A three-digit number is such that when its reverse is subtracted from it, the result is 297. Also, thrice the tens digit is equal to the difference between its hundreds and units digits. How many possible values are there for the number?
You can also use reasoning to solve it.
"thrice the tens digit is equal to the difference between its hundreds and units digits."
The difference between any two digits cannot be more than 9-0 = 9. So the tens digit can be 3 at most.
But if the difference between the other two digits is 9, their subtraction will give us something around 900. We need something around 300 so the tens digit must be 1 and the difference between the other two digits must be 3.
So the first such number you can have is 310. If you subtract 013 out of it, you get 297 - Correct.
Next you can have is 411. If you subtract 114 out of it, you will get 297 - Correct.
Next you can have is 512. If you subtract 215 out of it, you will get 297 - Correct.
and so on goes the pattern till you have 916.
So in all, you have 7 numbers.
Veritas Prep | GMAT Instructor
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews