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Manager  Joined: 27 Oct 2011
Posts: 124
Location: United States
Concentration: Finance, Strategy
GPA: 3.7
WE: Account Management (Consumer Products)
S and T are two-digit positive integers that have the same  [#permalink]

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13 00:00

Difficulty:   25% (medium)

Question Stats: 76% (01:55) correct 24% (02:09) wrong based on 313 sessions

### HideShow timer Statistics 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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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: S and T are two-digit positive integers that have the same  [#permalink]

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6
4
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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##### General Discussion
Math Expert V
Joined: 02 Sep 2009
Posts: 56300

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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.

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Manager  Joined: 29 Sep 2008
Posts: 89
Re: S and T are two-digit positive integers that have the same  [#permalink]

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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
Math Expert V
Joined: 02 Sep 2009
Posts: 56300
Re: S and T are two-digit positive integers that have the same  [#permalink]

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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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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 ?
Manager  B
Joined: 18 Jun 2017
Posts: 59
Re: S and T are two-digit positive integers that have the same  [#permalink]

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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.
Intern  B
Joined: 28 Feb 2018
Posts: 6
Re: S and T are two-digit positive integers that have the same  [#permalink]

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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.

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.
Intern  Joined: 16 Mar 2018
Posts: 1
Re: S and T are two-digit positive integers that have the same  [#permalink]

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1
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?
VP  P
Joined: 07 Dec 2014
Posts: 1206
S and T are two-digit positive integers that have the same  [#permalink]

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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

all differences between reversals are multiples of 9
closest multiple of 9<40=36
36/9=difference between digits=4
so digit possibilities are 9 & 5, 8 & 4, 7 & 3, 6 & 2, 5 & 1
for all such digit possibilities, difference between reversed integers=36
D

Originally posted by gracie on 19 Mar 2018, 10:18.
Last edited by gracie on 13 May 2019, 08:25, edited 2 times in total.
Manager  G
Joined: 29 Nov 2018
Posts: 169
Re: S and T are two-digit positive integers that have the same  [#permalink]

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Two-Digit reverse order number properties:

Sum of such 2 numbers= Multiple of 11
Difference of such 2 numbers= Multiple of 9
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Re: S and T are two-digit positive integers that have the same  [#permalink]

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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

We need 2 two-digit numbers that have the same digits but reversed e.g. 19 and 91, 26 and 62 etc.
When the gap between the digits increases, the gap between the numbers increases.
16 and 61 have a difference of 45 but this is not acceptable.
Hence 15 and 51, giving a difference of 36 would represent the largest value of S - T.

Note that diff between 15 and 51 = Diff between 26 and 62 = Diff between 37 and 73 and so on...

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Veritas Prep GMAT Instructor Re: S and T are two-digit positive integers that have the same   [#permalink] 13 May 2019, 05:48
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