1.
assume x = 21 y y = 12 x-y = 9

Hence x-y/9 = integer
Now consider x = 31 y = 13
x - y = 18


now consider x = 71 y = 17

x-y = 54

ashhchdg wrote:Sorry typo error...i have corrected the question.

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.

OA is A
I checked the beat the gmat forums for the answer explanation and found them correct. But my problem lies in here.What if both x and y are the same ?...will not the first option be ruled out in that case ?

x and y can't be the same. From only the question stem, we have no info about x and y. But from statement 1 we get that x and y are two distinct numbers with digits reversed. So when the statement specifically tells us that x and y are different, how can we assume that they are the same? That being said

Statement(1) Lets try different combinations 72-27=45 which is divisible by 9
91-19=72 which is divisible by 9
56-65=9. Whichever combination you try, the answer will be divisible by 9. Hence, SUFFICIENT

Statement(2)
let x be 86 and y be 46 so 86-46=40 not divisible by 9
let x be 64 and y be 46 so 64-46=18 which is divisible by 9. We get conflicting answers hence INSUFFICIENT

Answer is A. Hope your doubt has been clarified.

ashhchdg wrote:Sorry typo error...i have corrected the question.

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.

OA is A
I checked the beat the gmat forums for the answer explanation and found them correct. But my problem lies in here.What if both x and y are the same ?...will not the first option be ruled out in that case ?

If x and y are the same, for example, x = 33 and y = 33 (in reverse order, the same two digits), then (x-y)/9 = (33-33)/9 = 0/9 = 0. 0 is an Integer. Still Yes, still Sufficient.

However, I agree that there is nothing that implies that the digits must be distinct or that x and y must be distinct. You are absolutely right to consider the possibility ... but it results in the same answer!

knight247 wrote:

ashhchdg wrote:Sorry typo error...i have corrected the question.

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.

OA is A
I checked the beat the gmat forums for the answer explanation and found them correct. But my problem lies in here.What if both x and y are the same ?...will not the first option be ruled out in that case ?

x and y can't be the same. From only the question stem, we have no info about x and y. But from statement 1 we get that x and y are two distinct numbers with digits reversed. So when the statement specifically tells us that x and y are different, how can we assume that they are the same? That being said

Statement(1) Lets try different combinations 72-27=45 which is divisible by 9
91-19=72 which is divisible by 9
56-65=9. Whichever combination you try, the answer will be divisible by 9. Hence, SUFFICIENT

Statement(2)
let x be 86 and y be 46 so 86-46=40 not divisible by 9
let x be 64 and y be 46 so 64-46=18 which is divisible by 9. We get conflicting answers hence INSUFFICIENT

Answer is A. Hope your doubt has been clarified.

Great approach mate!!