Last Updated on May 4, 2023
GMAT OFFICIAL GUIDE PS
Solution:
Let’s first label the original two-digit integer as N. We can then say that N = 10A + B, where A is the tens digit and B is the units digit of N.
If this is hard to see let’s try it with a sample number, say 24. We can say the following:
24 = (2 x 10) + 4
24 = 20 + 4
24 = 24
Getting back to the problem, we are given that if the integer N has its digits reversed the resulting integer differs from the original by 27. First let’s express the reversed number in a similar fashion to the way in which we expressed the original integer.
10B + A = reversed integer
Since we know the resulting integer differs from the original by 27 we can say:
10B + A – (10A + B) = 27
10B + A – 10A – B = 27
9B – 9A = 27
B – A = 3
Since B is the tens digit and A is the units digit, we can say that the digits differ by 3.
Answer A
