By how much do the digits differ?

[GmatGreen]

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

[Patrick_GMATFix]

Any two-digit number (eg: 27) can be expressed as 10*tens + 1*units (eg: 10*2 + 7). This is the basis for how to solve this question quickly. The difference between 2 two-digit numbers with the same digits in reverse order can be expressed as (10t+u) - (10u+t) where t and u are the original tens and units digits.

The answer is A. I go through the question in detail in the full solution below (taken from the GMATFix App).



-Patrick

[GMATGuruNY]

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

TEST CASES between 10 and 20 until the required difference of 27 is yielded.

Case 1: 12 and 21
21-12 = 9.
Doesn't work.

Case 2: 13 and 31
31-13 = 18.
Doesn't work.

Case 3: 14 and 41
41-14 = 27.
Success!
Difference between the digits = 4-1 = 3.

The correct answer is A.

[theCodeToGMAT]

Original = (10X + y)
Reversed = 10Y + X

10Y + X - 10X - Y = 27
-9X + 9Y = 27
Y - X = 3
[spoiler]{A}[/spoiler]

[[email protected]]

Hi GmatGreen,

You can actually TEST Values on this question (as Mitch's approach shows). One of the great aspects about this question is that there are a variety of options that you can use to find the correct answer.

Mitch ended up using 14 and 41....

But you could also use...
25 and 52
36 and 63
47 and 74
58 and 85
69 and 96

Each of these possibilities fits the "rule" that the difference is 27 AND provides the exact same correct answer: 3

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

[Abhishek009]

Original = (10X + y)
Reversed = 10Y + X

10Y + X - 10X - Y = 27
-9X + 9Y = 27
Y - X = 3
[spoiler]{A}[/spoiler]

There is a cute rule for solving these quickly ...

Remeber the form as any number ( having 2 digits ) when reversed forms -> 9y - 9x

Here 9y - 9x = 27

x - y = 3

[theCodeToGMAT]

Original = (10X + y)
Reversed = 10Y + X

10Y + X - 10X - Y = 27
-9X + 9Y = 27
Y - X = 3
[spoiler]{A}[/spoiler]

There is a cute rule for solving these quickly ...

Remeber the form as any number ( having 2 digits ) when reversed forms -> 9y - 9x

Here 9y - 9x = 27

x - y = 3

Will advise you to not to mug-up such shortcuts but rather spend 10 seconds more to reach to such solutions... Trust me, GMAT doesn't need such shortcuts..

[Jeff@TargetTestPrep]

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

[nikhilgmat31]

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

TEST CASES between 10 and 20 until the required difference of 27 is yielded.

Case 1: 12 and 21
21-12 = 9.
Doesn't work.

Case 2: 13 and 31
31-13 = 18.
Doesn't work.

Case 3: 14 and 41
41-14 = 27.
Success!
Difference between the digits = 4-1 = 3.

The correct answer is A.

36 & 63 is another good example.
25 & 52 is another good example.

difference is 3 always.