How many 4 digit numbers exist where digits are in ascending

Let's take the ascending 4 digit number.
The smallest ascending 4 digit number is 1234.
So a thousand places could hold digits up to 9
And the second one up to 8
So the combination of numbers will be 9*8*x*x

Eliminate the options which don't have 72 as it's a factor.

A. 1620/72 => 22.5 (eliminate A)
B. 1080/72 => 15 (keep this)
C. 960/72 => 13.333 (eliminate C)
D. 1080/72 => 15 (keep this)
E. 1440/72 => 20 (keep this)

Now,
Let's take the descending 4 digit number.
The smalled descending 4 digit number is 3210.
So the one's place could hold digits up to 10 (0.....9)
So the combination of numbers will be a factor of 10 and will have fewer numbers than those of ascending as the ascending series smallest number is 1234, which goes up to 9999 and descending order series is already 3000 numbers short of the 1000-9999 series.

Eliminate the options which don't have 10 as it's a factor and the number is not less than the ascending one.

B. 1024 (it is smaller than the ascending number, but 10 is not a factor) (Eliminate B)
D. 1260 (10 is a factor but the number is larger than the ascending numbers total) (eliminate D)
E. 1230 (has 10 as a factor and is less than 1440)

Answer is E

Hope this helps.

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