GmatGreen wrote:If a two-digit positive integer has its digits reversed, the resulting integer differs from the original by 27. By how much do the two digits differ?
A) 3
B) 4
C) 5
D) 6
E) 7
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 the idea of N = 10A + B is hard to see, let’s use a sample number, say 24. We can say the following:
24 = (10 x 2) + 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
Because we know the resulting integer differs from the original integer by 27, we can say either one of the following:
(10B + A) – (10A + B) = 27 or (10A + B) – (10B + A) = 27
If it’s the former, we have:
10B + A – 10A – B = 27
9B – 9A = 27
B – A = 3
If it’s the latter, we have:
10A + B – 10B – A = 27
9A – 9B = 27
A – B = 3
In either case, we can see that the digits differ by 3.
The answer is
A
Jeffrey Miller
Head of GMAT Instruction
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