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S and T are two-digit positive integers that have the same [#permalink]

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11 Feb 2012, 18:02

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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?

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? A. 27 B. 30 C. 33 D. 36 E. 39

Two-digit integer ab can be expressed as 10a+b, for example: 45=10*4+5.

Given: S-T=(10a+b)-(10b+a)=9(a-b)<40 --> greatest multiple of 9 which is less than 40 is 36. For example S can be 51 and T can be 15.

Concentration: General Management, International Business

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Re: S and T are two-digit positive integers that have the same [#permalink]

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03 Nov 2013, 03:13

I calculated it this way 9x-9y = difference. 9(x-y) = difference. For difference to be max difference between x and y must be larger. I calculated putting actual values 39 Difference between digits 6 : Difference between Numbers : 54 (Eliminated because its > 40) 27 Difference between digits 5 : Difference between Numbers : 45 (Eliminated because its > 40 ) 30 Difference between digits 3 : Difference between Numbers : 27 ( possible answer) 36 Difference between digits 3 : Difference between Numbers : 27 (possible answer) 33 Difference between digits 0 This will never be the answer because of 0

between 36 & 30 I eliminated 30 because reverse of it will be 03, which wont be considered as two digit integers. Is that reasoning right ?

Re: S and T are two-digit positive integers that have the same [#permalink]

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03 Apr 2015, 01:25

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This question is actually based on a 'math truism' of a sort. If you've ever taken an accounting class, then you might have learned about "transpositional errors" - errors that happen when you put the same digits in the wrong "order." While this question focuses on 2-digit numbers, the issue is exactly the same and works in any variation.

Putting a set of digits in a different order will ALWAYS lead to a difference that is divisible by 9.

23 and 32 is a difference of 9, which is divisible by 9 147 and 714 is a difference of 567, which is divisible by 9 34567 and 56374 is a difference of 21,807 which is divisible by 9

Here, we're told that the positive difference between S and T is LESS than 40, and we're asked to find the GREATEST difference between S and T. In simple terms, we're looking for the largest multiple of 9 that is less than 40:

Re: S and T are two-digit positive integers that have the same [#permalink]

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09 May 2016, 21:49

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: S and T are two-digit positive integers that have the same [#permalink]

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11 Aug 2017, 04:25

S-T=9(X-Y)<40 Hence the RHS should be a multiple of 9 to deduce the difference. Now from the options we should select 36 as it is the gretaest possible option in the list. Option D.

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