Greatest possible value of S minus T

[gmattesttaker2]

Hello,

Can you please assist with the following:

S and T are two-digit positive integers that have the same digits but in reverse order. If the positive difference between S and T is less than 40, what is the greatest possible value of S minus T?

Answer Choices:

27
30
33
36
39

OA: 36


I tried to solve this as follows:

S = 10a + b
T = 10b + a

Now the question says "If the positive difference between S and T is less than 40". I was just wondering what exactly "positive difference" means? Can there be a "negative difference" as well here?

Thanks for your help,
Sri

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Hi Sri,

Your algebraic approach will work to help you solve this question. The "positive difference" means that you should take into account that the S or the T might be the bigger number. It essentially means that the "big number" - "smaller number" is less than 40, regardless of which number is the bigger number.

With the math formulas you've created, you would then have:

(10a + b) - (10b + a) < 40

9a - 9b < 40
9(a-b) < 40

Since a and b are "digits", the biggest possible difference would be 4 and the correct answer would be 36.

You could also use "brute force" on this question.

Try 71 and 17
then 61 and 16
then 51 and 15
etc.
until you find the biggest answer that is less than 40. You'll get the same result.

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