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S and T are two-digit positive integers that have the same

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

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New post 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?

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

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

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New post 03 Apr 2015, 11:32
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Hi All,

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:

36

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Re: s minus t  [#permalink]

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New post 11 Feb 2012, 18:17
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calreg11 wrote:
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.

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

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New post 12 May 2012, 12:14
I found this question a little confusing when i solved it during the test

S-T=9(X-Y)<40
X-Y<40/9
i.e X-y<4

therefore the value of S can be 52,74...and the value of T can be 25,47

As a result the value of S-T comes to 27
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Re: S and T are two-digit positive integers that have the same  [#permalink]

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New post 12 May 2012, 12:30
mrinal2100 wrote:
I found this question a little confusing when i solved it during the test

S-T=9(X-Y)<40
X-Y<40/9
i.e X-y<4

therefore the value of S can be 52,74...and the value of T can be 25,47

As a result the value of S-T comes to 27


That's because the math is wrong: 9(x-y)<40 --> x-y<4.4, so x-y can be 4 too, S can be 51, 62, ... and T can be 15, 26, ... S-T=36.
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Re: S and T are two-digit positive integers that have the same  [#permalink]

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

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

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New post 09 Mar 2018, 08:26
Bunuel wrote:
calreg11 wrote:
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.

Answer: D.


All other solutions are satisfying but I have a quick 10s Solution by PLUG IN ELIMINATION method.
1. Highest number in option is 39, so other possible number will be 93. 39+40 = 79 ---- Eliminated
2. Then Highest number in option 36, other number 63. 36+40 = 76. -- Mark the answer.
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Re: S and T are two-digit positive integers that have the same  [#permalink]

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New post 19 Mar 2018, 08:21
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Can't we do:

99 - 40 = 59 we know that S has the same value in reverse order: 95

95-59=36

am i right? what do you think?
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S and T are two-digit positive integers that have the same  [#permalink]

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New post 19 Mar 2018, 10:18
calreg11 wrote:
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


we know that all differences between reversals are multiples of 9
let x and y be the two digits of S and T
10x+y-(10y+x)→9x-9y
if 9x-9y=36, the greatest of only two possible answer options
then x-y=4
if x is 9 and y is 5
then 95-59=36
if x is 5 and y is 1
then 51-15=36
D
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S and T are two-digit positive integers that have the same &nbs [#permalink] 19 Mar 2018, 10:18
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