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.
Let's gather all the info in the question as well as analyze the Q. stem.
x and y are integers between 10 and 99, inclusive: x and y are 2 digit positive integers.
Q. Stem : is (x - y)/9 an integer?
A normal Yes/No type DS question, where you need to find Is (x- y ) exactly divisible by 9 or not?
Statement 1:
x and y have the same two digits but in reverse order.Whenever you deal with a question based on a two-digit number and its reverse, the most effective method would be to represent them in an
algebraic expression.Let's assume that x is a two-digit number 'ab' and y is the reverse of it i.e 'ba'.
We can represent x as
10a + b and y as
10b + a.x- y = 10 a + b - ( 10b + a ) = 10a + b -10b -a = 9a - 9b =
9(a-b)We can conclude that
x-y is a multiple of 9.
Hence,
(x - y)/9 will be an integer. Statement 1 alone is 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.There are 2 ways to tackle this statement, either by plugging values or using algebraic expressions.
#Approach 1: Plugin values
The tens’ digit of x is 2 more than the units digit, Let's assume x= 42
The tens digit of y is 2 less than the units digit, y = 13
x - y = 42 - 13 = 29
Is x - y /9 is an integer? No, 29/9 is not an integer.
This doesn't mean that it's a NO in all cases.
If you plugin values in yes/No type DS Questions, you should always try to get a yes as well as a NO as answer, else you will fall for the GMAT traps.The next question is how do you get the values for x and y that give a YES to the Q.stem. Are there any such values?
These are ambiguities you might face when you plugin values in DS questions and it will cost some of your time as well.
Instead of randomly plugin values, if you could apply some logic when you choose numbers then the task would be a lot easier.
For eg: in St2, we can see that difference between ten's and unit digit of x is 2 . Also the difference between unit and ten's digit of y is 2.
Already in St1, we found that the difference between 2 digit number and its reverse is divisible by 9.
Why don't we use this in St2 for our advantage to find out the values?Let's say x = 31 . Assume any 2 digit number where ten's digit is greater than unit digit by 2.
For y, you take the reverse of x i.e 13. The ten's digit will be less than the unit digit by 2.
Since y is the reverse of x, x-y should be a multiple of 9 as explained in St 1.
x-y = 31-13 = 18
18 is exactly divisible by 9.
Is x - y /9 is an integer? Yes
Another plugin options : ( 42,24) (53,35) (63,36)..
Since you are getting Yes as well as No as answers,
Statement 2 alone is not sufficient.Option A is the correct answer.Thanks,
Clifin J Francis,
GMAT Quant Expert
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