How many integers are there between 25000 and 33000..

There are 8000 numbers between 25,001 and 33,000, and exactly 1% of them will have a specific tens and units digit (a number in this range is as likely to end in '32' as in any other two digits), so the answer is 80.

Hello Mr. Ian IanStewart

Can you please explain exactly 1% of them will have a specific tens and units digit little bit more.

Among the numbers from 25,001 through 33,000, each tens and units digit combination occurs equally often. A number in that range is just as likely to end in "03" as it is in "55" or "97" or "32". Since there are 100 different tens and units digit combinations in total, 1/100 of the numbers in that range will end specifically in "32" (or in any other two specific digits). Hope that answers your question!

25000 - 33000

So let us see number of digits

_ _ _ 3 2

Hundreds digit can have 10 digits (0 to 9)

Thousands digit has dependency with Ten Thousands digit

Case 1:-

if Ten Thousands digit is 2, then Thousands digit will have 5, 6, 7, 8, 9 = 5 digits

So, we have

2 (5 digits) (10 digits) 3 2 which makes 5 x 10 = 50

Case 2:-

if Ten Thousands digit is 3, then Thousands digit will have 0, 1, 2 = 3 digits

So, we have

3 (3 digits) (10 digits) 3 2 which makes 3 x 10 = 30


Adding both the cases.. 50 + 30 = 80

B

Scenario 1: 3 in the 1st Place (Ten Thousands Place)


10,000s Place ---- 3 Anchored ---- 1 Option

and

1,000s Place ---- Options 0 or 1 or 2 (33, 000 is the MAX) ----- 3 Options

and

100s Place ----- can take any Digit ----- 10 Options

and

Tens Place ---- Anchored 3 Digit ---- 1 Option

and

Units Place ---- Anchored 2 Digit ---- 1 Option


1 * 3 * 10 * 1 * 1 = 30 Numbers


OR


Scenario 2: 2 in the Ten Thousands Place Anchored

10,000s Place ---- 2 Anchored ---- 1 Option

and

1,000s Place ---- since Lower Boundary is 25, 000: Available Options are 5 or 6 or 7 or 8 or 9 ---- 5 Options

and

100s Place --- any Digit is Possible ---- 10 Options

and

Tens Place --- 3 Digit Anchored --- 1 Option

and

Units Place ---- 2 Digit Anchored ---- 1 Options

1 * 5 * 10 * 1 * 1 = 50 Numbers


Scenario 1 + Scenario 2 =

30 + 50 = 80 Possible Numbers

-B-