How many 3-digit numbers greater than 500 contain the digit 9 appearin

Question

How many 3-digit numbers greater than 500 contain the digit 9 appearing at least once?

A. 191
B. 189
C. 176
D. 175
E. 153

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ScottTargetTestPrep · Accepted Answer

All 100 numbers in the 900s have at least one digit of 9, The number of numbers in 500s, 600s, 700s, and 800s that have at least one digit of 9 must be equal. That is, there is the same amount of numbers in 500s that have at least one digit of 9 as in 600s, 700s, or 800s. If this amount is x, then the total number of numbers is 4x + 100. Notice this must be an even number and since 176 is the only even number in the given choices, 176 must be the correct answer.

Answer: C

nick1816 · Answer

Number that contains only one 9= 1*9*9+4*1*9+4*9*1= 153

Number that contains two 9's= 1*1*9+4*1*1+1*9*1= 22

Number that contains three 9's= 1*1*1=1

Total numbers = 153+22+1=176

Kulka123 · Answer

Total nos - Nos that contain no 9

5*10*10 - 4*9*9 =176

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rsrighosh · Answer

I think the answer is 175
As statement says  3-digit numbers greater than 500  . This means  501<=x<=999 
Therefore

Step 1:-  total number of numbers between 501 and 999 (all inclusive) =  5 * 10 * 10 = 500 - 1 = 499  
We can also find this by  999-501 = 498+1 = 499  (Adding 1 to include 501)

Step 2:-  total number of numbers which does not contain 9 =  4 * 9 * 9 = 324

Step 3:-  total number of numbers containing at least one 9 =   499 - 324 = 175

nick1816 · Answer

You count 500 in Step 2....Deduct there too. You'll get 176. Point is it does not matter whether you count from 500 or 501, Numbers that contain 9 remain the same

Another way is-

Numbers from 501-599 that contain 9 = 10+10-1=19 (Deduct 1, as we counted 599 twice)

Numbers from 600-699 that contain 9 = 10+10-1=19

Numbers from 700-799 that contain 9 = 10+10-1=19

Numbers from 800-899 that contain 9 = 10+10-1=19

Numbers from 900-999 that contain 9 = 100

Total numbers = 19*4+100=176

Mck2023 · Answer

Hi  rsrighosh 
Can you please further elabourate step 2. Or first solution jn step 1. I coukdnot understand that method.

Thank you!

Posted from my mobile device

NitishJain · Answer

C.

500-599 => 19 times
600-699= > 19 times
700-799 => 19 times
800-899= > 19 times
900-999 => 100 times

Counting: 176

bumpbot · Answer

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How many 3-digit numbers greater than 500 contain the digit 9 appearin

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How many 3-digit numbers greater than 500 contain the digit 9 appearin

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