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

Final Answer:

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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

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 ?

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.

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