9 only once

[sanju09]

How many integers between 500 and 600 include the digit 9 only once?
(A) 21
(B) 20
(C) 19
(D) 18
(E) 17

[selango]

500>100a+10b+10c<600

a cant be 9

b=9,the possible values are 590,591,592,593,594,595,596,597,598-9 integers.

c=9,the possible values are 509,519,529,539,549,559,569,579,589- 9 integers.

Total - 18 integers having digit as 9 only once

[frank1]

18
but i used manaual method
90 ...to 98 ---9
89 ,79 ...to 9-----9

so 18
ok making eq is sure shot method but in this case....
manual method was shorter...

[kvcpk]

Number should be of the form 59X or 5X9

if its 59X, X can be filled in 9 ways (0-8)
if its 5X9, X can be filled in 9 ways (0-8)

We need either of these 2 to happen. so 9+9 = 18

[outreach]

d

[sanju09]

Number should be of the form 59X or 5X9

if its 59X, X can be filled in 9 ways (0-8)
if its 5X9, X can be filled in 9 ways (0-8)

We need either of these 2 to happen. so 9+9 = 18

wonderful

[kvcpk]

Number should be of the form 59X or 5X9

if its 59X, X can be filled in 9 ways (0-8)
if its 5X9, X can be filled in 9 ways (0-8)

We need either of these 2 to happen. so 9+9 = 18

wonderful

Thank you!!