exchanging digits

ahahkhyati.j wrote:Hi
Can someone please help me solve this. Thank you.

If 2 two digit positive integers have their tens digit exchanged, the difference between the resulting pair of integers differs from the difference between the original pair of numbers by 4. what is the greatest possible difference between original pair of integers?

(A) 76
(B) 80
(C) 82
(D) 90
(E) 94

Let S = the smaller 2-digit integer and L = the larger 2-digit integer.

We can PLUG IN THE ANSWERS, which represent the greatest possible value for L-S.
Since we must determine the GREATEST possible value for L-S, we should start with the greatest answer choice.
The smallest possible value for S = 10.

Answer choice E: 94
If L-S = 94 and S=10, we get:
L-10 = 94
L = 104.
Not valid, since L must be a 2-digit integer.
Here, the least possible value for S yields a value for L that is too great, implying that it is not possible that L-S = 94.
Eliminate E.

Answer choice D: 90
If L-S = 90 and S=10, we get:
L-10 = 90
L = 100.
Not valid, since L must be a 2-digit integer.
Here, the least possible value for S yields a value for L that is too great, implying that it is not possible that L-S = 90.
Eliminate D.

Answer choice C: 82
If L-S = 82 and S=10, we get:
L-10 = 82
L = 92.

If S=10 and L=92 exchange tens digits, the new difference = 90 - 12 = 78.
Difference between L-S and the new difference = 82-78 = 4.
Success!
The two differences differ by 4, as required by the prompt.

The correct answer is C.